FIBEROPTIC SENSOR

TECHNOLOGY HANDBOOK

by

Charles M. DavisEdward F. CaromeMartin H. WeikShaoul EzekielRobert E. Einzig

Publisher and Distributor

Optical Technologies (OPTECH)A Division of Dynamic Systems, Inc.

360 Herndon Parkway, Suite 1200Herndon, VA 22070-5225

Tel: (703) 478-0844 Fax: (703) 478-0649

Copyright Optical Technologies, Inc., 1982; 1986Registration Number TX 1-094-758

All rights reserved.

No part of this publication may bereproduced, copied or transmitted, in anyform or by any means - graphic, electronic,or mechanical, including photocopying,taping or information storage and retrievalsystems - without the prior writtenpermission of Optical Technologies (OpTECH).

FOREWORD

THE FIBEROPTIC SENSOR TECHNOLOGY HANDBOOK

The FIBEROPTIC SENSOR TECHNOLOGY HANDBOOK reflectsthe latest technology concerning the field offiberoptic in general and fiberoptic sensors inparticular. The fiberoptic sensor technology principlesand practices laid down in this HANDBOOK will give thereader a solid basis for mastering a relatively newtechnology. Only a nominal general technical backgroundis needed to fully comprehend its contents. Thecontributing authors have been as explicit and rigorousin their presentation as time and space constraints inthis HANDBOOK would permit. All the material has beenedited to ensure coherency and consistency.

OPTICAL TECHNOLOGIES, INC.

Optical Technologies, Inc. (OPTECH) is a young andrapidly growing corporation devoted to the research anddevelopment of useful fiberoptic sensor applications andto the advancement of fiberoptic sensor technology.OPTECH is recognized as a leader in this field. The co-founders of OPTECH, Dr. Charles M. Davis and Mr. RobertE. Einzig, who are also authors of this HANDBOOK, arepioneers in the field of fiberoptic sensor technology.Dr. Davis headed the branch at the Naval ResearchLaboratory that designed and produced the firstfiberoptic hydrophore. He has since collaborated in thedesign of numerous other fiberoptic sensor systems. Mr.Einzig has also designed fiberoptic sensor systems forprivate research laboratories, industry and government.Finally, both men were the key contributors to thedevelopment of the Navy’s Fiber Optic Sensor System(FOSS) Program in 1977. Presently, their experience andtalents are being applied at OPTECH where, together withother physicists and engineers specializing infiberoptic sensing, advances in the field are continuingto be made. To date, OPTECH’S experience withfiberoptic sensors includes development of sensors forthe measurement of temperature, pressure, acousticsignals, acceleration, magnetic fields, and seismicdisturbances.

AUTHORS

Charles M. Davis, PhD. Currently Dr. Davis is VicePresident of Optical Technologies, Inc. He has over 30years of experience in acoustooptics and physicalacoustics. As head of the Physical Acoustics Branch atthe Naval Research Laboratory, he was instrumental inthe development of the fiberoptic hydrophore and theestablishment of the FOSS Program.

Edward F. Carome, PhD. Currently Dr. Carome is aProfessor of Physics at John Carroll University. Heparticipated in the initial research at the NavalResearch Laboratory that led to the development of thefiberoptic hydrophore.

Martin H. Weik, D.SC. Currently Dr. Weik is asenior systems analyst at Dynamic Systems, Inc. Dr.Weik has written several comprehensive dictionaries inthe fields of computers, information processing systems,fiberoptic, lightwave propagation, and generalcommunications.

Shaoul Ezekiel, D.SC. Currently Dr. Ezekiel is aProfessor at MIT. He has conducted research concernedwith ultraprecision measurements using opticaltechniques. More recently, he has investigated the useof passive resonators and fiberoptic interferometers forrotation measurements.

Robert E. EinziR, MSEE. Currently Mr. Einzigserves as President of Optical Technologies, Inc. Hehas extensive applications experience in fiberopticsensors and data transmission systems, which adds to hisbroad underwater acoustic sensor background.

ACKNOWLEDGEMENT

Appreciation is extended to Dynamic Systems,Inc.and specifically to Mickey Hedrick, Sandee M. Boyer, andSue M. Gift, and their supporting staff for theirsecretarial, word-processing, and graphics support inthe preparation of this Handbook.

Robert E. EinzigPresidentOptical Technologies, Inc.

TABLE OF CONTENTS

FOREWORD

CHAPTER

1.0

1.1

1.2

1.3

2.0

2.1

2.2

2.3

2.4

3.0

3.1

3.2

3.3

4.0

4.1

INTRODUCTION

Background .

Purpose . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . .1-1

. . . . . . . . . . . . . . . . . . . . . . . . . . . .1-1

. . . . . . . . . . . . . . . . . . . . . . . . . . . .1-1

Contents by Chapter . . . . . . . . . . . . . . . . . . . . . . . .1-1

FIBEROPTIC SENSOR COMPONENTS . . . . . . . . . . . . . . . . . . . .2-1

Optical Fiber Properties . . . . . . . . . . . . . . . . . . . . . .2-12.1.1 Design Objectives . . . . . . . . . . . . . . . . . . . . . .2-12.1.2 Lightwave Propagation . . . . . . . . . . . . . . . . . . . .2-42.1.3 Propagation Modes . . . . . . . . . . . . . . . . . . . . . .2-5

Optical Fiber Fabrication . . . . . . . . . . . . . . . . . . . . .2-122:2.12.2.2

2.2.3

Refractive Index Profile Control . . . . . . . . . . . . . .2-12Fiber Fabrication Processes . . . . . . . . . . . . . . . . .2-132.2.2.1 The Double-Crucible Process. . . . . . . . . . . . .2-132.2.2.2 The Inside Vapor-Phase Oxidation (IVPD) Process . .2-142.2.2.3 The Outside Vapor-Phase Oxidation (OVPD) Process . .2-152.2.2.4 The Vapor Axial Deposition (VAD) Process . . . . . .2-15Fiber Strength . . . . . . . . . . . . . . . . . . . . . . .2-16

Solid State Fiberoptic Light Sources . . . . . . . . . . . . . . .2.3.1 Energy Levels in Semiconductors . . . . . . . . . . . . . .2.3.2 Light Emitting Diodes (LEDs) and Diode Laaers . . . . . . .

Photodetector . . . . . . . . . . . . . . . . . . . . . . . . . .

FIBEROPTIC COMPONENT INTERCONNECTION . . . . . . . . . . . . . . .

Fiberoptic Connectors and Splices . . . . . . . . . . . . . . . .3.1.1 References. . . . . . . . . . . . . . . . . . . . . . . . .

Fiberoptic Couplers . . . . . . . . . . . . . . . . . . . . . . .3.2.1 References . . . . . . . . . . . . . . . . . . . . . . . .

Fiberoptic Cables . . . . . . . . . . . . . . . . . . . . . . . .3.3.1 General . . . . . . . . . . . . . . . . . . . . . . . . . .3.3.2 Commercial Fiberoptic Cables. . . . . . . . . . . . . . . .3.3.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . .

LICRTWAVES IN FIBEROPTIC SENSORS . . . . . . . . . . . . . . . . .

Interferometric Fiberoptic Sensors . . . . . . . . . . . . . . . .4.1.1 Intensity Interferometry . . . . . . . . . . . . . . . . .

4.1.1.1 Basic Principles . . . . . . . . . . . . . . . . .4.1.1.2 The Michelsen Interferometer . . . . . . . . . . .4.1.1.3 The Mach-Zehnder Interferometer . . . . . . . . .4.1.1.4 The Sagnac Interferometer . . . . . . . . . . . .4.1.1.5 The Fabry-Perot Interferometer . . . . . . . . . .4.1.1.6 Interferometer Sensitivity . . . . . . . . . . . .

4.1.2 Fiberoptic Intensity Interferometers . . . . . . . . . . .4.1.3 Polarization in Fiberoptic Sensors . . . . . . . . . . . .

.2-17

.2-17

.2-19

.2-22

.3-1

.3-1

.3-5

.3-5

.3-7

.3-7

.3-7

.3-8

.3-8

.4-1

.4-1

.4-1

.4-1

.4-1

.4-1

.4-2

.4-2

.4-2

.4-3

.4-3

4.2 Phase4.2.14.2.24.2.34.2.44.2.54.2.64.2.74.2.8

and Intensity Detection . . . . . . . .Phase Detection . . . . . . . . . . . .Homodyne Detection Applications . . . .Phase Noise . . . . . . . . . . . . . .Amplitude Noise . . . . . . . . . . . .Satellite Modes and Multimode OperationPhase-Locked-Loop Operation . . . . . .Heterodyne Detection . . . . . . . . .References . . . . . . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

.4-5

.4-5

.4-8

.4-8

.4-9

.4-9

.4-1o

.4-1o

.4-11

4.3 Integrated Optical Circuits (IOCS) . . . . . . . . . . . . . . . . .4-12

5.0 FIBEROPTIC SENSORS AND COMPONENTS . . . . . . . . . . . . . . . . .5-1

5.1 Phase Modulated Fiberoptic Sensors . . . . . . . . . . . . . . . . .5-15.1.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . .5-15.1.2 Fiberoptic Acoustic Sensors . . . . . . . . . . . . . . . . .5-2

5.1.2.1 Acoustic Pressure Sensors . . . . . . . . . . . . .5-25.1.2.2 Pressure Gradient Sensors . . . . . . . . . . . . .5-3

5.1.3 Fiberoptic Magnetic Sensors . . . . . . . . . . . . . . . . .5-55.1.4 Fiberoptic Electric Current Senaors . . . . . . . . . . . . .5-65.1.5 Fiberoptic Spectrophones . . . . . . . . . . . . . . . . . .5-65.1.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . .5-75.1.7 Reference . . . . . . . . . . . . . . . . . . . . . . . . .5-7

5.2 Intensity Modulated Fiberoptic Sensors . . . . . . . . . . . . . . .5-75.2.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . .5-75.2.2 Evanescent-Field Fiberoptic Sensor . . . . . . . . . . . . .5-85.2.3 Reflection Coefficient Fiberoptic Sensor . . . . . . . . . .5-85.2.4 Moving Grating Fiberoptic Sensor . . . . . . . . . . . . . .5-85.2.5 Microbend Fiberoptic Sensor . . . . . . . . . . . . . . . . .5-95.2.6 References . . . . . . . . . . . . . . . . . . . . . . . . .5-12

5.3 Fiberoptic Linear Accelerometers . . . . . . . . . . . . . . . . . .5-125.3.1 References. . . . . . . . . . . . . . . . . . . . . . . . . .5-14

5.4 Fiberoptic Rotation-Rate Sensors . . . . . . . . . . . .5.4.1 Introduction. . . . . . . . . . . . . . . . . . .5.4.2 Methods of Rotation Sensing . . . . . . . . . . .5.4.3 Interest in Optical Rotation Sensors. . . . . . .5.4.4 Sagnac Effect in a Vacuum . . . . . . . . . . . .5.4.5 Sagnac Effect in a Medium . . . . . . . . . . . .5.4.6 The Magnitude of the Sagnac Effect. . . . . . . .5.4.7 Methods of Optical Rotation Sensing . . . . . . .5.4.8 Fundamental Limits in Optical Rotation Sensors. .5.4.9 Fiberoptic Rotation-Rate Sensors. . . . . . . . .5.4.10 Photon Shot-Noise Limit . . . . . . . . . . . . .5.4.11 Ideal Performance . . . . . . . . . . . . . . . .5.4.12 Measurement of Nonreciprocal Phase Shift. . . . .5.4.13 Methods of Nonreciprocal Phase Modulation . . . .5.4.14 Open Loop and Closed Loop Operation . . . . . . .5.4.15 Problems in Fiberoptic Rotation Sensors . . . . .5.4.16 Integrated Fiber “Gyros”. . . . . . . . . . . . .5.4.17 Fiber Gyro Performance. . . . . . . . . . . . . .5.4.18 Summary of Rotation-Rate Sensors. . . . . . . . .5.4.19 General Conclusions Regarding Fiberoptic Sensors.5.4.20References. . . . . . . . . . . . . . . . . . . .

. . . . . .5-14

. . . . . .5-14

. . . . . .5-14

. . . . . .5-15

. . . . . .5-15

. . . . . .5-16

. . . . . .5-16

. . . . . .5-16

. . . . . .5-17

. . . . . .5-18

. . . . . .5-18

. . . . . .5-19

. . . . . .5-19

. . . . . .5-20

. . . . . .5-21

. . . . . .5-21

. . . . . .5-22

. . . . . .5-23

. . . . . .5-23

. . . . . .5-23

. . . . . .5-23

6.0 FIBEROPTIC SENSOR ARRAYS AND TELEMETRY SYSTBMS . . . . . . . . . . .6-1

6.1 Fiberoptic Sensor ArraYs . . . . . . . . . ● . . . . . . . . . . . .6-16.1.1 Fiberoptic Senaor Array Design Considerations . . . . . . . .6-1

6.1.1.1 General Design Considerations . . . . . . . . . . .6-16.1.1.2 Specific Design Considerations . . . . . . . . . . .6-1

6.1.2 Fiberoptic Sensor Array Basic Configurations . . . . . . . .6-16.1.3 Fiberoptic Sensor Array Budgets . . . . . . . . . . . . . . .6-5

6.2 Fiberoptic Telemetry Systems . . . . . . . . . . . . . . .6.2.1 Fiberoptic Telemetry System Design Options . . . .6.2.2 Fiberoptic Telemetry System Basic Configurations .6.2.3 Telemetry System Budgets . . . . . . . . . . . . .

6.2.3.1 Risetime Budget Analysis . . . . . . . . .6.2.3.2 Optical Power Budget Analysis . . . . . .6.2.3.3 Cost Budget Analysis . . . . . . . . . . .

6.2.4 Fiberoptic Telemetry System Specific Configurations

. . . .

. . . .

. . . .

. . . .

. . . .

. . . .

. . . .

. . . .

.6-5

.6-6

.6-6

.6-7

.6-7

.6-9

.6-9

.6-9

6.3 Fiberoptic Sensor Array Telemetry Transmission Line Parameters . . .6-116.3.1 Transmission Line General Parameters . . . . . . . . . . . .6-116.3.2 Transmission Line Specific Parameters . . . . . . . . . . . .6-116.3.3 Multiplexing with Optical Fibers . . . . . . . . . . . . . .6-126.3.4 Connector Parameters . . . . . . . . . . . . . . . . . . . .6-13

6.4 End-Terminal (Receiver) Consideration . . . . . . . . . . . . . . .6-13

6.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6-13

APPENDIX - Fiberoptic Sensors Glossary. . . . . . . . . . . . . . . . . .A-l

CHAPTER 1

INTRODUCTION

1.1 BACKGROUND

The ever-present need for increased communi-cation aystem capacity and reduced cost per messageunit has spurred the development and installation ofhundreds of operating lightwave communication ayatemsaround the world. Compared to wire aystems, opticalfiber transmission syatems operate with less energy permessage unit-mile, lower signal attenuation per unitdistance, higher bandwidth for increased channel capa-city, lower electromagnetic interference, lower cross-talk, higher resistance to clandestine tapping, lowershock hazard, amaller size, less weight, reduced con-sumption of critical metals, and many others. Theseadvantages have encouraged improvements in lightsources; optical fibers, cables, and connectors; andphotodetectors. Optical fiber data links are off-the-shelf ready-to-install items. Hundreds of millions ofdollars are being spent annually for improving opticalcommunication system component.

Capitalizing on the availability of opticalcomponents, there haa been significant progress duringthe past few years toward the development of a newclaaa of sensors employing fiberoptic. These sensorsare capable of detecting acoustic fields, linear androtational acceleration, electric and magnetic fielda,and many other physical parameters. In effect, thesenaor modulates some feature of the lightwave in anoptical fiber such as the intenaity OT the phase.Usually phase modulation must be converted to an inten-sity modulation prior to detection. This may be accom-plished by means of an optical interferometer. The re-sulting signals (intensity or phase) can be telemeteredto places other than the location of the sensor (trans-ducer, modulator) by means of a fiberoptic signal trans-mission (telemetry) system. The optical signal may bein analog or discrete form and the system may operatewith or without optical-to-electrical or electrical-to-optical signal conversion. The fiberoptic aensors de-scribed in this manual may use fiberoptic transmissionsystems as well as electrical or electromagnetic trans-mission systems. Even for the simplest case, one inwhich a visual field or image is to be transmitted ina coherent-fiber cable, the fiber bundle itself mustserve as the sensor and all the aspects of achievinglightwave acceptance by optical fibers must be consid-ered.

1.2 PURPOSE

This manual on fiberoptic sensors is designedto be a stand-alone document intended to serve many pur-poses. It provides a basic background for understand-ing the concepts that make up the field of fiberoptic,particularly as they apply to fiberoptic sensors. Itdescribea the propertied of optical fibers, then fab-rication, and the properties of light sources and de-tectors associated with fiberoptic sensora. Specific

1-

emphasis is placed on design considerations for thesemajor components and for associated connector,splices, couplers, and cables.

Different schemes may be used for controllinglightwaves in order to sense a physical parameter. Manyof these control schemes are discussed in this manual,including interferometry, polarization, and modulation.Intensity and phase modulation are discussed in termsof homodyne and heterodyne detection. Integrated opti-cal circuits are introduced with emphasis on their fab-rication and operating principles.

Many different types of fiberoptic sensorsare described in terms of their design and operation.Some of these include intensity and phase modulationsensora, rotation sensors, and accelerometers. Devicesdiscussed include the fiberoptic sensora (transducers,modulators) used in hydrophores, magnetometera and geo-phones.

In most fiberoptic sensor and sensor arrayapplications there will be a requirement to telemetersensed data over the full range of distances. Variousfiberoptic aensor arrays and telemetry schemes are dis-cussed. Information is given concerning risetime andpower budgeting. Overall design considerations for tele-metry systems are also briefly discussed.

1.3 CONTENTS BY CHAPTER

Following thia brief Introduction, (Chapter1), Chapter 2 is devoted to the properties of the baaiccomponent of the fiberoptic sensor: the optical fiberitself. Electromagnetic wave (lightwave) propagationin optical fibera in terms of the wave equation; thecoupling of lightwaves in and out of fibers; power lossby absorption, leakage, and scattering; are all discuss-ed in some detail. Various properties of fibers, theirbasic construction and limitations are discussed, in-cluding basic concepts of total internal reflection,critical entrance angles, and numerical aperture. Theconcepts of mode propagation, refractive index profiles,and polarization are introduced. Various methods offiber fabrication are covered, including several meth-ods of drawing fibers. Obtaining deaired refractiveindices and the size, strength, and level of purity offibers are also described. Finally, in Chapter 2, thecharacteristics of various types of light sources arediscusaed in sufficient detail to understand their usein connection with fiberoptic sensors. The chaptercloses with a discussion of the characteristics andlimitations of photodetectors with apecial emphasis ontheir importance and use in connection with the outputsignal from a fiberoptic sensor.

Chapter 3 follows with a diacuasion of thevarious means for connecting fiberoptic aenaor inputsto electrical or optical sources and outputs to photo-

1

detectors or display devices. The sensor may be con-nected to optical fibers and cables by various typesof connectors, splices, couplers, mixers, and cables,the connector and splice being used primarily to joinfibers and cables, the couplers being used to connectone source to many fibers (divergence), the mixer beingused to couple many fibers to one photodetector (con-vergence).

The operation of fiberoptic sensors cannot bewell understood without an understanding of the variouaactions and interactions that can take place by andamong lightwaves. Many of these interactions are thebasis for sensing physical parameters. The lightwavecharacteristics discussed in Chapter 4 include inter-ferometrics, polarization, and intensity and phase mod-ulation in relation to homodyne and heterodyne detec-tion. Chapter 4 ends with lightwave control techniqueused in integrated optical circuits.

Chapter 5 turns primary attention from gen-eral principles and techniques used in the operation offiberoptic aensora to a description of the sensorsthemselves and their components. Intensity modulationsensors; phase modulation devices, such aa those usedin hydrophores and magnetometera; rotation sensors, ac-celerometers, and geophones are discuased as exampleaof fiberoptic sensor applications.

The grouping of fiberoptic aensors into sen-aor arrays and the telemetering of their outputs toother locations are covered in Chapter 6. Design op-tions; basic configuration; riaetime, power, and coatbudgeta; and specific configurations of fiberopticarrays and telemetry aystema are diacuased in depth,along with light sourcea, transmission lines and end-terminals as they relate to fiberoptic senaors.

Bibliographies pertinent to the subject areincluded at the end of each chapter. The appendix con-tains an authoritative glossary of terms and definitionain the field of fiberoptic with emphasia on the termsused to describe the design, fabrication, and operationof fiberoptic aenaors. Particular attention in thegloasary is devoted to the terms used in this manual.Many topics and concepta related to fiberoptic senaors,their operating principles, and supporting theory areincluded in the glosaary ao aa not to overburden thereader with too many detaila while the main topics arebeing discussed. For example, concepta concerning dia-peraion, Msxwell’a equations , modulation, polarization,reflection and transmission coefficient, and varioustvpes of fiberoptic sensors and interferometers aredescribed in the glosaary.

1-2

CHAPTER 2

FIBEROPTIC SENSOR COMPONENTS

2.1 OPTICAL FIBER PROPERTIES

In this section the basic properties of opti-cal fibers are discussed in some detail with emphasisplaced on concepts that are important in optical fibersensor technology. The structure of optical fibers isquite simple, as shown in Fig. 2.1. Basically theyconsist of layered cylinders of glass or plastic withsmall diameters. There is a central cylinder calledthe core, which is made up of one type of glass orplastic. Surrounding the core is a cylindrical shellcalled the cladding that is made of a slightly differ-ent type of glass or plastic. The difference betweenthe core and cladding materials will be discussed later.Finally, this layered cylinder is usually surrounded bya Protective jacket. The light-guiding capability ofthe fiber is dependent upon the properties of the coreand cladding while the mechanical strength of the fiberis maintained by the jacket that is usually made ofplastic.

‘A’!” A1/ L

CL’

CORE

Fig. 2.1 The basic structure of an optical fiber.

2.1.1 Design Objectives

Some of the design objectives considered inthe development of a good optical fiber are illustratedby the simple system shown in Fig. 2.2. The system con-sists of a pulse-modulated optical source. The inputsignal at the left represents the intelligence (infor-mation) that is impressed on (modulates) the light beamthat, after emerging from the source, is focused witha lens into one end of an optical fiber. The lighttravels through the fiber and emerges from the oppositeend, where it is directed into an optical detector(photodetector), possibly focused again with a secondlens.

2-

MODULATING SIGNAL

LIGHT PULSES

OPTICALDET&CT- .

INPUT OUTPUT

Fig. 2.2 A basic optical fiber link.

Four major optical fiber design objectiveswill be discussed. The first major objective is thedesirability of maximizing the amount of available lightthat is transferred (coupled) into the core of thefiber. It is only the light in the core that is propa-gated along the length of the fiber with relatively lowoptical power loss. In order to maximize the amount oflight transferred (coupled) into the core, it is neces-sary to maximize the numerical aperture (NA) of thefiber. This is one of four important fiber parametersthat strongly affect the behavior of the simple systemshown in Fig. 2.2. After introducing the other threeimportant parameters, each will be discussed in somedetail.

The second fiber design objective is the de-sizability of minimizing the light lost from a beam asit travels through the core from the input end to theoutput end of the fiber. This light loss is describedas the attenuation (power leas) rate, usually express-ed in dB (decibel) per kilometer of fiber.

The third optical fiber design objective isthe desirability of maximizing the information carryingcapacity of the fiber. The input to the fiber may bea light beam of continuously-varying intensity or agroup of well defined pulses of light as shown in Fig.2.2. As the light pulses propagate through the fiber,their amplitude will decrease due to attenuation. Inaddition, due to a number of other effects to be dis-cussed, the individual pulses also may broaden (spread).If they become too broad they will overlap or coincidewith one another in both time and space. If this OC-

curs, the intelligence (information) originally impres-sed on the light beam would be lost. Pulse broadeningthat occurs in the fiber is called dispersion. Thisparameter places a limit on a fiber’s information carry-ing capacity (signaling rate).

The fourth design objective is the desirabil-ity of maximizing the strength of fibers when they areInitially drawn and maintaining this strength when thefibers are formed into cables or are used in sensorsand other applications.

Before considering these and other fiber de-sign objectives in some detail, the basic theory oflight propagation in optical fibers will be discussed,beginning with light-ray propagation in layered media.

1

The light-ray concept is a convenient approximate ap-proach that may be used to introduce other importantconcepts such as total internal reflection and ray trap-ping. To extend the theory of light propagation far-ther, however, it is necesaary to take into account thenotions that light is an electromagnetic wave pheno-menon and that optical fibers are cylindrical dielec-tric waveguides. With these in mind it is possible todevelop concepts regarding the allowed electromagneticpropagation modes of a cylindrical waveguide and tointroduce the frequently encountered optical fiber wave-guide V-Parameter (V-value) that must be consideredwhen selecting a suitable fiber for a particular appli-cation.

In accordance with the ray theory of lightpropagation, a light beam incident from below on theinterface surface between two transparent media, at anangle e 1 with the interface surface behaves as shown inFig. 2.3. When fll ia large, part of the incident beam

MEDIUM2 ! .-”’”n1>n2

1X6;

n2

k

Fig. 2.3 Reflection and refraction at the interfacewhen a lightwave travels from a higher toa lower refractive index medium.

is transmitted into the upper medium and vart is re-flected. Their relative intensities depend upon therefractive indices of the two media. The refractiveindex of a medium is defined as the ratio of the velo-city of light in a vacuum to the velocity of light inthe medium. The higher the refractive index of a med-ium the slower light will travel in it. The refrac-tive index of medium 1 is designated as nl and thatfor medium 2 as n2 as shown in Fig. 2.3.

These indices alao determine the directionof the beam transmitted into medium 2, i.e., @2 inFig. 2.3 is determined by the indexes of both media.Snell’s law of refraction of light at an interface pre-dicts that the ratio of the cosine of the angle 131 tothe cosine of the angle of t12 is equal to the ration2/nl which is equal to the velocity ratio v1/v2. Thus,as shown in Fig. 2.3, if light propagates in medium 1at a lower velocity than in medium 2, the angle 01 willbe greater than the angle 02 and the ray will be benttoward the interface when entering medium 2. The angleof the reflected beam is equal to the angle of the inci-dent beam. These are an application of the well knownlaws (Snell’s laws) of refraction and reflection thataPPIY in ray treatments of wave phenomena.

When the angle 81 is progressively decreased,the results shown in Fig. 2.4 are obtained. Beginningat the left, a ray is shown incident at a relativelylarge angle 01 with the interface between the two media,with nl > n2. There is both a refracted and a reflectedbeam and, from the conservation of energy, the sum oftheir energies must equal the energy in the incidentbeam.

2-

nl > n2

v,< V2

+’*NG)I \ MEOIUMI’(CORE)

CASEI 01>0, CASE2 e)=ec CASE3: 01<8.

Fig. 2.4 Internal reflection of light rays strikingan interface surface at angles greater than,less than, and at, the critical angle.

As the angle f31 is decreased the refractedbeam entering medium 2 bends further toward the inter-face until finally the angle E12 reaches zero as shownin the center of Fig. 2.4. At the same time the inten-aity of the light entering the medium 2 steadily de-creases and approaches zero as the angle 92 approacheszero; thus the intensity of the reflected beam ap-proaches that of the incident beam. The value of fJlcorresponding to the limiting value of e2 = O is defin-ed as the critical angle Oc. At that condition cosine02 is equal to unity and the critical angle ec is givenby:

Oc = cos-1n2/nl (2.1)

For all values of angle 01 equal to or lessthan the critical angle ec as shown at the right inFig. 2.4, the incident ray will be totally refected andenergy will not be transmitted into medium 2. It shouldbe emphasized that this phenomenon of total internalreflection at an interface occurs only when the velo-city of light in the medium of incidence (medium 1) isless than the velocity of light in medium 2, i.e., whenthe refractive index nl is greater than the refractiveindex n2. As an example, suppose that light is incidentfrom water on the surface between the water and air.The velocity of light in water is approximately 2.25 x108 m/see as compared to 3.00 x 108 mfsec in a vacumm.Thus, the refractive index of water is 1.33 and thecritical angle at the water to air interface is approx-imately 41”. Total internal reflection will occur forall rays that make an angle of 41” or less with thewater-air interface surface.

It is this phenomenon of total internal re-flection that is the basis of operation of opticalfibers. The refractive index of the material making upthe core of a fiber must be slightly larger than therefractive index of the surrounding cladding. A raytraveling in the core at an angle equal to the criticalangle is shown in Fig. 2.5. Such a ray is totally re-

CLADDING -n2,

Fig. 2.5 A step-index optical fiber showing thecritical angle, 6C for total internal re-flection.

2

ttoc

fleeted each time it is incident on the core-claddinginterface so that it remains ““trapped”” in the core.This, and any other ray with f31<f3c, will remain in thecore until it reaches the end of the fiber. Ideallyit will propagate without attenuation through the coreof the fiber.

The refractive index of the cladding is heldslightly less than that of the core and thus it is con-venient to introduce a quantity A, the fractional dif-ference between the two refractive indices, defined bythe equation:

A = (nl - n2)/nl (2.2)

From Eqs. (2.1) and (2.2), and for a meridion-al ray (a ray that travels in a plane containing thecentral axis of the core) the cosine of the criticalangle is given by:

cosOc=n2/nl = 1 -A (2.3)

Cos%lc = 1 -2A+A2 (2.4)

Using the Pythagorean theorem,

sin2f3c = 1 -cos2ec=2A-A2 (2.5)

sinoc= (2A - A2)1/2 (2.6)

When A2 << 2A, which is usually the case foroptical fibers, then:

sin’dc . (2A)1f2 (2.7)

Typically the refractive Index nl of the coremight be 1.46 while that of the cladding n2 might be1.44, in which case A = 0.14. In this case, 2A = 0.28and A2 = 0.0002, or 1.4% of 2A, and to this extent theapproximation is valid. Critical angles are usuallyonly a few degrees. Therefore, it is sufficiently ac-curate to compute them using the value for the sine asgiven in Eq. (2.7).

As previously atated, rays propagating in thecore at angles equal to or less than Oc will be trappedin the core while rays that propagate at angles 01greater than ec will be partially transmitted into thecladding each time they encounter the core-claddinginterface. These latter rays rapidly decrease in inten-sity as they travel through the core and thus do notcontribute to propagation over long-distances in fibers.

Fibers with two different types of refractiveindex profiles are widely used. One of these is thestep-index fiber. The left portion of Fig. 2.6 shows

STEP-INDEX FIBER GRADED-INDEX FIBER

INDEXPROFILE

Fig. 2.6 Refractive index profiles for cylindricalwaveguides (optical fibers).

he variation of the refractive index as a function ofhe distance from the center of the core to the outsidef the cladding for a step-index fiber. Within theore, the refractive index does not vary with the rad-

2-3

ius, i.e., it has a constant value nl. At the corecladding interface there is a step decreaae in the indexfrom nl to n2. It remains constant throughout the clad-ding. The refractive index profiles of another type offiber, the graded-index fiber, is shown at the right inFig. 2.6. In this type of fiber the refractive indexnl decreases as a function of the radial distance fromthe center of the core. Beyond the core-cladding inter-face the index n2 remains constant with respect to theradius all the way to the outer surface of the cladding.

Typical rays that may propagate with minimaloptical power loss within the core of a step index fiberare shown in the lower left of Fig. 2.7. Within the

CENTRAL RAY MERIDIONAL RAY THROUGH CENTER

MERIDIONAL RAY THROUGH CENTER HELICAL RAY AVOIOING CENTER

Fig. 2.7 Differently–directed rays in the core of anoptical fiber.

core a central ray is shown that propagates parallel tothe axis of the fiber. There also are meridional raysthat propagate in planes containing the central axis ofthe fiber. They travel in the core, reflecting backand forth each time they strike the core-cladding inter-face.

The meridional ray for the graded index fiberis shown on the upper right in Fig. 2.7. Because theindex varies continuously from the center of the coreout to the core-cladding interface, such rays, ratherthan traveling along straight lines, propagate alongcurved lines, continuously being bent back and forth;however they travel in planes containing the centralaxis of the fiber. There are other rays that travelalong helical paths that do not intersect the centralaxis of the fiber as shown at lower right of Fig. 2.7.There other similar rays, called skew rays, in step-index fibers. There are many more helical and skewrays than there are meridional rays and they have con-siderable importance in light ray propagation in opti-cal fibers. They contribute substantially to the trans-fer of energy and information from the input end to theoutput end of a fiber. However, the geometric descrip-tion of the propagation of helical and skew rays ismore difficult than that of merdional rays, as shown atthe lower left of Fig. 2.7. Therefore, for the sakeof simplicity in developing the ray theory of light pro-pagation in fiber, this treatment is confined to theconsideration of meridional rays. This approach provid-es an adequate background for defining and understand-ing the basic parameters of light propagation into,within, and out of, optical fibers.

The numerical aperture (NA) of an opticalfiber is defined aa the sine of the half-angle of thecone of light that is incident from air on the inputend of an optical fiber, such that all the rays havinga direction that lies within the cone will be trappedwithin the core once they enter the fiber as shown inFig. 2.8. Thus, at the core-air transverse interface

,..

[--::= ”’’-”.! (----

\ACCEPTANCE

J-’’”

&

CONE

Fig. 2.8 The acceptance cone for a ~tep~i~~$x opti-cal fiber. (N. A.=sinec=(nl ‘n2 )

end surface, where the refractive index of air, no7 ISequal to unity, there is another critical angle,3c ,such that all ,the light contained within the cone ofhalf angle Clc , will be trapped within the fiber. Ap-plying Snell’s Law, this time in the sine form becauseec ‘ is the angle between the cone edge (elements) andthe normal to the surface of incidence (end face of fi-ber), the ratip of the sine of ec within the core tothe sine of ec in air is equal to the refractive indexn. of air divided by the refractive index nl of thecore. Thus, since n. = 1:

(sinoc)/no = sinec = (sin9c’)/nl (2.8)

At the core-cladding interface within the fiber it wasshown that Cosoc = n2/nl Eq. (2.3). Combining Eqs.(2.3) and (2.8) and using the Pythagorean theorem:

sin28c + c0s20c=l=(sin20c’ )/n12 + n22/n12 (2.9)

Transposing:

(5in2ec’ )/n12=l-n22/n12=(n12-n22)n12 (2.10)

Thus, from the defini~ion that the numerical aperturei s

As

equal to the sin ec” :

2 1/2N.A. = sinoc’ = (n12 - n2 ) (2.11)

defined in Eq. (2.2) above:

A = (nl - n2)/nl (2.12)

Solving for n2:

n2 = nl (1 - A) (2.13)

Substituting Eq. (2.13) in Eq. (2.11) and simplifying:

N.A. = nl(2A - A2)1/2 (2.14)

If A2 << 2A, which iS usually the case for opticalfibers, then:

N.A. = nl(2A) 112 z [2nl(nl - n2)11’2 (2.15)

Eq. (2.15) statea that the amount of light that will re-main trapped and propagate in the core is directly pro-portional to the square root of the product of the corerefractive index and the core-cladding refractive indexdifference.

Examples of these various concepts about raypropagation in optical fibers are shown in Fig. 2.9 andin the following table:

A ‘$raec (3C’ ec’deg rad deg

0.010 0.142 8.13 0.214 12.240.001 0.045 2.56 0.067 3.85

2-

CLADDING -.2 ACORE -., 8>!9’

—

~

Fig. 2.9 Light rays in a step-index fiber core.

Two rays are ,showo in Fig. 2.9. One entersfrom air at an angle, 0 , such that on intersecting thecore-cladding interface, it makes an angle less thanthe critical angle, 13c, with the interface. This raywill be totally internally reflected and will be trap-ped in the core, so that it propagates with minimalloss through the fiber core. A second ray, incidentfrom air at a larger angle, intersects the core-clad-ding interface at an angle greater than tic. At eachreflection part is reflected back into the core andpart is transmitted into the cladding. Such a ray isstrongly attenuated, rapidly decreasing in intensityas it propagates along the core of the fiber.

The Eqs. (2.8), (2.11) and (2.15) show thatthe critical angle at the core-cladding interface fortotal internal reflection in radian measure for thetrappin of light in the core is approximately equal

fto (ti) 12 when A2 << 2A, while the $orreaponding en-

:n::;f72:ritica1 angle ‘rem air’ ‘c ‘ ‘s ‘qwl ‘0As indicated in the above table for A = 0.01,e: = 0.14 radians or about 8“ for the core-claddinginterface. The maximum angle f3c that the trapped raysmy make with the axis of the fiber as they enter fromair is 0.21 radians, or 12”, assuming that the nl ofthe core is equal to 1.5. Thus a cone of light with a24” full apex angle could enter the fiber from air andbe totally trapped in the core. ForA = 0.001, Oc is0.045 radian or about 2.6”. Light rays entering fromair,would have to lie within a cone full apex angle of2ec , or only about 8°, in order that they be trapped.

2.1.2 Lightwave Propagation

The ray theory is an approximate representa-tion of light propagation in confined media. It ap-plies only at wavelengths that are small in comparisonto the dimensions of the cross section of the waveguide.For cylindrical fibers “small” is in comparison to theradius of the core. For helium-neon light the wave-length is 0.63 pm and the ray theory applies well tofibers with a core radius greater than 25pm. Forguides with a core radius of 2 pm, the ray theory is apoor approximation since in this case the wavelengthis only about one third of the core radius. Therefore,electromagnetic wave theory is used to obtain a goodrepresentation or description of light propagation.

Maxwell’s equations correctly describe boththe space and time interdependence of the electric andmagnetic fields in linear, homogeneous, isotropic, andsource-free media. From these equations, the generalform of the electromagnetic wave equation can be deriv-ed. The wave equation deacribes the propagation of anelectromagnetic wave in spatial and time coordinates.If the source-free medium is a nonconductor (dielec-tric) the wave equation can be simplified for describ-ing propagation in optical fibers.

Optical fibers are cylindrical dielectricwaveguides. In order to describe light propagation inthem it is convenient to use the conventional system ofcylindrical coordinates ahown in Fig. 2.10.

4

,> = (JREFERENCE

6=0REFERENCE PLANE

LIz

Fig. 2.10 The cylindrical coordinate system for ex-pressing lightwave propagation in an opti-cal fiber. The point P is designated as p,0, z.

The Z-axis of this coordinate system is takento be the central axis of symmetry of the waveguide.The z-coordinate is the distance from a reference planedesignated as Z. (zEO). A spatial point in a fiber islocated by defining a radius coordinate, p, as the dis-tance radially from the Z-axis; an azimuthal (angular)coordinate, $, measured from an arbitrary referenceplane ($=0); and a value of z. This coordinate systemis commonly known as the cylindrical coordinate system.

In the simple case where the refractive indexdepends only on the radial coordinate, the solution tothe wave equation, derived from Maxwell’s equations forthe electric fields, can be expressed as the productof two functions as follows:

E(p, $,z,t) = E(p, $)e-j(~t-W) (2.16)

= E(p, $)sin(ut-&) (2.17)

The variable t is the time measured from a time refer-ence of to. The first is an amplitude factor E(P ,$)that depends on the radius vector P and the azimuthal(angular) coordinate $. The second, which can be ex-pressed as complex exponential or sinusoidal function,indicates that the electric fields are sinusoidal wavesin time and in space. The angular frequency is u= 2nfwhere f is the optical frequency. The B is the propa-gation constant, defined as the refractive index, n,times the z component of the wave vector k, where kn=2h/io, and i. is the optical wavelength in a vacuum atfrequency f. Thus, optical energy transfer in dielec-tric media takes place in the form of wave propagationalong the axis of the guide. The absolute value of kis also called the wave number.

2.1.3 Propagation Modes

When the geometric boundary conditions at thecore-cladding interface are introduced only particular(discrete) solutions of the wave equations are permitt-ed. Only these values can exist, each designated by avalue for i, for the amplitude factor Ei(P,$) and cor-

responding discrete values for the propagation constant~. The velocity of propagation of each allowed wave,i.e. mode, along the axis of the waveguide is givenby the ratio of the angular frequency divided by thepropagation constant Bi, of a particular wave designat-ed by the subscript. Thus, the various allowed solu-tions represent discrete waves with discrete amplitudes

2-5

that propagate along the axis of the guide each with adiscrete velocity.

In order to characterize light propagation ina step-index optical fiber it is convenient to use aparameter, usually referred to as the waveguide V-para-meter (V-value). It is defined by the equation:

V = 2ma(nl 2 - 2 112/in2 ) o (2.18)

and therefore from Eq. (2.11):

V = 2~a(N.A.)/& (2.19)

where a is the core radius; N.A. is the fiber numericalaperture, a function of the refractive indices of thecore and cladding; and i. is the wavelength of the in-cident light in a vacuum. (The wavelength of a light-wave in a vacuum is nearly equal to its wavelength inair.) These are the main parameters needed to describelight propagation in a step-index optical fiber. TheV-parameter may be designated as the light propagationcharacteristic of an optical fiber. The larger the V-value the larger the number of modes (different discretewaves) the fiber can support, i.e., allow to propagate.

The predictions or conclusions that may bedrawn from the wave theory of light propagation infibers may be summarized in graphical form. As alreadymentioned, only particular (discrete) solutions of thewave equation exist. These correspond to discrete wavespropagating along the axis of the guide with particularvelocities. Some of the characteristics of these par-ticular (allowed) modes are shown in Fig. 2.11. The

kn,

kn2

V=? GwAVEGUIDE PARAMETER

Fig. 2.11 The propagation constant, i3, and the velo-city of various modes as a function of theV-parameter of an optical fiber.

curves show the allowed values of the propagation con-stant & as a function of the V-parameter (V-value).Each curve corresponds to a particular allowed solutionof the wave equation. This graph indicates that theallowed values of %for the various solutions are inbetween knl and kn2, corresponding to the wave numbersin the core and in the cladding, respectively. Sincethe wave (phase) velocity in the Z-direction is givenby the quantity m/6 the curves in Fig. 2.11 also showthe phase velocity versus the waveguide V-parameter (V-value). Thus, the velocity of the allowed waves (modes)represented by the different curves is seen to rangefrom the higher velocity in the cladding (lower ordi-nate, higher value) to the lower velocity in the core(upper ordinate, lower value) as the waveguide V-para-meter increases. Thus each curve in Fig. 2.11 corres-ponds to an allowed solution of the wave equation ap-plied to dielectric waveguides. The waveguide V-para-

meter varies directly with the core radius and numeri-cal aperture and inversely with the wavelength of light.As the V-parameter increases, the number of allowedmodea increasea. For V less than 2.40, only one waveor mode, designated in Fig. 2.12 as the HE1l mode,ia permitted. For V in the range of 2.4 to 3.8, fourmodes are allowed, these being the HE1l, TEOl, TMol,and HE21 modes. These particular alphanumeric designa-tions are standard for electromagnetic waveguides.They have been chosen because of the specific formsof the spatial variations for the electric and magneticfields associated with the particular solutions for thewave equation. As V increases, more and more modes arepermitted (supported).

Consider the specific case in which V is lessthan 2.40 as shown in Fig. 2.12. This is especially

k“,

WAVEGUIDE PAR&METER

J!kiii

@CORE

CLADDING

V<2.40– SINGLE MODE FIBER~1 r

Fig. 2.12 The electric field of a lightwave for thecase in which only the first mode, HE1l issupported by an optical fiber.

important since it defines the condition required fora single-mode fiber. A vertical line is shown corres-ponding to a V-value of 2.15. It intersect only theHEll curve indicating that there is only one effectivevelocity value. Under this condition the wave equationreduces to an especially simpl$ form. The magnitudeof the electric field vector, E, varies approximatelyas a Gaussian function of the distance from the corecenter, p, decreasing monotonically from the center ofthe core to the core-cladding interface as shown in thelower right of Fig. 2.12. The electric field does notgo to zero at the core-cladding interface. It extendsinto the cladding some distance. In the cladding, how-ever, it decays rapidly (exponentially) with distancefrom the center. The dominant direction of the elec-tric field within the core is shown in the middle dia-gram of Fig. 2.12. In this case it has been assumedthat light polarized in the direction shown has beenintroduced into the circular core of the fiber and thearrows represent the magnitude and direction of thedominant electric field component of the electromagne-tic wave. The electric field is always vertical inthis figure, but decreases in magnitude aa the claddinginterface is approached. The dominant magnetic fieldcomponent will also be tranverse to the core axis andperpendicular to the electric field. The direction ofpropagation is perpendicular to both the electric andmagnetic fields. The cross section of the output beamemitted from the fiber is shown in the upper right ofFig. 2.12. The beam is conical and in this case the

2-

pattern is circularly symmetric and shows no fine struc-ture. Horizontally polarized light could also havebeen introduced into the same fiber at the same time.Such light would remain horizontally polarized in anideal fiber. In fact this same type of behavior ap-plies to any direction of polarization and gives riseto one scheme for multiplexing.

In an ideal singlemode fiber with perfect cy-lindrical symmetry the direction of light polarizationonce introduced remains constant and there is no energytransfer among the waves with different polarizationdirections. However, in real fibers, due to slight

ellipticities in the core cross section, imperfectionsin the core cladding interface, variations in the re-fractive indices throughout the core, effects due tobending, and other causes, there is usually some coupl-ing between the different directions of polarizationand some variations in the velocity of each of thewaves with different polarizations. These effects mustbe considered in certain applications. They will bediacussed later when lightwave polarization effects inainglemode fiberoptic sensor applications are consid-ered.

Returning again to a consideration of the spa-tial modes of lightwaves in optical fibers, considerthe case of a fiber that can support four separate elec-tromagnetic modes. This occurs when the V-value is inthe range 2.4 < V < 3.8, as shown in Fig. 2.13. The

k.,

1 //EEE1*:. :;:( ~Eol

HE)) I .

T,o>1 ,..

!+.3,

& @

CLADDING

.--——- ,~,, HE,,

,.21 <$2?$ COREJ“’< ,.02

T,o,“,22

123456

v-~ GWAVEGUIDE PAFIAMETEI?

A

E

/

CORE

/CLADDING

2.4 <V ~ 3.8&

Fig. 2.13 The propagation constant, B, and the velo-city of various modes as a function of theV-parameter (V-value) of an optical fiber,showing in particular a four-mode fiber.

vertical line in the figure, corresponding to the spec-ific case of V = 3.6, intersects the B versus V curvesof the HEll, TEOl, TMol, and HE21 modes. Energy inject-ed into them may propagate with very low 10SS. Thesemodes have different velocities, though as indicated,the TMO1 and the HE21 velocities are nearly equal.Their spatial field distributions differ, however, sothat a number of different patterns can be producedwhen the output beam from the fiber is allowed to ex-pand and illuminate a screen. For example, by careful-ly adjusting the incident beam at the input end of thefiber, it is possible to excite the TEOl mode to producethe output pattern shown in the upper right in Fig.2.13. This consists of a doughnut shaped pattern witha dark spot in the center. From a detailed examinationof the appropriate aolution of the electromagnetic waveequation, one would find that the electric field vec-tors in the core are mainly circumferential, as shown

6

in the right center of Fig. 2.13. They increase inmagnitude from zero along the axis of the core to amaximum and then decay as the core-cladding interfaceis approached, as shown in the lower right. As alreadypointed out for the HE1l mode in this case, the fieldsagain extend beyond the core into the cladding.

Returning to the graph at the left in Fig.2.13, as V is increased further, for example by de-creasing the wavelength, ,10, of the light injected intothe fiber, additional relatively lossless modes are per-mitted and, very rapidly, propagation phenomena changefrom the single or few mode types to multimode behavior.In fact, for V > 10 the number of allowed modes is ap-proximately equal to V2/2 for a step-index fiber. Asalready pointed out above in the discussion of the rad-ial electric field distribution for the HE1l and TEOlmodes, shown in the lower right in Fig. 2.12 and 2.13,respectively, the ~-fields may extend well beyond thecore cladding interface. In fact when each mode isfirst allowed much of its energy is associated withfields that penetrate the cladding. This phenomena isshown in Fig. 2.14 where the ratios of the power in the

Fig. 2.14 The variation of the ratio of optical powerin the cladding to the total optical powerin a fiber as a function of the V-parameter(V-value).

cladding, pclad, to the total power, F’, in a particularmode are plotted as functions of the V-parameter. Atlow values of V, for example V less than 1.0, most ofthe energy transmitted by the HE1l mode is associatedwith the field in the cladding. The spatial characterof each new allowed mode becomes more complex withinthe V-values, for example, most of the energy transmit-ted by the HE1l mode is associated with the fiel~s in$he cladding. As the V-value is increased, the E andH fields of the HE1l mode extend a smaller distanceinto the cladding and a larger portion of its transmit-ted energy is confined to the core, reading approxi-mately 80% of the total when V = 2.4, as shown in Fig.2.14. At this value of V, the TEOl, TMOl, and HE21modes first come into existence and initially, again,pcladtpz 1. As the V-value increases further the energyassociated with these three modes also become more con-

2-

fined to the core. At V = 3.8, three additional modes,the HE12, EH1l, and H31, are allowed. In this case, dueto the radial and azimuthal structure of their ~ and Pfields they initially propagate with approximately halfof their energy in the core and half in the cladding,so that the power ratio Pclad/P starts off at 0.5 andand then decreases rapidly as V increases.

This characteristic of mode propagation inoptical fibers is employed to advantage in a number offiber sensor applications. It is the basis of opera-tion of evanescent wave couplers, or beam splitters,wherein a portion of the light propagating in one fiberis transferred to a second fiber by bringing theircores close together by etching or lapping away a por-tion of the cladding. Another application of this samephenomenon is as the transduction mechanism in a numberof different intenaity-type aensors, where, throughcarefully controlled micro-displacements induced bybending, light can be ejected from the loosely-boundhigh-order core modes. These and other useful applica-tions of this core-into-cladding energy transfer of theelectromagnetic wave fields are discussed in detail inlater sections.

After the above brief discussion of the rayand the waveguide theories of light propagation in op-tical fibers, it is appropriate to return to a moregeneral consideration of the macroscopic propertied offibers. The conceut of attenuation will be discussednext. Assume that-a pulse of light, of(optical power) 1., is injected at thecore of a fiber, as shown in Fig. 2.15.

peak intensityleft into theIn general, as

OUTPUT INTENSITY DECREASES WI’H INCREASINGIIZ)=Ioe–az

ATTENUATION EXPRESSED IN DECIBELS PER KILOMETER (dB/km)

I(z)F O R Z . 1 km, dB/km=–lOloglo~

Fig. 2.15 Light intensity (optical power) relativeattenuation as a function of distance in anoptical fiber.

it propagates through the fiber its intensity, I, willdecrease exponentially so that the intensity of anypoint (transverse plane) z in the fiber is given by:

I(z) = Ioe-az (2.20)

where 10 is the intial intensity of the point of entryinto the core (z = O), z is the longitudinal distancealong the fiber, and = is the intensity attenuation co-efficient. Thus, as indicated in the graph in Fig.2.15, if in traveling a particular distance, z1, theintensity decreases to 0.51., then at z = 2z1, it willbe 0.251., i.e., at the end of each Z1 incremental in-

7

crease in distsnce the intensity is reduced to l/2 ofthe intensity at the beginning of the incremental in-crease. For example, for this case, at the end of 521the intensity will be 2-5 = 1/32 of the initial value.For optical fibera, the attenuation rate is uauallyspecified in terms of the decibels loss per kilometer,i.e., (dB/km). In the case of z = 1 km, the attenua-tion rate may be defined by the equation:

Attenuation Rate = -10 loglO(I1/Io) dB/km (2.21)

In a fiber with an attenuation rate of 10 dB/km the in-tensity (optical power) will fall to one tenth of theincident intensity after traveling one kilometer. A 3dB/km attenuation rate corresponds to a reduction toone half the incident intensity after one kilometer,since loglo 0.5 is equal to 0.3. In this latter caae,after 5 km the intensity would be down 15 dB from theinitial value, i.e., the attenuation will be 15 dB.

A historical picture of the change in attenu-ation rates of available fibers, from about 1968 to thepresent, is shown in Fig. 2.16. The graph indicates

o0

‘%a

,0

0

0011 I , , , , ,1968 1970 7972 1974 1976 1978 19s0 1982 1984 +

YEAR

Fig. 2.16 The reduction of fiberoptic attenuationrates over the years. The + is a projectedvalue.

why fiberoptic communication links were impractical inthe late 1960’a, since attenuation rates in the range1000 to 100 dB/km correspond to a decrease to one tenthof the input intensity after traveling only 10 to 100metera, respectively. A very evident atep decreaae inattenuation rate occurred around 1970, with the intro-duction of a new fiber fabrication technique, the vaporphaae deposition proceas. This led to the availabilityof the first high-priority silica fibers, and the de-velopment of a group of related techniques for produc-ing extremely high purity, low leas fibers. Today fi-bers are available with minimum lossea, at selectedwavelengtha, in the range 0.2 to 1.0 dB/km so that therepeaterless optical communication links of longer than50 kilometer are an achievable reality.

A clear understanding of the factors that ef-fect attenuation in optical fibers is of importance notonly to the fiber designer but also to the fiber user.

The causea of attenuation may be divided intothree aeparate categories: The first, called material

2-8

absorption, ia due to absorption of optical energy intothe electronic energy levels of transition metal impuri-ties, such as iron, copper, chromium and nickel, andinto the vibrational levela of hydroxyl ions (OH-) inthe core and innermost sections of the cladding. Inthis case, energy is absorbed from the optical beam andreradiated into the molecular lattice in the form ofheat. The second type of attenuation is due to bendin~losses of which there are two typea. One is due to:regular bending of the entire fiber at nominal radii.For example, bending loss may be due to winding the fi-her on a small-diameter mandrel. The second, referred1:0 as mlcrobend loss, arise because of random variationsin the direction of the axia of the core. These mayeven be microscopic, due to external forcea, imperfec-tions in the coating or cladding, ripples in the core-(:ladding interface, ticrocracks, and other causes. Ineither caae, light will be injected from the core intothe cladding, and thus cause a decreaae in the lightintensity transmitted through the core to the outputend of the fiber. Finally, there are three types ofscattering losaes. The first, called Rayleigh scatter-ing la cauaed by microscopic density fluctuation thatare frozen into the random molecular structure of theglass making up the fiber core when it cools to itsrelatively high solidification temperature. These den-sity fluctuations may be resolved into spatial frequen-cies that have wavelengths much shorter than the opticalwavelength. Rayleigh scattering losses vary inverslyas the fourth power of the optical wavelength. In addi-tion to the static denaity fluctuations, there are alsodynamic density fluctuation due to thermal sound waves.These waves originate and propagate becauae the temper-ature of the glass is above absolute zero. These pro-pagating density fluctuations (thermal phonons) lead toBrillouin scattering. Finally, there is scatteredlight caused by absorption and reradiation from atomicvibrational and rotational energy levels, i.e., Ramanscattering. These latter two scattering processes,i.e., Brillouin and Raman, are non-linear processesand are significant only at high optical intensities.

The strength and wavelength-dependence ofsome of these loss mechanisms is shown in Fig. 2.17.

351I I I I I I

30

25

c

220

~.15

x0J

10

5

005 06 07 08 09 10 11

WAVELENGTH (MICRONS)

● TRANSITION METAL IMPURITIES (Fe, Cu, Cr,Ni)

● HYDROXLION (OH)-1 PPM—~ldB/km@.95#m

● RAYLEIGH SCATTERING w l/A4

● LEAKAGE LOSSES (MICROBEND, REGULAR BEND, ETC.)

Fig. 2.17 Sources (causes) of optical power attenua-tion rate as a function of wavelength in atypical optical fiber.

The vertical height of the various cross-hatched re-gions represent the loss as a function nf the wave-length arising from the various sources. Note that theminimum total attenuation at approximately 0.8 micronwavelength is approximately 10 dB/km. This is a some-what mediocre fiber by today’s standards. The lowestfour regions in Fig. 2.17 correspond to the loss dueto 1 part per million by weight, in silicon oxide (Si02)glass, of the metallic impurities Cu, Ni, Fe, and Cr,from bottom to top, respectively. The peak in thevicinity of the 0.95-micron wavelength is due to thethird harmonic of the hydroxyl (OH-) vibrational mode,and corresponds to roughly a 20-part-per-million impur-ity content. The black dots are predicted values oflosses based on calorimetry-type optical absorptionmeasurements made on the glass sample from which thefiber was drawn. The upper cross-hatched region repre-sents the attenuation due to Rayleigh scattering whilethe white region is the remaining difference betweenthe total loss versus wavelength (the uppermost curve)and the sum of the previously mentioned losses. Thelatter is attributed to regular bending and microbend-ing losses.

The attenuation versus wavelength curve shownin Fig. 2.18 is for a currently available very-low-

5.0 .‘.

3.0 — ‘.>‘.

2.0 — ‘\

1.0

0.5 -\

0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6

WAVELENGTH (pm)’

Fig. 2.18 Attenuation rate of optical power in a low-10SS optical fiber as a function of wave-length. The arrows along the abscissa in-dicate the wavelengths of commerciallyavailable lasers.

loss, single mode fiber. The arrows along the lowerabscissa correspond to the wavelengths of currentlyavailable lasers. The peak in the loss curve at the1.4-micron wavelength is due to the OH- radical, whichhas been reduced to a relatively low concentrationlevel. The minimum at approximately the 1.3 micronwavelength is of special interest, not only because theattenuation rate is down to 0.5 dB/km, but also becausethis wavelength is very close to the zero-dispersionwavelength of Si02 which is of special interest in someapplications, as will be discussed shortly. Fig. 2.18shows that extremely low attenuation rates attainablewith current fiber fabrication techniques at wave-

lengths where high intensity long-life, solid statelaser sources are becoming commercially available. Itis now up to the fiber user to devise techniques andconfigurations that can maintain this low loss by notintroducing significant regular (macro) bending andmicrobending losses.

A ray picture of the regular (constant) bendradius loss mechanfsm is shown in Fig. 2.19. Assume aray is traveling to the right at an angle of o lessthan the critical angle ec in the straight fiber sec-

2-

bend radius, all of the solutionsrepresent waves that decay withalong the centerline of the core.

of the wave equationincreasing distance

/\

6

//

6< 9.

e’ 70,

Fig. 2.19 Leakage of optical power froman opticalfiber at a constant-radius bend.

tion. In the bent region, the ray intersects the core-cladding interface at an angle 13 that is greater than‘dC and thus it will be partially transmitted out of thecore and into the cladding. This will occur at eachsuccessive reflection from the outer interface and largelosses may occur. Another qualitative explanation ofthis type of loss is as follows. In the beam propagat-ing in the fiber, assuming plane wavefronts, if thevelocity at the center of the core in the bent sectionwere equal to the c/nl, the “proper” velocity in thecore, then the velocity at the outer edge of the frontwould have to be higher than c/nl, which cannot occur.Radiation in the form of core-to-cladding scatteringresults. Finally, from the electromagnetic wave theoryit may be shown that in a waveguide with a constant

Using the latter approach it is possible tocompute the expected loss due to a constant bend radius.The results of such calculations are shown in Fig. 2.20,where loss curves versus bend radius are shown forsinglemode fibers at the 0.83-micron wavelength havingdifferent numerical aperture (N.A.). Note the strongdependence on bend radius and N.A. Referring to Fig.2.20, consider a fiber with a numerical aperture of0.1. When a 10-meter length is wound on a l.2-cm-radius mandrel, the attenuation due to bending is ap-proximately 6 dB, i.e., 75 percent of the light energyinjected into the core at the input end is scatteredout of the core while propagating in the ten metersto the output end. Nhen 10 meters of identical fiberare wound on a 1.0 cm radius mandrel, the attenuationdue to bending will increase by a factor of about250,000 to 60 dB, so that only about one millionth ofthe original light remains at the end of the fiber.Just about all of the input light is scattered out ofthe core. On the other hand, using the 1.2 cm radiusmandrel and increasing the numerical aperture (N.A.)to 0.12 reduces these attenuations to 0.16 dB and 1.6dB, respectively. Therefore, care must be taken indesigning fiberoptic sensors that require bending andwinding of fibers and in specifying fibers for suchapplications.

9

-2 3 4 5 6 7 8 9 10 11 12

BEND RADIUS (mm)

Fig. 2.20 The variation of optical power attenuationrate as a function of bend radius for con-stant radius bends in typical optical fibersfor various values of constant numericalapertures (N.A.) using 0.83-micron wave-length light.

C.H. Bulmer, private communication.

The effect of a microbend on ray propagationin an optical fiber is shown in Fig. 2.21. A ray pro-

+==2si-Fig. 2.21 The angle between an incident ray and the

core-cladding interface surface exceeds thecritical angle and therefore total internalreflection does not occur at the microbend,allowing part of the ray to leave the coreand enter the cladding.

pagating in the core at less than the critical angleis totally reflected before it reaches a section offiber distorted by a small imperfection. On successivereflections from the core-cladding interface it is in-cident at an angle with the interface surface largerthan the critical angle so that some light is transmit-ted into the cladding. Random distortions such as this,due to imperfections in the core-cladding interface ordue to bending or tensile forces exerted at scatteredpoints along the interface surface of the fiber can in-duce microbends in the core surface that lead to sub-stantial cumulative losses. Such distortion losses areusually undesirable and detrimental, for example, whenthey arise in fiber cabling operations. on the otherhand, microbending is employed in fiberoptic sensorsas a transduction mechanism, as will be discussed later.

2-1

The optical fiber property to be consideredlast is velocity dispersion, i.e. , differences in velo-city among various portions of the light that may bepropagated in the core of a particular fiber. It willbe shown later how dispersion directly affects the be-havior of specific fiberoptic sensors. For now, thesignificance of dispersion will be illustrated in termsof how it affects pulse broadening and thus limitsbandwidth in fiberoptic data links and other communica-tion applications.

In the introduction to this chapter, it waspointed out that one of the aims of the optical-fiberdesigner is to design a fiber that will preserve theinformation impressed on a beam of light as it propa-gates through its core. A measure of success in thisregard, as pointed out in the discussion of Fig. 2.2,Subsection 2.1.1, is how well the width of an indivi-dual narrow pulse is maintained without broadening.When a light pulse is injected into a step-index multi-mode fiber, its energy is divided among several differ-ent modes. Each mode travels at a particular velocity,or range of velocities, and thua they may arrive at theoutput end of the fiber at different times depending ontheir velocity and the length of the path they take.Obviously this contributes to pulse broadening and, infact, this modal dispersion is the major source of pulsebroadening in step-index multimode fibers. This typeof dispersion is reduced substantially in graded-indexmultimode fibers in which the various modal propa-gation times are nearly equal to one another and thusthe various portions of an injected pulse arrive at theend of the fiber at the same time though their propaga-tion velocities and paths will differ. In this case,however, the next lower level of pulse broadening ef-fects becomes evident. This is the so-called materialor chromatic dispersion that occurs because the velo-city of an electromagnetic (light) wave is usually afunction of the wavelength in dielectric material. Ifan optical source emits a pulse of other than purelymonochromatic (single-wavelength) radiation, the vari-ous wavelengths preaent will propagate at differentvelocities and thus lead to pulse broadening.

The effects of modal and material dispersionare shown in Fig. 2.22 where the theoretically-predict-ed dipersion or pulse broadening, expressed in nano-seconds increase of pulse width for each kilometer oftravel in a fiber, is plotted as a function of numeri-cal aperture (N.A.) for various operating conditions.Two types of 0.85 micron nominal wavelength opticalsources are considered. One is an injection laser emit-ting light with a apectral width (linewidth or varia-tion of wavelength) of 20 Angstroms. The other is alight emitting diode (LED) emitting light with a spec-tral width (linewidth) of 350 Angstroms. When narrowpulses of light are injected into either graded-indexor step-index fibers, Fig. 2.22 shows that for lasersources and for numerical apertures less than 0.15, thepredicted broadening is only 0.2 nsec/km for the grad-ed-index fiber, however, the dispersion is more than 10nsecfkm for the step-index fiber. This increase is dueto modal diaperaion, because increasing N.A. corres-ponds to increasing the waveguide V-parameter so thatadditional optical modes are allowed. Initially at lowN.A. values with the light emitting diode, material dis-persion leads to a broadening of approximately 5 nsecper km in commercially available step-index and grad-ed-index fibers,further increasesvalues.

and then modal dispersion leads toin step-index fibers at higher N.A.

o

60

40

20

10.C

~8x

z 6nu 4%c

62muu$ 1.0

00.806

04

02

0.1

AO = 0.85 pm

LED S1 FIBERPRACTICAL LED

/

PRACTICAL LASERGI FIBER

\

I 1 I I I I I I I II I I I I 1 I I I I I I I I I I I

o 0.05 0.10 0.15 0.20 0.25 0.28

NUMERICAL APERTURE

Fig. 2.22 The variation of dispersion in nanosecondsper kilometer as a function of numericalaperture (N. A. ) for step-index (S1) andgraded-index (GI) optical fibers driven bylaser or LED optical sources.

After C. Keo and J. Goell, Electronics, 113, Sept.16, 1976.

The above results also can be expressed interms of the bandwidth of the modulation signals thatmay be transmitted by fibers. The bandwidth capacities(bandwidth-length product) currently attainable withvarious types of available fibers are summarized asfollows:

Modal-dispersion-limited behavior:Step-index fibers: 30 MHz-kmGraded-index fibers

Research grade 1000 MHz-kmProduction grade 400 MHz-km

Material-dispersion-limited behavior:Graded-index fibers (0.85 Urn):

LED (350 ~ spectral ~idth) 150 MHz-kmInjection laser (20 A) 2500 MHz-km

The capacities are expressed as the productof the highest modulating frequency in megahertz thatcan be applied (without excess decay) multiplied by thefiber length in kilometers. Thua, using high qualitygraded-index multimode fibers, it is now possible tosend signals with frequency components in excesa of 1GHz over fiber lengths approaching 1 km, or in excessof 5 GHz over fiber lengths approximately 200 m, andso on.

In singlemode fibera, material or chromaticdispersion IS a significant factor. In silicon oxide(si02), the main constituent of the core and claddingof most high-grade glass fibers, the curve of the re-fractive index as a function of the optical wavelengthhas a minimum point at approximately 1.3 microns as

2-

shown in Fig. 2.18. There are two other types of dis-persion effects that usually occur when singlemode fi-bers are employed. The first of these is called wave-guide dispersion which results from the variation inthe propagation constant, B, or wave velocity (phasevelocity), clneff, with changes in the V-parameters,and thus the wavelength, 1. This was considered earl-ier in the discussion of Fig. 2.11, but for the presentdiscussion, it is useful to present the same informa-tion in another form as follows.

In Fig. 2.23, typical curves of the opticalangular frequency, w, are plotted as functions of thepropagation constant, 6, for a few of the lower-orderallowed modes in a fiber waveguide. This graph shows

cln~

RADIATIONMODE

REGION

- - - -

~ ‘MODE ~

PROPAGATION CONSTANT B

Fig. 2.23 The optical angular frequency, u, as ation of the propagation constant, B, for afew low-order modes for lightwaves propa-gating in typical optical fiber, showingthe phase and group velocities.

the difference between the phase velocity of a single-frequency continuous optical beam and the group velo-city of an optical pulse. The wave velocity (phasevelocity) is defined by the values of the ratio u/fi forany point on the curves for the allowed modes. Thesecurves terminate on the straight lines that define theplane wave phase velocity in the core and claddingi.e., cfnl and c/n2, respectively.

A narrow impulse of light, by its very nature,consists of a band of modulating frequencies and thenarrower the pulse, the broader is its modulating fre-quency spectrum. Light at a wavelength of 1 micron ina vacuum has a frequency of 3 x 1014 Hz. If it is pulse-modulated to produce impulaes 0.1 nsec wide, theirbandwidth would exceed 10 GHz (Actually 20 GHz if theNyquist criterion is applied). The velocity of propa-gation of such a pulse would be defined as the velocityof the maximum of its envelope, referred to as thegroup velocity, Vg, which can be shown to be equal tothe slope d~ld~ of the modal curves in Fig. 2.23.Since the individual frequencies, or wavelengths, mak-ing up the pulse propagate at different velocities thepulse tends to broaden and this is the source of thewaveguide dispersion.

Another type of dispersion or velocity varia-tion that may affect propagation in singlemode fibersis referred to as polarization dispersion. It has notbeen emphasized up to this point, but in fact opticalfibers operating in a so-called singlemode are in factat least bimodal. This is due to birefringence, or

11

azimuthal dependence of the refractive index, i.e.,variations of the optical wave velocity, with changesin the direction of the radial component of the elec-tric field vector. 7!his will be discussed in more de-tail later. The concepts are mentioned at this pointbecause birefringence can be a source of pulse broaden-ing and related effects in singlemode fiber due torandomly-induced transitions between different polari-zation atates.

In cloaing this section on the various pro-perties of optical fibers, it is appropriate to comparesome of the propagation characteristics of optical fi-bers with thoae of more conventional waveguide communi-cation links. This is done in graphical form in Fig.2.24. Three curves are shown that represent the atten-uation of radio frequency (RF) signals with bandwidthsin the frequency range from 1 MHz to 1 GHz for variouswidely-uaed coaxial cablea. Also shown ia the range ofattenuation rates currently obtained for lightwaves,propagating in high quality fibers, that are modulatedby signala over the same frequency range. For modula-tion frequencies above a few megahertz, optical fiberaare far auperior to even the largeat diameter (> 2 cm)RG/u219 coaxial cable. Signals with a bandwidth up to1 GHz may be propagated up to fifty kilometers in high-quality fibera without using repeaters (signal proces-sors).

2.2 OPTICAL FIBER FABRICATION

It was indicated in Section 2.1, and shown inFig. 2.1, that many fibera consist of a core of refrac-tive index nl; a cylindrical cladding layer of alightlylower refractive index n2 surrounding the core, and anouter layer that serves as a protective jacket. It was

1000

500

5321

12 5 10 20 50 100200 5001000MODULATION BANDWIDTH (MHz)+

Fig. 2.24 The variation of attenuation rate as afunction of modulation bandwidth for sever-al coaxial cables and a fiberoptic cable.

T. Giallorenzi, Proc. IEEE ~, 744 (1978).

alao shown that important parameters of optical fibe~a

~:~)f~~, ~;~rical aperture (N.A.), equal tO (nl -is, the sine of one-half of the apex

angle of the cone of light that can be injected andtrapped in the core of the fiber; the radius of thecore, which together with the numerical aperture, deter-mine the modal atructure of the electromagnetic wavesthat may propagate in the core; the attenuation coeffi-

2-1

cient that determines the rate of the exponentialdecay of the core light intensity with increasing dis-tance of travel within the core; the dispersion (pulsebroadening) that depends on the differences betweenthe propagation velocities of the various allowed modesand the variation of the modal velocities with opticalwavelength; and finally the strength of the fiber thatdepends on how free from scratches and other imper-fections the outer surface of the cladding is immedi-ately after drawing, and on how well the cladding sur-face is protected during spooling, cabling, and use.

This brief listing of some of the importantparameters of optical fibera emphasizes the need forprecise control of the refractive indices of the coreand cladding.

2.2.1 Refractive Index Profile Control

There are several techniques being uaed byoptical fiber manufacturer for maintaining preciae con-trol of refractive index profiles and refractive indexdifferences.

A step-index fiber with a cladding of puresilica (ailicon oxide, Si02) that has a refractive indexof 1.458 for a lightwave of wavelength of 0.83 ~m andthat has a core of refractive index 1.461, has a numer-ical aperture of 0.10 as ahown in the following table:

DEPENDENCE OF NUNERICAL APERTURE ON CORE INDEXSILICA CLADDING n2 = 1.458 (0.83pm)

N.A. = (n12 - n22)1/2

N.A.1 .:*1 0.101.464 0.141.469 0.181.472 0.20

When the refractive index of the core is increased to1.472, and the cladding index remains at 1.458, thenumerical aperture increasea from 0.10 to 0.20 and thuschanges the critical acceptance cone apex angle from11.5” to 23.0”. From the above table it may be seenthat the refractive index of the core must be control-led to about one part in a thousand to obtain a desiredN.A. and hence an appropriate acceptance angle to wfth-in a few degrees.

The desired refractive index of the core isusually obtained by adding varioua typea of otherglasaea or dopants, to the pure silica. For example,suppose that germanium oxide (Ge02) iS added to thesilicon oxide (Si02). The addition of Ge02 to Si02increases the refractive index of the mixture as ahownin Fig. 2.25a. The addition of 10 percent, by molec-ular content, of Ge02 to pure Si02, increases the re-fractive index from 1.468 to approximately 1.471.

Si02 and Ge02 form glaasy (vitreoua) mater-ials. They have microscopic molecular structures inwhich the moleculea are somewhat randomly distributedand disoriented rather than arranged in highly-orderedcrystalline-type lattices. They have indefinite solid-ification temperaturea and behave aa liquida that haveextremely high viscosities. Thus, under ordinary con-ditions, glaas fiber may be considered as consisting ofsuper-cooled liquida. The core glaas, as diacussedabove, may be considered as a mixture of two supercool-ed liquids, Si02 and Ge02. Their molecular density andthermal expansion coefficient are so closely matchedthat in the mixed state their combined structure is re-

2

: 1.5

v

GeOzz

o 0=1.49 ~u w~1.48

>1-

0 v:1.47 aL E:1.46 u

u,4, ~

10

(a) DoPANT CONCENTRATION(MOLE PERCENT)

x

P*051.49 r

1.48

1.47

1.46K

1.45 ~10 20 30

(b) DOPANT CONCENTRATION(MOLE PERCENT)

<fu 5 10 15K

(c) DOPANT CONCENTRATION(MOLE PERCENT)

Fig. 2.25 The variation of the refractive index ofsilica glass (Si02) as a function of theconcentration of various dopants.

latively strong and free of localized stresses. Theaddition of phosphorus pentoxide (P205) to pure silicaglass (Si02) also brings about an increase in refrac-tive index as shown in Fig. 2.25b. Thus, P205 is fre-quently employed as a core dopant. On the other hand,the addition of boron trioxide (B203) to pure silica(S102) produces a decrease in the refractive index asshown in Fig. 2.25c. Thus, B203 is employed as a dopantfor cladding glass. The addition of dopants to puresilica, and to other glasses that are used to make op-tical fibers, yields the refractive indices requiredfor the core and cladding, to produce fibers with par-ticular numerical apertures.

Large numerical apertures allow light fromwide entrance angles (large acceptance angles) to beaccepted into the fiber cores and still maintain totalinternal reflection. It was indicated in Section 2.1that bending losses are lower in fibers of higher N.A. ,so that when it is necessary to wrap fibers on smallmandrels, in order to make fiberoptic sensors, it againappears to be desirable to employ fibers with as highan N.A. as is possible. Unfortunately, the additionof dopants to either the core or the cladding causes anincrease in the oDtical attenuation, as shown in Fig.

The attenuation versus

.3 EK’RADIUS (mm,

EFFECT OFFENDING

bend “radius curves that

(b)

NIJ$.4ERICAL WE RT”RE

EFFECT OF COMPOSITION

.26 The variation of attenuation in silicaFig. 2.glass (Si02) optical fibers as a functionof ordinary bend radius, numerical aperture(N.A.), and type of dopant at a wavelengthof 0.83 pm.

C. H. Bulmer. private communication.

2-1

were shown as Fig. 2.12 in Section 2.1 are shown againin Fig 2.26 together with data that shows the increasein attenuation observed in fibers with various N.A.lS,obtained by adding dopants to the Si02 in the core orcladding. Dopant concentration high enough to producenumerical apertures of 0.2 or greater cause scatteringand absorption leases in exceas of 10 dB/km, which isthe theoretically predicted bending loss for an 0.2 N.A.fiber wound on a 3 mm radius mandrel. Thus in this re-spect, it may be necessary for the fiber designer anduser to optimize the dopant concentration of fibersspecified for a particular application.

2.2.2 Fiber Fabrication Processes

Several different methods are being used toproduce fibers with particular dopant conce~trationa,gradients, and refractive-index profiles throughout thecore and cladding.

2.2.2.1 The Double-Crucible Process

The most direct method is the double-crucibleproceas. The construction of the furnace portion of adouble-crucible system ia shown in Fig 2.27. The core

cOREF=:G-n l-cMDD’NG FEED RODR

CLADDING GLASS

INNER CRUCIBLE IBLE

L~ TO FiBER DRAWINGMACHINE WINDING DRUM

Fig. 2.27 The double-crucible process for opticalfiber fabrication.

glass is contained in the inner crucible, usually madeof platinum, while the cladding glass is in the outercrucible , which is actually a cylindrical shell thatsurrounds the inner crucible. The two glasses areheated in such a way that they begin to flow out of theorifices at the bottom of the two crucibles as veryhighly ViSCOUS liquids. They then are cooled rapidlyto below the solidification temperature almost immedi-ately after they are combined in the region below theorifices. The resulting fiber is drawn under control-led tension so that its outer diameter is held nearlyconstant. As the fiber is drawn, the glass in the twocrucibles may be maintained at a conatant level byslowly feeding rods of core and cladding-type glassescontinuously into the two crucibles.

A simplified overall view of a double-cruciblefiber drawing system is shown in Fig. 2.28. As thefiber is drawn from the bottom of the furnace it passesthrough a non-contacting thickness gage and a feedbacksystem that controla the rate of rotation of the take-UP drum to maintain a constant outer diameter of thecladding. The fiber then passes through a pool of thejacketing material (or materials) that coats the out-side of the cladding. The fiber is then dried, cured,and wound continuously on to the take-up drum.

3

n

+

FURNACE—

PREFORM —

THICKNESS GAGE— - - -

JACKETING UNIT zP

II

DRYING FURNACE —-----r!l I I+

6)TAKEUP DRUM -~> ‘

Fig. 2.28 The double-crucible optical fiber drawingsystem.

In principle, the double-crucible process hasthe advantage that it may be used to draw continuousfibers of any desired length. Unfortunately, becausethe core and cladding glasses must be contained andheated within the crucibles, it is difficult to main-tain the very high purity levels required to yield thevery low-loss fibers.

A much different procedure for producing ex-tremely low-losa fibers was developed during the earlyand middle 1970’a. Though several variations of thesame approach are being used by manufacturer, theyall are based on the production of glass fiber using avapor-phase oxidation (VPO) process.

2.2.2.2 The Inside Vapor-Phase Oxidation (IVPO)Process

The inside vapor-phase oxidation process(IVPO) is shown in Fig. 2.29. Vapors of various metal

SILICA BAIT TUBE

GeC14

Q

Fig. 2.29

SiCl4

J.

‘+== BURNER

H2+02TORCH

MIXING MANIFOLDAND FLOW

r

CONTROLLER 1

i)He

The vapor-phase oxidation (VPO) process forproducing optical fiber preforms.

halides are mixed with oxygen and helium to desiredhighly-controlled concentration levels and fed into ahollow silica cylinder (bait tube). The chlorides ofsilicon and germanium exist as liquids at atmosphericpressure and room temperature, while those of phospho-rus and boron must be stored under high pressure, as

2-1

shown in Fig. 2.29. In each case, the halides are in-troduced into the mixing manifold by means of a vapordistillation process. For example, high purity oxygenmay be bubbled through the liquid silicon tetrachloride(SiC14)”and germanium tetrachloride (GeC14). This pro-cess reduces the level of impurities in the halidevapors that are fed into the reaction tube. Heat isapplied to the outside of the tube using a movablehydrogen-oxygen torch. This leads to oxidation of themetal halides, yielding a precipitate of very fineglass particles (soot) that builds up on the walls ofthe bait tube.

The tube is mounted in a glass-working latheand continuously rotated during the oxidation processso that the precipitate deposits uniformly around theinner circumference of the tube, as shown in Fig. 2.30.

/ BAIT TUBE

REACTANTS_ SOOT FORMATION_

(METAL HALIDES+ 02) :)EXHAUST

u’

SINTERED GLASS SOOT DEPOSIT

TRAVERSINiG BURNER

Fig. 2.30 The inside vapor-phase oxidation (IVPO)process for producing optical fibers.

After P. Schultz, Appl. Opt. Q, 3684 (1979)

The traversing burner not only provides the heat re-quired to oxidize the various metal halide vapors butalso transforms the porous soot deposit into thinsintered glass layers that are built up as the burnerslowly traverses back and forth along the length of thebait tube. By controlling the concentration of thevarious reactants fed into the bait tube it ia possibleto build up layers of Si02 glass with any desired levelof doping. These will eventually form the cladding andthe core of fibers that may be drawn from the resultingglass boule (preform) that is produced in this process.

Several other steps are carried out beforethe tube is ready for fiber drawing. These are showin Fig. 2.31. After the cladding and core glasses aredepoaited, the tube is heated so that under surface

SUSSTRATETUBE

CLADDINGDEPOSITED

COREDEPOSITED

COLLAPSEDPREFORM

Fig. 2.31

c1 Q+,- d FIBER DRAWING

I

@

/

‘1 ~ÿÿÿÿÿÿÿÿÿÿÿ/; SUBSTRATE REMOVED

gjjj/p”FIBER DRAWING

1// THIN LAYER DEPOSITED‘, //oc’? (3”—u FIBER ORAWING

Stages in the processing of preforms inproduction of optical fibers.

the

4

tension it collapses to eliminate the remaining centerhole. In order to obtain various desired physical pro-perties, fibers can be drawn either without removingthe substrate tube, after removing the substrate tube,or after a final layer of glass haa been deposited onthe outside of the collapsed preform, as shown in Fig.2.31.

In the drawing process, the boule is placedin an induction furnace and fibers are drawn and coatedin almost exactly the same manner as in the double-cru-cible technique that was shown in Fig. 2.28.

2.2.2.3 The Outside Vapor-Phase Oxidation (OVPO)Process

Preforms also are made by precipitating sooton the outside of a rod that is turned in a glaas-work-ing lathe, as shown in Fig. 2.32a. In the outside vapor

(a) SOOT DEPOSITION

g“’+ww’””’

4—.—...o:,::.#.:~C:DING

>0 INDEX n

(b) PREFORM SISTERING (c) FISER DRAWING

Fig. 2.32 The outside vapor-phase oxidation (OVPO)process for producing optical fibers.

After P. Schultz, Appl. Opt. l&, 3684 (1979).

phase oxidation (OVPO) process, the core material isdeposited first and then the cladding is deposited onthe outside, just in the IVPO process described earlier.The amount of doping may be continuously varied duringthe core material deposition process. It is thus poa-sible to produce preforms for graded-index fibers, aswell as for step-index fibers, as shown in the exampleof refractive index versus radial displacement curve atthe extreme upper right in Fig. 2.32. The refractiveindex of the porous material deposited on the centerbait rod decreases monotonically out to what will cor-respond to the core-cladding interface, and then itremains constant to the outer surface of the porouscylindrical shell.

Thus, preform fabrication by the OVPO processis a multistage procedure, including center bait rodremoval, followed by porous preform sintering and thecollapsing of the central hole, either prior to or dur-ing the fiber drawing process. Aa in the IVPO process,the deposition process is carried out on a glass-work-ing lathe. Thus, the preforms produced by both proces-ses have a limited size so that usually fiber lengthsfrom 10 to 20 kilometers may be drawn from a singlepreform.

2.2.2.4 The Vapor Axial Deposition (VAD) Process

Length limitations are overcome in the vaporaxial deposition (VAD) process that is ahown in Fig.2.33. Core and cladding glass particles ejected fromoxygen-hydrogen burners are deposited longitudinallyand radially on to the end of a silica rod. By care-fully controlling the concentration of the metal halides

2-1

fed to the burners, a porous preform with the desiredradial variation of refractive index is built up, be-ginning at the end of the silica rod. The rod is slowlypulled vertically upward as deposition continues at aconstant rate at the lower end of the porous preform.The porous section then passes through a concentricheater ring that collapses and sinters the porous sec-tion to form a clear glass rod with the desired radialrefractive index profile. The entire process is car-ried out inaide a reaction chamber with a carefully con-trolled inert atmosphere to reduce the level of impuri-ties. The VAD process permits the production of largepreforms capable of yielding single pieces of fiberover 100 km long. The optical quality of current VADfibers is very high. Data on attenuation rates versuswavelength for VAD and IVPO fibers is shown in Fig.2.34. The IVPO process produces a fiber with a rela-tively large attenuation rates peak at 1.4 pm and small-er peaks in the vicinity of 1.23 pm and 0.94 Um. Theseare due to the vibrational mode absorption lines of theOH- radical. In the VAD process, the OH- radical con-tamination is reduced substantially by careful dryingduring the preform fabrication process thus eliminatingthese attenuation peaks.

-..

}!(’ ;=> STARTING SILICA ROD

T

f--lI I TRANSPARENT PREFORM

$!!$. -— -.-- CARBONHEATER.,.. .,,,,,,.,,,‘..-=-, =..

1’ Il..

t POROIJS PREFORMI :+ I,.. I

& ~~•

% ~%-.+’

‘\FINE GLASS PARTICLES

QOxy-HyDROGEN BURNERSSiC14+BBr3

SiC14+GeC14+PC13

Fig. 2.33 The vapor axial deposition (VAD) processfor producing optical fibers.

After P. Schultz, Appl. Opt. l&, 3684 (19791

0.8 1.0 12 1,4 1.6 1.8

WAVELENGTH (pm)Fig. 2.34 The variation of attenuation as a function

of wavelength in optical fibers produced bythe vapor axial deposition (VAD) and theinside vapor-phase oxidation (IVPO) proces-ses.

5

2.2.3 Fiber Strength

The operational and shelf-life of fiberopticsensors will depend to a large extent on the mechanicalstrength of the glass fibers used in them. In a cer-tain way, glass fiber is much atronger than steel.Short, pristine silica fibers, immediately after draw-ing, have elastic limits, and ultimate and breakingtensile strengths, greatly exceeding that of steelwires. Stress-strain curves for priatine silica fiberand steel wire are shown in Fig. 2.35. The elaatic

10’0

- 109“E~

$ 108wu

G107

106

FIBER

WIRE

10–4 10–3 10–2 10–’ 10°STRAIN

Fig. 2.35 Stresa versus strain curves for steel wireand pristine silica (Si02) fiber under idealconditions.

limit of steel typically uaed in wire is about 0.2 x10-9 Newtons/m2 at a atress of about 0.1 percent. Steelwires tend to break at strains of the order 0.5 percentand a stress of about 1.5x109 N/m2. On the other hand,unscratched fibers remain elastic to strains in excessof 10 percent, corresponding to stresses of about 5 x109 Newtona per square meter. However, unlike steel,which may be made malleable and capable of flow-healingsmall surface cracks, glass is brittle. Thus, very finecracks in glass fibers tend to become stress concentra-tion centers that propagate transversely across the fi-ber. They lead to exceasive strain and ultimately tocomplete rupture.

A length of fiber is only as strong as itsweakest section. Under constant tension a length offiber will tend to break at its weakest point. Thebreak will most likely occur where there is a scratchon the outer surface of the fiber. A long length offiber ia more likely to have a weakest point that isweaker than the weakest point of a short length offiber. Thus, fiber strength determination is a procesaof collecting statistics of failure. This is illus-trated by the reaults of a seriea of tests performed ona group of test samples, each 60 cm long, cut from sec-tions distributed uniformly along a 1 km length of fi-ber. Each sample was streased to rupture in a tensiontest machine. The percentages of the total number ofspecimens that failed below a given stress level areshown as a function of the breaking stress in Fig. 2.36.

2-

Fig.

1 I I 1 ! , ( ! , , ,

99 - *# .:

./”””80 -

./”60 -

~ 40 - /um3~ 20 GAGE LENGTH= 60cm

if

8 -

4

1 , I I , [

0.5 0.8 10 2.0 3.0 4.0TENSILE STRENGTH (GN/m2)

2.36 The percentage of optical fiber specimenathat failed as a function of breaking ten-aile strength.

From the graph it may be seen that the first apecimenbroke at approximately 0.5 x 109 N/m2, approximate 10

Jpercent of the specimens broke at 0.8 x 109 N/m orleas another 10% broke at atresses between 0.8 and 1.0

4x 10 N/m2, and so forth. A few of the s eclmens, how-ever, %withstood stresses of 4.0 x 109 N/m before break-ing.

From a practical, application-oriented view-point, it is the weakest point in a length of fiberthat determines ita overall strength. Thus, in spec-ifying fibers for a given application, the maximumstreas or strain to be encountered ahould be determinedand the entire length of fiber to be employed shouldbe pre-tested at some acceptable safety margin abovethis level. Such testing is usually done by reelingthe fiber from one spool to another at a fixed rate,while maintaining the interreel section under the fixedspecified stress (tension).

There is evidence that preform preparationand treatment, as well aa the manner in which fibersare handled after they are drawn, contribute substan-tially to their overall atrength. Data on the breakingor tensile strength of a particular type of fiber drawnfrom identically produced preforms is shown in the bar-graph in Fig. 2.37. In the upper portion of Fig. 2.37,the number of specimens versus breaking strength iaplotted for 40 specimens taken from a length of fiberdrawn from an ordinarily prepared preform that washeated as usual in an RF induction furnace. As indi-cated, the breaking strengths ranged from approximately0.50 x 109 N/m2 to 5.5 N/m2 with a maximumof 12 speci-

4mena that broke at 3.0 x 10 N/m2. Results are presentedin the center aection of Fig. 2.37 on 46 specimens froma length of fiber drawn, using the RF induction fur-nace, from a preform that had been fire-polished priorto drawing in an effort to eliminate any fine cracks(microcracks) and other imperfections that might haveexisted in its outer surface. In this caae, the firstspecimen to break withstood stresses up to 1.8 x 109N/m2 and 36 of the specimens broke at a stress exceed-ing 3.8 x 102 N/m2. In the third case, as ahown in thelower portion of Fig. 2.37, 42 specimens were testedfrom a fiber that waa drawn using an infrared laser toheat the preform, that also had been fire polishedprior to drawing. All of the specimens withstood ten-sile atresses up to 4.0 x 109 N/m2 before breaking.However, instead of being distributed over a very widerange of breaking tensile strengths, the breaking pointswere all in the range from 4.0 to 5.25 x 109 N/m2.

16

NO FIRE POLISHN = 40

:

FURNACE FIRE POLISH ~N = 46 ;

bm

LASER FIRE POLISH :N = 42 ~

z

MAXIMUM TENSILE STRENGTH (GN/m2 = log N/m2)

10

5

:L_.—dJuo 200 400 600 800 1,000

MAXIMUM TENSILE STRESS (KPSI)

Fig. 2.37 The variation of maximum tension stress ofa number of optical fibers for unpolished,furnace polished, and laser polished fibersshowing the number of fibers that failed atthe various stress levels in total testedfor each polishing condition.

These results clearly indicate how important it ia tocarefully prepare the preforms and to accurately controlthe drawing process in order to maintain the strengthof the final drawn fibers and thus get as cloae as pos-sible to the ideal strength of silica glass.

2.3 SOLID STATE FIBEROPTIC LIGHT SOURCES

Solid state optical sources and detectorsutilized in compact fiberoptic sensors will be discus-sed in this section. This information will serve as abackground for understanding later discusaiona of sen-sor noise and packaging. In order to understand thetrade-offs required, a knowledge of light productionmechanisms and fabrication processes is helpful.Finally, such information is important for estimatingwhat is likely to be available in the future.

2.3.1 Energy Levels In Semiconductors

Electrons in free atoms are normally tightlybound in discrete energy levels. When the atoms arelocated in a crystalline structure these discreteenergy levels are replaced by energy bands. Some ofthe electrons remain tightly bound to the atom whileother, more energetic electrons, have energies corres-ponding to the valence or conduction bands. Those inthe valence band are atill localized at individual atomsbut have the highest energy of such bound electrons,while electrons in the conduction band are free to movethroughout the crystal. Materials can be divided intoa number of classes depending on the energy gap (separ-ation between the top energy level of the valence andthe bottom energy level of the conduction band) andupon the number of electrons, if any, in the conductionband and lack of electrons in the valence band as shownin Fig. 2.38. Electrons cannot possess energies thatlie in the gap.

In an insulator the valence and conductionenergy bands are separated by a wide energy gap. Ifthe gaps in Fig. 2.38 were drawn to scale, the gapbetween the valence and conduction bands of the insu-lator would be much wider than that of the other mater-ials. The conduction band in insulators is normallydevoid of electrons while the valence band is filled.Therefore, when an electric field is applied across

2-1

INSULATOR CONDUCTOR

1~

; ~z”NDucT’oN’’NE~KLu BAND-GAP EG

—6

VALENCE BAND— —

P-TYPE SEMICONDUCTOR N-TYPE SEMICONDUCTOR

I 1 I 1I 1 DONOR LEVEL I a. a. * a. I

ACCEPTOR LEVEL

Fig . 2.38 Energy band diagrams in which the cross-hatching symbolizes that there are manyelectrons in the various energy bands forvarious types of materials.

the insulator, no current flows. If sufficiently hightemperatures are applied (thousands of degrees) it ispossible to excite some of the electrons with valenceband energies up to the energy level of the conductionband. At such an elevated temperature, insulators be-come conductors with conduct ivities that increase withtemperature. Electrical conductors, such as metals,consist of materials in which electrons fill the val-ence band and about half the conduction band. In thiscase when an electric field is applied the electronamove through the crystal easily and the material isreferred to as a conductor. In metals an increaae intemperature increases lattice vibrations and electronscattering, therefore the conductivity decreases withincreasing temperature. Materials with properties be-tween insulators and conductors are known as semicon-ductors. Semiconductors are similar to insulators inthat the valence band is filled and the conduction bandis empty. However, the energy gap separating the con-duction and valence bands is much smaller than that ofinsulators. For such semiconductors, thermal energycan excite a few electrons from the valence to the con-duction band. Such materials are known as intrinaicsemiconductors. Their conductivity increases with in-creasing temperature. By doping these materials withcertain impurities, it is possible to greatly increasethe number of carriers and increase the conductivity.If the dopant has carriers with an energy level thatlies in the band gap just slightly below the conductionband, then thermal motions can readily excite electronafrom these impurities (or dopants) into the conductionband where they are free to move through the crystalcausing the material to become more conductive. Suchdopants are known as donors and the resultant materialsare known as negative or n-type semiconductors due tothe fact that the carriers are electrons. Galium arse-nide (GaAs) crystalline materials are important as room-temperature light-emitting diodes (LED’s) and diode (orinjection) lasers. In these materials, tin and tellur-ium serve as dopants that contribute (or donate) elec-trons to the conduction band while germanium (an accep-tor impurity) introduces trapping sites with energylevels slightly above the valence band in the band gapitself. In the case of an acceptor, thermal motionswill provide sufficient energy to permit electrons fromthe valence band to be trapped by an acceptor impurityatom. The holes left behind in the valence band actas positive conductors. These materials are known asp-type semiconductors.

An important semiconductor energy state is

7

shown in Fig. 2.39. This state is known as the popula-tion inversion state. It corresponds to the conditionin which holes exist in the valence band and electronsexist in the conduction band simultaneously. Thisleads to the production of photons. The energy gap isindicated by E in Fig. 2.39. When electrons from theconduction ban~ lose some of their energy and drop down

TCONDUCTION

BAND

+BAND-GAP,EG Q—Fc

hv

Fc= CONDUCTION SANOENERGY LEVEL

SPONTANEOUS: h.=EG

STIMULATED: tWCEFcPHOTONS AMPLIFY

THEMSELVES

FERMI

‘EFV

Fig. 2.39 Electrons (cross-hatch) from the valenceband are stimulated to the energy level ofthe conduction band in a population inver-sion situation. Their return to the valenceband causes the emission of photons.

into the valence band they recombine with holes andphotons are produced. This process is known as recom-bination. In the desired case, the energy is given upentirely in the form of photons. If this process oc-curs spontaneously, the energy of the emitted photoniS approximately equal to the band gap energy, Eg. Thephotons produced travel in random directions. On theother hand, if sufficient density of photons exist inthe recombination region both spontaneous emission (orrecombination) and stimulated recombination occur. Thestimulated photons that are produced travel in the samedirection as the primary photons. In the latter casethe photon energy is less than the difference betweenthe Fermi energy level in the conduction band, EFc, andthe Fermi level in the valence band, EFV. These condi-tions, spontaneous and stimulated emission, are neces-sary for the proper operation of light emitting diodes(LED’S) and diode lasers, respectively. In order tounderstand how LED’s or diode lasers can be producedand operate in practice, consider the condition at ap-n junction as shown in Fig. 2.40. In this case, GaAs

}

&1%zw

-CONDUCTION BAND

I1,,I

I

, 1 I

m

P N

4P-N JUNCTION

Fig. 2.40 The

1:~~energy levels in a p-n junction.

2-

is doped with an acceptor material on one side of thejunction, resulting in a p-type semiconductor region,and with a donor material on the other side, resultingin an n-type semiconductor region. The spatial separa-tion between the p- and n-type regions is known as thep-n junction. The electron energy levels in the con-duction and valence bands are as shown in the upperpart of Fig. 2.40. Notice that when a bias voltage isnot applied, as on the left, a population inversiondoes not occur. Electrons from the valence band of thep-type region flow into the conduction band of the n-type region until the electron energy levels on eachside of the p-n junction are equal, then essentially nomore electrons flow across the junction. The energylevel difference across the junction constitutes a bar-rier to further current flow. If a forward bias volt-age is applied, as shown on the right of Fig. 2.40,electrons are forced or injected into the n-type regionand holes are formed in the p-type region. When theenergy level of a sufficient number of electrons areraised to the energy level of the conduction band, theirelectron energy level exceeds the barrier energy andelectrons flow across the junction into the p-region.More detail is shown in Fig. 2.41. In the population

RECOMBINATIONl-REGlON*HOMOJuNcTlON

!

4, hvrFv

Lcc1,1

I .1 ‘ I ‘ I ~VG= EG/e

FORWARD BIAS

Fig. 2.41 The various regions and energy levels at aforward-biased p-n junction of a semicon-ductor diode.

inversion region, just on the left of the p-n junction,electrons can spontaneously recombine with holes pro-ducing photons. Since in this region there is a finitelifetime for the electrons depending upon the averagetime it takes for such recombination to occur (typical-ly 3 to 5 ns), the inversion region is restricted inspatial extent as shown in Fig. 2.41. In this case thejunction is known as a homojunction and under properconditions may be used to fabricate a homojunction LEDor diode laser.

Current density is directly proportional tothe thickness of the recombination layer. Therefore,in order to reduce the current it is important to re-duce the thickness of the recombination layer. This canbe accomplished in a gallium arsenide (GaAs) crystal bythe use of layers alloyed with varying amounts of alum-inum (Al). The substitution of aluminum (Al. ) for gal-lium (Ga) occurs with little or no distortion of thecrystal lattice. The energy gap plotted against thefraction of aluminum that replaces an equal fractionof gallium ( Ga) , forming gallium aluminum arsenide(GaAIAs) is shown in Fig. 2.42. For up to 37% Al sub-stituted for Ga, the energy gap increaaes from 1.43electron-volts to 1.92 electron-volts. This is approxi-

18

mately a 0.5 electron-volt increase. For fractionalparts of Al greater than 0.37, i.e., x > 0.37, mechan-isms in addition to simple photon production occur dur-ing recombination with the result that not all of theenergy goes into producing photons, part of it goes in-to thermal energy with the possibility of crystal dam-age and a reduced tendency for lasing. The wavelengthcan be obtained from the photon energy relation Et = hfand from the wavelength-frequency-velocity relation ~f== c/n, from which the relation 1 = hc/nEt is obtained,where h is Planck’s constant, c is the velocity of lightin a vacuum, n is the refractive index taken as unity,and Et is the energy lost by a particle. For a parti-cle with a charge of one electron that loses energyequal to the gap energy, A = 1.24/Eg, where h is thewavelength in microns and Eg is the gap energy in elec-tron-volts. Thus for GaAs, 1 = 0.90 micron and for 37%Al, 1 = 0.64 micron. Longer wavelength lasers (1.1micron to 1.6 micron) can be produced by using thequarternary alloy iridium-gallium-arsenic-phosphorous(InGaAsP).

‘“’~ “’:;’v:;:N:;GAp<’”’2ev

b:● FOR X>0.37COMPETING

9 /.~ ,- PROCESSES OCCUR MAKING

/-m2.Ou ...” ONSET OF LASING LESS..0” PROBABLE

n-a>0 AIXGal.XAs ● FOR X INCREASING FROM

%OT00.37 THE REFRACTIVE

z300”K INDEX DECREASES BY 5%

u.1 15

[1111111111o 0.5 1.0

GaAs x AIAs

Fig. 2.42 The band-gap energy level versus aluminumgalium arsenide composition (AIXGA(l-X)AS).

Another important effect is that as the frac-tional part of Al, x, increases from zero to 0.37 therefractive index decreases by 5%. Thus, as x in-creases, the energy gap increases and the refractiveindex decreases. The energy gap increases by almost30% and the refractive index by about 5%.

The energy band structure for a crystal inwhich a higher concentration of aluminum in two regionssandwich a third region of lower aluminum content be-tween them is shown in Fig. 2.43. The correspondingcrystal structure can be formed by a number of proces-ses one of which is the liquid-phase epitaxial growthprocess. Epitaxial growth is the growth of a crystalfrom the surface. For the case of interest the follow-ing is a highly simplified description. The processbegins with a crystal of gallium arsenide (GaAs), onesurface of which is put in contact with a high tempera-ture solution of gallium aluminum arsenide (GaAIAs).The crystal is maintained at a slightly lower tempera-ture than the liquid and crystal growth occurs from thesurface. Once the proper thickness of this particularcomposition has been achieved, the crystal is removedfrom the bath and put in contact with another liquidhaving the composition corresponding to that of thenext layer. A crystal results with a p-type and an n-type layer, each of which have a higher aluminum con-tent, larger energy gap, and lower refractive index,

2-

1 P,

A —P—~ qi -N—

II II I1 11

++++++++++++++++++++++++++

1

Gal.xA~As:Ge ,~Ga l-y A’yAs ~ Gal_xAlxAs:Sn/Te

I Ge ‘S;;Te

Fig. 2.43 The energy levels of a semiconductor for-ward-biased double heterostructure laser ina junction of lower concentration alumlnumsurrounded by higher concentration alumi-num.

and between which is a recombination layer with loweraluminum content, smaller energy gap, and higher re-fractive index. The amount of aluminum in the recom-bination layer determines the wavelength of the lightemitted. In this manner the structure corresponding tothe energy diagram shown in Fig. 2.43 can be formed. Bythis process the recombination layer can be made thin,often as small as a few tenths of a micron. The long-er-wavelength quarternary InGaAsP alloys are producedby liquid-phase epitaxial growth on an iridium phospho-rus (InP) substrate.

The recombination layer has lower aluminumcontent and therefore, a smaller energy gap, while thelayers on each side have greater aluminum content anda resulting larger energy gap. In this case, when anelectrical bias is applied, electrons are introducedfrom the n-type layer into the recombination layer.Recombination occur overwhelmingly more often in thelayer with the lowest energy gap.

2.3.2 Light Emitting Diodes (LEDs) and DiodeLasers

The use of crystal structures to fabricateeither an LED or a diode laser is shown in Fig. 2.44.Electrons are introduced into the bottom of the crystaland holes are introduced into the top. In the recom-bination layer, holes and electrons recombine to formphotons that tend to move outward in all directions asshown on the left of Fig. 2.44. In this case, the devicebehaves as an LED. The light, emitted in all direc-tions, results from spontaneous emission.

In order to produce a laser it is necessaryto confine and guide the emitted light. This increasesthe light intensity to the level where stimulated emis-sion occurs. This is accomplished in the followingway. The recombination layer has less aluminum there-fore it has the lower energy gap and recombination oc-curs here. The use of some aluminum in the recombina-tion layer allows the wavelength to be adjusted but inaddition it reduces the probability of crystal damage.Furthermore, the layer with the smallest energy gapalso has the highest refractive index. Thus, a higherrefractive index layer is sandwiched between two layersof lower refractive index. This is exactly the situa-tion that leads to lightwave trapping in optical fibers.Similarly for the structure shown on the right in Fig.2.44, photons tend to be reflected from the lower re-fractive index surface back into the higher-refractive-index recombination layer. Photons are retained in the

19

LED“’SPONTANEOUS”’ RADIATON\

WOTOhu=Eg

LASER‘“STIMULATED’’RADIATION

m

Fig. 2.44 The structure of a light emitting diode(LED) and a diode laser showing radiationof photons from recombination.

recombination region for a longer period of time by thepartially reflecting mirrors that are in effect formedat the cleaved ends by the difference in refractive in-dex between the crystal and air, as shown on the rightin Fig. 2.44. Thus, photons formed in the recombina-tion layer tend to reflect back and forth a number oftimes. In this process, the light intensity is increas-ed in the recombination region. When the light inten-sity becomes sufficiently high, stimulated emission be-gins. This is the condition for lasing. When the num-ber of energy gains matches the number of energy losses,for every photon that escapes one or more is formedwithin the recombination layer, thus resulting in aneverincreasing recombination rate and photon produc-tion. Ultimately, equilibrium is reached and the numberof photons being emitted (radiated) from the ends equalsthe number of photons being produced. The requirementfor this to occur is that both carriers (electrons andholes) and radiation (photons) tend to be confined tothe recombination layer. The carrier confinement re-sults in the required population inversion. This in-sures that electron-hole recombination and the result-ing photona will occur in the recombination layer. Thehigher refractive index in the recombination layer andthe effectively partially-mirrored ends reflect orguide the photons back into the layer thus increasingthe light intensity by several orders of magnitudeabove that of spontaneous emission.

The emitted optical power versus applied di-rect current is shown in Fig. 2.45. The emitted opti-cal power initially increases linearly with current.This is the region where spontaneous emission dominates.Once a sufficiently high photon intensity level isreached, stimulated emission begins to dominate and theemitted optical power increases sharply as shown in Fig.2.45. The spontaneous emission portion of the curve isrelatively temperature independent compared to thestimulated emission portion. The electrical currentlevel corresponding to the onset of stimulated emissionincreases with increasing temperature, however the slopeof the stimulated emission curve remains approximatelyconstant, as shown by the T1 and T2 curves in Fig. 2.45.Thus, diode lasers are mounted on heat sinks and mayrequire temperature control devices and feedback cir-cuitry to control the light intensity. LED’a operateby spontaneous emission and do not require such tempera-ture compensation. If one extrapolates backward thesteeply riaing stimulated emisaion region of the curve,the intersection with the current axis, known as thethreshold current, is temperature dependent. In the caseshown in Fig. 2.45, the threshold current is approxi-

2-2

mately 360 ma at temperature T1. Currently, diode lasersexhibit threshold currents in the range of 20 to 200 ma.The solid curve shows the optical power emitted versuscurrent and the superimposed dots indicate repeatedmeasurements taken after 8000 hours. As can be seen,no essential change in laser characteristics occurred.The operational lifetimes of currently manufactureddiode lasers are as long as 106 hours.

4 -

2 -SPONTANEOUS

0

T2>T1

0 100 200 300 400 500

DIRECT CURRENT (mA)

Fig. 2.45 The optical power emitted by a diode laseras a function of applied electrical current.

Diode lasers produced in the manner describedabove are known as double heterojunction lasers. Thecharacteristics of such a laser are shown in Fig. 2.46.The refractive index is plotted on the left and theband gap energy is plotted on the right, both relativeto the layera of the laser. The refractive index andenergy gap both undergo step-function changes at theedges of the recombination layer. Other fabricationcharacteristics of the diode laser include the partial-ly-mirrored ends and the electrical contacts parallelto the recombination layer. Holes and electrons areinjected into the recombination region. Optical energyis distributed across the recombinationapproximate Gaussian distribution shown

)—INDEX

n

Fig.

laver the

2.46 A double-heterojunction

The smaller the volume of thelower the reauired threshold

layer in thein Fig. 2.46.

<

Eg=O.3eV

S~GAPENERGY

laser.

recombinationcurrent. As

previously stated. recombination layers in double~eterojun~tion diode lasers are as thin as severaltenths of a micron. However, the layer shown in Fig.2.46 extends across the entire crystal. With a recom-bination layer this wide, the onset of lasing does notoccur uniformly throughout the layer. Lasing can start

0

in one portion of the recombination layer but not inanother. ‘Lhis is known as filamentary lasing. Suchlasing behavior tends to produce noise. If the widthof the layer is less than 10 microns, it is too narrowfor such filamentary behavior to occur and when lasingdoes begin it occura uniformly throughout the layer.Furthermore, when the width is less than 15 micronssinglemode propagation usually occurs. Finally, theless the width of the recombination layer the less therequired threshold current. Double-heterojunction diodelasers with threshold currents as low as 20 ma havebeen produced. However, trade-offs may be required.For example, reducing the recombination layer widthalso reduces the maximum safe photon intensity. A safecw optical power output that can be maintained withoutdanger of facet damage is approximately 1 mW for eachmicron of recombination layer width. Thus, a laser witha recombination layer 10 microns wide can produce 10 mWof optical power safely.

A striped-geometry injection laser diode,such as that shown in Fig. 2.47, has the desired thinand narrow recombination region. With this geometry,the emitted light spreads out in the vertical directionby as much 50” and in the horizontal by 8° or more.The dimensions of the recombination layer are of theorder of 0.3 microns thick, 10 microns wide, and Up to500 microns long. These dimensions and light spreadingangles must be taken into account when the laser iscoupled to an optical fiber or substrate.

-4 l-+=

Fig. 2.47 A GsAs-GcAIAs geometry CW injection laserdiode.

The distribution of optical energy across thelasing region is shown in Fig. 2.48. The fundamentaland second harmonic of the longitudinal modes are shown.In the longitudinal fundamental mode, the energy tendsto be concentrated more heavily towards the center, andtapers off towards the edges in a Gaussian distributioncurve. If this lasing region is sufficiently wide, thesecond harmonic mode can occur and the emitted opticalenergy is concentrated in two regions.

Several techniques have been employed to fab-ricate such stripe geometry. Some of these are shownin Fig. 2.49. The upper left (a), an oxide protectivestripe is shown between the metal contact and the cry-stal. The stripe is formed where the oxide layer isomitted in the center. Electrons tend to be injectedinto this region only. In this case, the current canspread out underneath the oxide layer where it is notconfined. Another technique, shown at the lower left(b), reduces such current spreading by increasing theresistivity in the regions on each side of the stripe.This can be accomplished by photon bombardment that

2-2

UDINAL (q)

FUNDAMENTAL MODE

{ (!:;)

~

,-I 2ndMODE,’‘ ‘,,, (m::)

DISTANCE

I u 1

TRANSVERSEY

(m) E LATERAL(s)

Fig. 2.48 The light intensity as a function of dis-tance across the face of a laser for thefundamental and second lightwave modes gen-erated by a laser.

METAL CONTACT

-’”’P

(a) STRIPE CONTACT

METAL CONTACT II(Zn-DIFFUSED)

) /[ nP

N PeuBsTRATE

(c) DOPING-PROFILE

METAL ~ONTACT PROTON METAL CONTACT

SOMSARDED(SEMI t+SULATING)

‘P

(b) PROTON-BOMBARDMENT (d) STRIPE MESA

Fig. 2.49 End views of various stripe geometry diodelasers.

produces a semi-insulating layer on each side of thestripe. A third technique, shown at the upper right(c), uses the diffusion of a dopant, such as zinc, intothe stripe region to significantly lower the resisti-Vity. Finally, almost complete electric current con-f inement occurs in the structure shown at the lowerright, (d). A stripe mesa (plateau or table) such asthis is formed during the process of growing the cry-stal. Often such a mesa is buried by depositing addi-tional material over it.

For diode laser operation one major concernhas been the reduction of the spontaneous emission re-gion that was shown in Fig. 2.49. However, spontaneousemission is the mechanism responsible for light emis-sion in LED’s. These devices are cheaper. Simplerconstruction techniques may be used. The light theyproduce is not coherent and is emitted over a muchwider angle (approximately 180° ) with the result thatless optical power may be coupled into a fiber. Onthe other hand, the spontaneous emission portion ofthe optical output power versus input direct currentcurve is far less temperature dependent than the stimu-lated emission region. Thus , because LED’s are lesstemperature dependent than diode lasers, temperaturecontrol and optical feedback problems are reduced.

1

LED’s are fabricated both as edge and surfaceemitters. An example of surface emission is shown inFig. 2.50. A well is etched in the substrate to within

FIBER

EPOXY= d

GE~ SUBSTRATE

ELECTRICAL NCONTACT N RECOMBINATION

LAYER (N OR P)

INSULATING

/ LAYER

Fig. 2.50 A surface-emitting LED with an etched well.

approximately 1 micron of the recombination layer. Thisputs the surface close to the recombination layer andreduces the tendency for the light generated in the re-combination layer to be reabsorbed before it can escapefrom the crystal. The optical fiber into which thelight is being coupled is epoxied to the LED is alsoshown. This arrangement is satisfactory for a multi-mode optical fiber but, for coupling into singlemodefiber, edge emitters mounted in the same manner asdiode lasers are more desirable. The waveguide char-acter of the heterojunction structure leads to improvedcoupling efficiency and greater directionality, thatis, it confines the emitted light to a narrower beam.In this case, the ends are cleaved at an angle severaldegrees from the normal to the surface of the recombin-ation region in order to breakup optical standing wavesand thus extend the region of spontaneous emission.

In the discussion so far, the production ofphotons by electron-hole recombination has been consid-ered. The reverse can also occur. A photon can be ab-sorbed and thus produce an electron-hole pair. Thisphenomenon occurs in photodetectors and will be consid-ered next.

2.4 PHOTODETECTORS

The simpleat type of photodiode is the homo-junction or p-n diode as shown in Fig. 2.51. The most

1 >DEpLET10t4 REGloNL-

1- ABSORPTIONREGION -1

Fig. 2.51 The electric field and regions of a p-n(homojunction) photodiode with bias supply.

successful photodetectors employ silicon ( Si ) althoughgalium arsenide (GaAs) is sometimes used. When thedevice is reverse (back) biased as shown, the electricfield is not uniform. It peaks around the p-n junctionas shown the bottom of Fig. 2.51. Thus , electron-holepairs formed by the absorption of photons in this re-gion are swept away (depleted) , electrons going to then side and holes to the p side. This region of in-creased electric field is known as the depletion re-gion. AS shown, the depletion and absorption regionsdo not necessarily coincide, the absorption regiontending to be larger. Electron-hole pairs, formed bythe absorption of photons from the depletion region,randomly diffuse, often recombining to produce photons.A depletion region may exist even without a reverse(back) bias, but then it is narrow. However, thereare circumstances where unbiased operation is impor-tant, such as for low electrical power operation. Alsowith a bias, a “’dark field” current (dark photocurrent)flows due to thermally generated electron-hole pairseven in the absence of light. Removing the reverse(back) bias eliminates the “dark field” current. Opera-tion with zero bias that is, without a bias supply, isknown as photovoltaic operation.

In order to make the depletion region aslarge, or larger than, the absorption region, the ar-rangement shown in Fig. 2.52 is used. Here a wide re-

P-REGIONFDEPLETIONREGIONfi

N-REGION

3~LIGHT INTRINSIC REGION

b ●

l—ABSORPTION~OUTPUT

REGIONR

1-,1~1BIAS SUPPLY

Fig . 2.52 A p o s i t i v e - i n t r i n s i c - n e g a t i v e (PIN) photo-diode with bias supply.

gion with little or no dopant is placed between heavilydoped n-type and p-type regions on opposite ends. Anundoped semiconductor is referred to as an intrinsicsemiconductor, therefore the broad lightly-doped regionis called the intrinsic or i-type region, or simply thei-region. Such photodiodes are known as poaitive-in-trinsic-negative or PIN diodes. The corresponding elec-tric potential curve is also shown in Fig. 2.52. Thehighly doped n- and p-type regions at each end have lowresistivity and therefore make good electrical contact.The resistivity of the i-region is often so high thateven without a reverse (back) bias the depletion regionextends half way through the i-region. The voltage re-quired to extend the depletion region completely throughthe i-region ia called the ‘punchthrough voltage.”

When considering fiberoptic microbend sen-sors, reference will be made to dark field operation.A current exists in a reverse-biased photodiode evenwith no incident light. This current is called thedark field current and results from the thermally gen-

crated electron-hole paira that are driven by the biasvoltage. Thus, the amount of dark current depends onthe temperature of the photodiode, the energy gap, andthe geometry of construction. Silicon photodiodes havebeen manufactured with very low dark currents.

In order to insure that nearly all of thephotons are absorbed (high quantum efficiency) the widthof the i-region should exceed that of the absorptionregion by a factor of 2 or 3. However, the photodiodeshould be as thin as possible for fast response. Thus,high quantum efficiency and fast response represent de-sign tradeoffs. Photodiodes such as those shown in Fig.2.53 are known as avalanche photodiodes (APD). Here ahighly-doped layer of p-type material is sandwichedbetween the i- and n-regions. This results in a regionof high electric field just before the positive contact.In this arrangement, an electron freed in the i-regiondrifts toward the positive electrode. When it entersthe high field region it speeds up achieving sufficientkinetic energy to produce another electron-hole pair ifit collides with the lattice. The new carriers generatedin this manner can likewiae produce additional carriers.Thus, a “primary” electron freed in the i-region canfree numerous “secondary” electrons in the high fieldregion. The resultant devices exhibit high quantum ef-ficiency. An example of one type of APD constructionis shown in Fig. 2.54. The temperature dependence ofAPD’s is greater than that of either p-n or PIN photo-diodes.

hi~w kDEpLETION REGION+SECONDARY ELECTRON

PRODUCTION REGION

34LIGHT P I P NOUTPUT

-111~+

BIAS SUPPLY

Fig. 2.53 Field regions in an avalanche photodiode(APD) with bias supply.

L!IGH!

‘k;:;;:;LL v A b OUTPUT

,,, ,;;; ::,, ,,, ,,,,,:< ,,/,;;;; ,,//:: 4’, *;,P-.~

R

—

INTRINSIC BIAS

P.—– SUPPLY+

r * IN

[ ,’,, , ,,’ ,~,,,’,

TELECTRICAL

CONTACT

Fig. 2.54 The physical construction of an avalanchephotodiode (APD).

2-23

CHAPTER 3

FIBEROPTIC COMPONENT INTERCONNECTION

Optical power loss (attenuation) has beendrastically reduced in optical fibers since 1970. Apower loss of 0.2 dB per kilometer has been achievedand the prospect is good for another order of magnitudeimprovement to 0.02 dB per kilometer. If this occurs,approximately 50 kilometers of fiber would exhibit onlya 1 dB leas. One consequenceof this progress inreduc-ing attenuation in fiber is the increased importance ofthe attenuation associated with component-to-fiber,fiber-to-fiber, and fiber-to-component interconnect-ions. Little is accomplished if 0.02 dB per kilometerattenuation is achieved in optical fibers and at thesame time a number of Interconnections are required,each resulting in an appreciable fraction of a dB loss.In the case of fiberoptic sensora, where much shorterlengths of optical fiber are utilized than in communi-cation systems, such as several hundred meters of fiberor less per sensor, and where the fiber used in mostcases is not chosen for low 10SS, problems with inter-connections may be less important although connectioninsertion losses can still be a large portion of thetotal loss in a fiberoptic sensor. Interconnections,especially singlemode fiber interconnections, are stillrequired and therefore of importance. The currentstate of their development and manufacture will be con-sidered in the following discussions.

3.1 ‘FIBEROPTIC CONNECTORS AND SPLICES

Some of the uses of interconnections in thefabrication of fiberoptic sensors include joiningsources and detectors to fiber , splitting the output ofa source (especially laser diodes) among a number ofsensors, beam splitting and combining of light in inter-ferometers, and providing fiber-to-fiber interconnec-tions. All interconnections must be designed takingreflection and consequent insertion losses into ac-count, with the aim of minimizing the insertion losses.

Interconnections can be grouped into threeclasses, namely (1) connectors (remountable intercon-nections between fibers or between a fiber and somecomponent, such’as a source, a detector, or an inte-grated chip), (2) splices, (fusion joints or permanentjoints between two fibers or a fiber and some opticalcomponent, and (3) couplers (connections that redistri-bute energy between two or more fibers). In the caseof singlemode fibers, splices are relatively easy toform. Splices and connectors with less than one tenthdB insertion loss per splice can be achieved. Also,in the case of singlemode couplers, especially simplefour-port couplers having two input ports and two out-put ports, losses of less than a dB have been achieved.Multimode connectors and couplers are now commericallyavailable and their singlemode counterparts are justbeginning to become available also. In the case ofmultimode connectors, the average loss is about 1 or 2dB. Goals are set for less than 0.5 dB. For purposesof discussion, the fiber from which light is emergingwill be designated the ‘source” fiber while the fiber

3-1

into which light is being introduced will be desig-nated the “sink” fiber.

In connectors and splices, power losses fallinto two general classes: intrinsic and extrinsic.Intrinsic losses are due to variations or imperfectionsin the fiber that occur during the manufacturing pro-cess and are not mechanically or externally correctable.Extrinsic losses are those that occur after the manu-facturing process and are mechanically or externallycorrectable, such as incorrect finishing of the fiberend-surfaces or incorrect mechanical mating of fibers.Some of these effects are shown in Fig. 3.1. Only the

INTRINSIC

x(I:CCORE AREA MISMATCH

NUMERICAL APERTURE MISMATCH

PROFILE MISMATCH

Fig. 3.1 Some causes of

EXTRINSIC

~ ~d

-c

END SEPARATION

+p’-

ANGULAR MISALIGNMENT

-L /t

LATERAL OFFSET

intrinsic and extrinsicpower losses in optical fiber interconnec-tions.

fiber cores are shown in these sketches. Intrinsiceffects are shown on the left of Fig. 3.1. If thecore areas of the source and sink fibers are not thesame, the mismatch can result in a power loss. Differ-ences in numerical aperture (NA) between the two fiberscan also result in losses. For the case of gradedindex fibers, discussed earlier, a refractive indexprofile mismatch can lead to intrinsic losses. Lossesoccur only when directing light from a fiber of largercore or NA into a fiber of smaller core or NA. Inthese cases some of the light from the core of thesource fiber will not be trapped in the core of thesink fiber. For the reverse, small-to-large core orNA, losses due to the mismatch do not occur.

Examples of causes of extrinsic losses areshown in the right column of Fig. 3.1. If the lightinput to a sink fiber or output from a source fiberdiverges, such as at cone angles of 15° to 20”, a coreseparation will allow some of the light emanating fromthe core of the source fiber to miss the core of the

sink fiber. Likewise angular misalignment can lead toa portion of the light from the source fiber enteringthe aink fiber at angles that will not allow trappingin the core. Finally, losses can occur due to lateraloffset between two fibers because they are not properlyaligned or their cores are not concentric with respectto the outer diameter of the fiber even when the outersurfaces of the cladding are properly aligned. In gen-eral, fibers are lined up by their outer surfaces.There are a number of other extrinsic effects that arenot indicated here. The fiber end might not be smooth.‘rhis can lead to scattering loaaea. The fiber endsmay not be flat cauaing lensing effects to occur. Thus,it is esaential that care be taken in the manufactureor acquisition of optical fibers, connectors, andsplicea in order to inaure that the intrinaic and ex-trinsic leases are or can be minimized. h effect thatcan be corrected easily ia reflection from the ends ofboth fibers due to refractive index difference betweenglass and air. For silicon dioxide (Si02) this reaultain a 0.4 dB loaa. In order to correct thia it is onlynesaary to employ an index-matching liquid or pottingmaterial between the ends of the two fibera being butt-joined.

The effect of the mismatch between either thecore areas or the fiber numerical apertures is shown inFig. 3.2. A problem exista when a source fiber with a

1.00.80.6

~ 0.2rnS 01~ 0.08

0.060.04

0.02

0.001 A I 1 1 I 1 1

2 4 6 8 10 12 14

PERCENT OF DIFFERENCE IN CORE DIAMETERSOR FIBERNA

Fig. 3.2 Approximate losa in dB due to larger-to-smaller core diameter difference or fibernumerical aperture difference for two butt-joined optical fibers.

larger core or larger numerical aperture ia joined toa aink fiber with a smaller core or a smaller numericalaperture. Furthermore, as their difference in numeri-cal aperturea or core diameters is increased, the losswill increase. The curves in Fig. 3.2 ahow the opticalpower loaa in dB as a function of either the percentagedifference in core diameters of larger source coresbutt-joined to amaller aink corea, or source fiberswith larger numerical apertures butt-joined to ainkfibers with amaller numerical aperturea. These specificcurves actually apply to step-index fibers but the gen-eral trenda shown are also true for graded-index fibers.A 10% mismatch in either the core diameters (larger toamaller) or the numerical aperturea (larger-to-amdler)would cauae approximately a 0.5 dB loss. For the largermultimode fibers it is not a difficult problem to main-tain diameters to within 10% of each other or within

3-2

the same fiber. For a fiber with a 50-micron core itwould be necessary to hold the dimensions to + 5microns, but when dealing with singlemode fibers w~tha 5 micron core or less it is necessary to hold the dia-metera to within a half a micron. Differences in numer-ical aperature also need to be controlled accurately,however in general, refractive indices are being con-trolled within and among fibers to within a variationof only a few percent. Thua, the primary problem isthe variation in the core diameter among fibera andwithin the aame fiber.

The extrinsic leas due to end separation foratep-index fibers is shown in Fig. 3.3. The core dia-

b 01 0.2 0.3 0.4 0.5

END SEPARATION (S/D)

Fig. 3.3 Variation of connector power loss with end-separation-distance-to-diameter ratio bet-ween two atep-index air-gap optical fiberends for several valuea of numerical aper-ture (N.A.).

meter ia indicated by D and the separation by S. Thecoupling leas in dB is plotted as a function of S/D.This effect is alao a function of numerical aperture.The greater the numerical aperture (NA) the greater thespreading of light from the source fiber and thereforethe larger the percentage of light that will miss thecore of the aink fiber. In thia figure, results areplotted for NA ranging from 0.15 to 0.50. For thefibera used in fiberoptic sensora the NA of Intereatis below 0.20 and in fact more nearly 0.15. In thiacase, as can be seen in Fig. 3.3, a difference of 10%in the core diameters will produce only a couple oftentha of a dB loaa. Indeed, for NA = 0.15, an endseparation of half the core diameter will produce about0.7 dB coupling loaa. In the caae of aplicea there isno end separation therefore this losa does not occur.

The effect of axial transverse (lateral) dis-placement of equal-diameter cores is ahown in Fig. 3.4.The fiber core diametera, D, and the transverse dis-placement, d, la shown. As can be seen, a 10% trans-verse displacement, which for ainglemode fibera can be0.5 urn (micron) can reault in a 0.5 dB losa. When pur-chasing fiber, carefully apecified fiber dimensions areimportant, e.g., fiber outaide diameter should be main-tained uniform to ~ 1% of some nominal value and coreashould be concentric to within 0.5%. For an 80 urnfiber, a 1% variation in the diameter is 0.8 pm. Itcould lead to a 0.4 ~m transverse displacement, whichfor 5 ~m core could lead to d/D = 0.08 corresponding toa leas of approximately 0.4 dB.

Another extrinsic effect, an axial angular

o 0.1 0.2 0.3 0.4 0:5TRANSVERSE DISPLACEMENT (d/D)

Fig. 3.4 Connector power loss due to transverse(lateral) displacement of the cores of twostep-index optical fiber butt-joined enda.

misalignment is shown in Fig. 3.5. It can occur whenthe fibers are not lined up axially or are not cleavedexactly at right angles to the core axes. This effectis also a function of NA, increasing as NA increases.As little as a 5° angular misalignment produces appro-ximately a 0.4 dB loss in the connection between twofibers each with NA = 0.15.

o 1“ 4~(DEGR&

Fig. 3.5 Connector power loss due to axial angularmisalignment of the cores of two step-indexoptical fiber butt-joined ends.

As indicated above, an important criterionfor the success of either a connector or a splice isthe proper end-preparation of the fibers themselves.Optical fibers used in sensors usually consist of aglass core surrounded by glass cladding that is in turnjacketed by a buffer material used to protect the sur-face. One type of jacket is made of acrylic materialthat can be removed with acetone and a swab. Anothertype of jacketing material consists of a IOO-micron-thick layer of silicone rubber surrounded by another100- or 200-micron-thick layer of a harder plastic,such as Hytrelc. This may be removed with a razorblade. In order to prevent scratching of the fiber,the blade must be held at a very shallow angle with re-spect to the axis of the fiber. Furthermore, a bladeshould be used only once. After the jacket has beenremoved the fiber can be cleaved in any of several ways.One of these is shown in Fig. 3.6. Another techniqueconsists of laying the fiber on a curved surface withapproximately a 5 cm radius and applying a tension ofabout 1/4 pound (120 grams). The fiber is then scribedwith a file causing a smooth cleave to occur. Another

technique is also shown in Fig. 3.6. The fiber islightly scored and then pulled. Care must be taken soas not to bend the fiber. If the fiber bends a liptends to form when it breaks and a smooth endface does

A)STRIPJACKET

tFIBER

C) RESULTS OFFENDING

Pv

h

&d

B)SCORE

~FILE

6 ?

D) RESULTS OF PULLING

—~.

Fig. 3.6 A method of cleaning an optical fiber andthe results obtained.

not necessarily result. An alternative approach toamooth cleaving consists of polishing the ends to pro-vide a flat surface. This can be rather costly and”take a great deal of time. Once a smooth end has beenformed, the fiber can be inserted into a connector orspliced to another fiber that alao haa a smooth end.

A simple snug-fit connector is shown in Flz.3.7. A hole in- the c&nector is provided so that tie

Fig. 3.7 A simple snug-fit connector with hole forindex-matching fluid.

index-matching fluid can squeeze out as the fiber endsare inserted. This is not an easily remountable typeof connector. A fairly good splice can be formed insuch a manner by using an index-matching epoxy in placeof the index-matching liquid. If the splice is snugenough to hold the fiber fixed, an index-matching liquidcan be used. The difficulty with such remountable con-nectors is that in order to be mounted and demountedmany times it is necessary to maintain a radial clear-ance of at least several microns. This technique isnot practical for singlemode fibers because no morethan an 0.5 urn lateral displacement is allowed In orderto avoid excesaive power losa.

A connector, recently marketed by TRW Incor-porated is shown in Fig. 3.8 (see Ref. 1 in Subsection3.1.1). Four relatively large diameter glass rods are

fused together. The ends are bent at an angle of ap-proximately 6° and the hole formed along the axis isenlarged at both ends. The fiber is factory filledwith an index-matching liquid or a fluid curable withultraviolet (UV) light. The fibers to be connectedare inserted into opposite ends. The curvature causesthe fibers to be pressed into the V-groove formed be-tween two of the larger fibera thus aligning the fibersbeing connected as they are brought together. The re-sultant arrangement ia inserted into a spring loadedholding device. The resulting splices cause losses of0.02 to 0.34 dB. These may be mounted and demountedmany times. If LJV-curable fluid is used they may bepermanently fused.

LENGTHWISE SECTION/ \

Fig. 3.8 A single-mode remountable optical fiberconnector recently marketed by TRW Incorp-orated.

Accurately etched V-grooves in a silicone sub-atrate may be used for aligning fibers. A small pres-sure is applied to keep them firmly seated. The useof such V-grooves to align fibers is shown in Fig. 3.9.The fibers are then welded with an electric arc. Anumber of fairly simple techniques may be used in thelaboratory. These techniques prove to be quite effec-tive in forming splices and remountable connectors butthey are not very useful in a more permanent environ-ment. The use of a sheet of thermoplastic material(Plexiglasc) into which a section of fiber is pressedto form a groove is shown in Fig. 3.10. An elevatedtemperature may be used to facilitate the process. Thegroove so formed is then utilized to align two aimilarfibers. An index matching liquid or potting material

OPTICAL FIBER

ELECTRODE

Fig. 3.9 Splicing two optical fibers with an elec-tric arc.

3-4

is applied and a second piece of plaatic-glass (Plexi-glass) or some other flat material is placed on top tohold the fibers in position. A connector formed inthis way is shown in Fig. 3.11.

Fig. 3.10 Joining two optical fibers using groovedplastic-glaas (Plexiglass) to form a sub-strate splice.

FI . 3.11 h optical fiber splice formed with twopieces of Plexiglasc.

A fusion splice is shown in Fig. 3.12 at the

CLAD/ ~ORE

— //

(a) BEFORE HEATING

(b) tititiING HEATING

\ 4(c) AFTER HEATING

x = AXIS OFFSET

zo1=vLuzzov

THEORETICAL CURVE6.0

/5.0

1/

+ BEFORE HEATING~ AFTER HEATING

4.0

3.0

L

/

2.0 i

4,/ ,’1

1.0

0--&.-4--+”-

0 0.5 1.0 1.5 2.0 2.5 3.0(x/a)

Fig. 3.12 Fusion splicing of two singlemode opticalfibers.

Adapted from Tsuchiya and Hatakeyana, Proc. Conf.Opt. Fiber Transmission, Williamsburg, VA Feb. 1977.

left. The ends of the two fibers are brought togetherwittmut necessarily eliminating lateral displacement.Upon heating, the fiber melts and surface tensions tendto align the fibers as shown. The graph on the rightside of Fig. 3.12 shows connector loss as a functionof lateral displacement both before and after heating.The results prior to fusing is a theoretical curve withexperimental reaults superimposed. As can be seen asignificant reduction in loss is realized as a reaultof fusion splicing.

One method of connecting an optical fiber toan encased laser diode is shown in Fig. 3.13. The laser

OPTICAL SPOT

EMITTING SOURCE

/1 I n/

SOURCE PACKAGE

Fig. 3.13 A laser-to-optical-fiber connection.

surface is displaced from the fiber end because of thecovering that protects the laser face. The resultingdisplacement between the fiber and laser source causesa great deal of the light to miss the fiber due tospreading. A lens can be used to collect the light andfocus it into the core. The problem is illustrated inFig. 3.14. At the top, the spreading (divergent) anglefrom the laser and the acceptance angle into the fiberare ahown. The laser emission is such that lightapreads out in a 20° to 40° cone, while the acceptanceangle (cone) for the fiber is 10° to 14”. Thus, evenif the fiber is brought into actual contact (buttcoupled) with the laser face aa shown at the bottom ofFig. 3.14, a large portion of the light being emittedwill mlaa the core or go into the core at such an anglethat it will beinterface, into

trans~tted through the core-claddingthe cladding, and lost. In order to

LASER

@ ,oo--EMISSION PROFILEOF ACCEPTANCE CONE FORAALASERIN THE PLANE TYPICAL STEP-INDEX FIBERPERPENDICULAR TOTHEJUNCTION

Fig. 3.14

LASER PELLET

E:

FIBER

+a.

LIGHT LAUNCHED ATAN ANGLE GREATERTHANaWILLBE LOST

Loas of optical power in a pigtail connec-tion between a laser and an optical fiber.The angle = is equal to or less than thecritical angle.

2-

prevent damage to the mirrored faces of the laser, aalight separation must be maintained. For butt coupl-ing, utilizing an index-matching liquid and no addi-tional optical elementa, it is us~i to couple lessthan 5% of the emitted light into the fiber. From 10to 20% coupling of the light would be considered excel-lent. If lenaes are used to focus the light into thefiber it is possible for 70% or more of the light tobe coupled into the fiber and trapped. The manner inwhich such a lens can be formed from the core of thefiber is shown in Fig. 3.15. In this case the core

Fig. 3.15 Fabrication of an integral elliptical lensat the end of an optical fiber.

glass haa a lower glass transition (softening) tempera-ture than the cladding. Thus, the end of the fiber canbe heated and preasure applied to force a portion ofthe core to bulge out aa shown, forming a lens. Avariety of other techniques for connecting lasers tofibers have been developed and described in technicalliterature. These should be reviewed In the eventsuch an Interconnection is required.

A mechanical device used to align and hold afiber and laser is ahown in Fig 3.16. The fiber ispositioned on one anvil in a V-groove and epoxied inplace. The laser sets on a second anvil that also aer-ves as a heat aink. The two structures are brought to-gether and the smooth faces are butted, aligned, andepoxied. A sleeve is placed over the connector. Inthis way a rather small fiber pigtailed laser can beformed.

ELECTRICAL LEAD

ER

CUTAWAYA

Fig. 3.16 A pigtailed anvil for laser-to-opticalber connection.

fi-

3.1.1 References

1. Fiberoptic Technology, p. 115, Dec. 1981.

3.2 FIBEROPTIC COUPLERS

It is often necessary to divide the beam emit-ted from a laser and insert it into two or more fibera.

5

A laboratory beam splitter set-up used to accomplishthis is shown in Fig. 3.17. It consists of a helium-neon (HeNe) laser, a prism 3-dB divider, an objectivelens to collect and focus the light into a fiber, andthe associated micropositioners. The prism coupler isshown in Fig. 3.18. In order to accomplish the samepurpose with a solid state device, the cores of two ormore fibers must be brought sufficiently close andparallel to each other such that the energy distributedin and around one core overlaps that in the other. Asshown earlier, the energy is not guided entirely in thecore but tends to be guided evanescently by the clad-ding material itself. The cores are surrounded by arelatively thick cladding that must be removed in orderto achieve coupling. After the claddings have been re-moved and the cores are brought close together, thedegree of overlap is adjusted in order to achieve thedesired coupling ratios. It is then necessary to cementor fuse the fibers together in order to fix their rela-tive position (ruggedize) and thus to maintain thecoupling ratios. The coupling ratios ahould remain con-stant with temperature.

Fig. 3.17 A helium-neon laser with 3-dB coupler(beamsplitter) and lens in a laboratoryset-up for coupling light into optical fi-bers.

Fig. 3.18 A 3-dB priam coupler in a laboratory.

A great deal of effort is being devoted tothe development of singlemode fiber couplers, particu-larly 3-dB couplers that couple light from an inputfiber equally into two output fibers. Such couplersare under development at Stanford University; the ITTElectrooptic Product Division; the Gould Research Lab-oratories; the U.S. Naval Research Laboratory; and theU. S. Naval Underwater Sound Center.

The use of pigtailed laaers and bulk couplerscan reduce volume by several orders of magnitude. Twosuch devices are considered next. The method developedat Stanford University is shown in Fig. 3.19. A fiber

(a) EMBED (b) POLISH (c) OVERLAp

Fig. 3.19 Steps in fabricating a polished fiberopticcoupler.

After Digonnet and Shaw, J. Quant. Electron, QE-18,746 (1982).

is cemented into a grooved slab and the combination isthen ground or polished until nearly half of the fiberis polished away virtually exposing the core. Ideallyit is desirable for some cladding to remain so that thecore-cladding interface is not disturbed. A coupler isformed by joining two such slabs with their faces to-gether and adjusting the amount of overlap or alignmentto achieve the desired coupling ratio. A satisfactorymethod of accomplishing temperature-independent fusinghas not been developed.

The technique developed by Sheem, et al, (seeRef. 1 in Subsection-3.2.1) is-sho~ in Fig. 3.20~ The

Fig. 3.20 Steps incoupler.

INDEXMATCHINGPOTTING

(b) ETCH (C) RUGGEDIZE

fabricating an etched fiberoptic

fibers are cleaned carefully after removing the jacket.Then they are twisted together and while remainingtwisted they are etched to remove most of the cladding,leaving approximately one or two microns of claddingaround the core. The diameters of the fibers afteretching are less than 10% of their initial diameters,therefore the resulting sections of fibers are quitefragile. The joint IS held fixed (ruggedized) by eitherpotting in an indexmatching material or by fusing underan axial tension that prevents the fiber from saggingdue to gravity and at the same time stretches the fiberslightly, thus forming a biconical taper. This is shownin Fig. 3.20 on the right. Index matching siliconeliquids have been proven to be highly temperature depen-dent. Better results are obtained with index-matchingsilicone rubber. However, there is still a temperature-dependence problem. A great deal of success has beenachieved recently using a gel glass material (see Ref.2 in Subsection 3.2.1) that is initially in liquid form.This material consists of metal oxides dissolved in anorganic material. When heated the organic material isdriven off and the metal oxides form a glass. The re-fractive index of the resulting glasa, and thereforethe degree of coupling, can be controlled by adjustingthe temperature and the length of time utilized to cureor form the gel glass.

Temperature dependence can be minimized ifthe fibers are actually fused. The biconical taperarrangement mentioned above is shown in Fig. 3.21. To

END VIEWOF FIBER

CROSS SECTIONVIEW

OF FUSED COUPLER

Fig. 3.21 A biconical (tapered)

make this coupler a portion of the

fiberoptic coupler.

cladding is removedfrom each of ‘the fibers. These are then twisted to-gether and etched until the thickness of the remainingcladding is about half the core diameter. The twistedpair is then fused under some axial tension causing adecrease in diameter, especially in the region of con-tact, i.e., the interaction region. The original coredimensions indicated in the upper right of Fig. 3.21are reduced as shown in the lower center of Fig. 3.21.The result is that optical energy that initially wasconfined close to the core tends to spread into thecladding in the region where the core diameter hasbeen decreased. This results in a stronger overlap andtherefore a higher coupling ratio. The ElectroopticsProduct Division of ITT has recently developed a spe-cialized optical fiber that allows them to producefused copulers by this method without the necesaity ofetching. These couplers are available for sale. Analternate to these fiber couplers is the use of mini-

3-

aturized bulk optical components similar to the labora-tory devices shown in Figs 3.16, 3.17, and 3.18. Thesebulk components and fibers may be connected by variousmeans, such as GRIN rods.

Using similar techniques star couplers havebeen fabricated that allow the light from one fiber tobe coupled equally into as many as 32 other fibers.Such devices would be useful for permitting a singleoptical source to simultaneously furnish optical powerto a number of sensors.

In summary, satisfactory techniques now existfor forming low-loss singlemode splices and remountableconnectors and for fabricating low insertion losssinglemode couplers. Recently, commercially availableremountable connectors have appeared on the market.Singlemode biconical tapered couplera are also becomingavailable. Several other types of couplers are underdevelopment by a number of groups and thus can be ex-pected to appear on the market in the near future.

3.2.1 References

1.

2.

3.

S. Sheem, Appl. Phys. Lett ~, 869 (1980).

D. Tran, K. Koo, and S. Sheem, J. Quant. Electron.QE-17, 988 (1981).

R. Ulrich, S. Rashleigh, ‘Beam-to-Fiber Couplingwith Low Standing-Wave Rtutio”, Appl. Opt. ~, 2453(1980).

4.

5.

6.

7.

8.

G.B. Hocker, “Unidirectional Star Coupler for Sin-gle-Fiber Distribution System”, Opt. Lett. ~, 124(1977).

S. K. Sheem, T. G. Giallorenzi, “Single-Mode FiberOptical Power Divider: Encapsulated Etching”, Opt.Lett. ~, 29 (1979).

J. G. Ackerhusen, “Microlenses to Improve LED-to-Fiber Optical Coupling”, Appl. Opt. ~, 3694(1979).

M. Saruwatari, K. Nawata, “Semiconductor Laaer toSingle-Mode Fiber Coupler”, APP1. Opt. ~, 1847(1979).

H. Kuwahara, N. Tokoyo, M. Sasaki, “EfficientCoupling from Semiconductor Lasers into Single-Mode Fibers with Tapered Heimspherical Ends”,Appl. Opt. g, 2578 (1980).

3.3 FIBEROPTIC CABLES

3.3.1 General

Just as with conventional wire interconnec-tions and communication links, there is a need for fi-beroptic cables to accomplish a number of differentpurposea. In many ways, the individual fibers in anoptical cable are treated very much like varnished orplastic insulated copper wires. The individual fiberaconsist of 100- to 200-micron-OD core-cladding wave-guide elements having an outer coating that may be asthin as several microns of lacquer or as thick as 200to 400 microns of plastic, such as nylon, teflon, orpolypropylene. Cabling serves the purpose of space-division multiplexing, combining anywhere from a few tomany individual fibers into a single conveniently-pack-

7

aged multichannel unit. High-strength reinforcing mem-bers are usually added to the structure and additionalinter-fiber separators (apacers) and outer protectivejacketing are provided within a cable with a relativelysmall outer diameter. The jacket reducea the effectaof cabling and protects the individual fibers from theexternl environment. Unlike copper wire and coaxialcables, crosatalk between individual fiber waveguidesis virtually nonexistent. The equivalent of low resis-tance shorts between two wirea and ground loopa do notexist for fiber interconnection. Breaks can occur infibers just as in wirea. However, increases in opticalpower loaaes in fibers due to microbend effects must beconsidered. These may be introduced during cable con-struction or installation. They also may be producedby environmental disturbance that cause differentialstress or thermally induced bends. Care must be taken,in cable design to prevent such effecta, particularlywhen low-leas fiberoptic links are required.

3.3.2 Commercial Fiberoptic Cables

An example of how conventional cabling proce-dures, developed for the communication industry forwire tranamiasion media may be employed for optical fi-ber cables is shown in Fig. 3.22. The figure ahows the

OUTER JACKET

COND

CENT

HEAVY DUTY CASLE WHICH CAN SE INSTALLEDBY REGULAR CREWS.EXTERNAL CONSTRUCTION FOLLOWS TRADITIONAL TELEPHONE CASLE PRINCIPLES

Fig. 3.22 A fiberoptic cable produced by GeneralCable.

structure of a heavy duty, combined wire and opticalfiber cable manufactured by General Cable deaigned foruse by the telecommunication industry. As indicated,it conaiats of two almoat identical multiwire and multi-fiber sandwich-like stripa that are parallel to eachother on opposite sidea of a channeled plastic rod thataeparates them. The atripa are held in place with tapewrapping. l%is is surrounded by a welded aluminum tubethat forms the main strengthening element of the cable,which in turn is aheathed by inner and outer plasticjacketa that encaae a corrugated steel reinforcing wrap.

A aecond type of cable developed for uae instandard telephone applications is shown in Fig. 3.23.Produced by Bell Telephone Laboratories, it contains144 separate multimode fibers. Twelve fibers are fuaedin each of twelve plastic ribbona that form a 12 x 12matrix that runs through the center of the cable. Thisis wrapped with paper tape and surrounded by inner andouter plastic jackets aeparated by flexible fiber andsteel wire strengthening elements.

TWO other aimilar cables produced for fiber-

3-

optic communication purpoae are shown in Fig. 3.24 and3.25. The first is an International Telephone andTelegraph cable that has a group of plastic-jacketedmultimode fibers relatively looaely packed within acentral polyurethane jacket surrounded by a layer ofhigh-atrength Kevlarc fibers and an outer plastic jack-et. The second is a SIECOR cable in which a group ofCorning lacquer-jacketed multimode fibers are threadedloosely through individual loose fitting protectivetubes that are distributed around a central steel re-inforcing wire. Theae tubea are surrounded by two suc-cessive layera of Kevlarc fibers separated by inner andouter plastic jackets. In each of these two cablea,special care haa been taken to allow some flexibilityand freedom of motion for the individual optical fibersto minimize the introduction of cabling-induced micro-benda.

POLYETHYLENE OUTER JACKE1

POL

FIBERS I

12x12 FISER ARRAY

Fig. 3.23 A fiberoptic cable producedphone Laboratories.

by Bell Tele-

KEVLAR STRENGTH MEMSERS ‘UTER <K>

// ;HicK P L A S T I C JAcKETING

Fig. 3.24 A fiberoptic cable produced by InternationalTelephone and Telegraph.

KEVLAR STRENGTHMEMBERS /’”

/LOOSE FITTING

PTFE TUSES

k

..’$’’.,:

STEEL WIRESTRENGTH MEMBER

‘y OUTER

/*w

.7 JACKET

PLASTIC INNERJACKET

LACOUER COATEDFISERS

Fig. 3.25 A fiberoptic cable produced by SIECOR.

8

Two cables manufactured in Japan by SUMITOMOfor underground and indoor telecommunication applica-tions are shown in Figs. 3.26a and 3.26b, respectively.In the cable designed for underground installations aset of four multimode fibers, separated by plasticstrings are spaced uniformly around a cushioned centralstrength member and surrounded first by a cushioningsheath and then a second high-strength outer polyethy-lene jacket. This cable has an outer diameter of only18 millimeters. The multifiber cable designed for in-door test is even smaller. As shown in Fig. 3.25b, ithas an outer polyvinylchloride (PVC) jacket only 8 mmin outer diameter, and an inner cushioning sheath thatsurrounds a set of plastic-jacketed graded-index opti-cal fibers.

PLASTIC TAPEISmmOD ~ PESHEATH

mO.D

PLASTIC STR

STRENGTHM

A. underground CABLE B. INDOOR CABLE

Fig. 3.26 Two fiberoptic cables produced by SUMITOMOof Japan.

A somewhat different cable design is employedby HITACHI to reduce losses induced by cabling and in-stallation. As shown in Fig. 3.27, channels are formedin the outer periphery of a plastic spacer that is re-inforced with a central high-strength metal or plastictension member. The individual plastic-jacketed opti-cal fibers, and copper wires if some are required, fitloosely in the channels and are held in by a thin outersheath. Thus, each fiber is well isolated from bothexternal and internal stress.

CU WIRE

SPACER \16mm O.D

NONMETALLIC CABLE coMPOUNDCASLE

Fig. 3.27 A fiberoptic cable produced by HITACHI ofJapan.

3.3.3 Summary

From the above brief discussion of currentfiberoptic cabling procedures, it should be clear thatin some cases conventional cabling techniques are being

3-9

used, especially for relatively short-run applicationswhere microbend losses introduced by cabling are notexcessive. For low-loss long-run applications, uniquedesigns aimed at eliminating random bending and theeffects of cabling and environmental disturbances havebeen developed that are capable of preventing the addi-tion of more than 1 or 2 dB/km to the original opticalpower losses in the uncabled optical fibers.

Discussions of fiberoptic cable risetime bud-gets, power budgets, bussing schemes, design parameters,environmental factors, and their use in connection withfiberoptic sensor arrays and telemetry systems is givenin Chapter 6.

CHAPTER 4

LIGHTWAVES IN FIBEROPTIC SENSORS

4.1 INTERFEROMRTRIC FIBEROPTIC

4.1.1 Intensity Interferometry

4.1.1.1 Basic Principles

SENSORS

The basic transduction mechanism employed inmany fiberoptic sensors now being developed is the phasemodulation of coherent light propagating through a sec-tion of singlemode fiber by the action of the energyfield that is to be detected. The techniques of opti-cal interferometry may be used to detect these phaseshifts in lightwaves. These techniques allow for theextremely high sensitivity that is achievable with thevarious types of interferometric fiberoptic sensors.Until recently, optical interferometry has been a re-search tool used in laboratories rather than an appliedor operational technique. With the development of low-10SS singlemode optical fibers, subminiature aolid-state laser light sources, photodetectors, and otherrelated purely optical and electrooptical devices,it is now possible to construct practical interferomet-ric-type devices for use in operational systems. Fiber-optic sensors have the potential to revolutionize sen-sor technology.

Four different interferometric configurationscurrently are being employed in fiberoptic aensors.These are the Michelson, the Mach-Zehnder, the Sagnac,and the Fabry-Perot configurations. It is convenientto review their operation in terms of a nonconventionalschematic arrangement using airpaths and bulk opticalcomponents before considering how they may be construct-ed with optical fiber elements.

There is one important aspect that these in-terferometric sensors have in common. In each one, theoutput beam from an optical source is split into two ormore portions. After traveling along different paths,these separate beams are recombined and allowed to ac-tuate a photosensitive detector.

4.1.1.2 The Michelson Interferometer

The basic principle is illustrated first inFig. 4.1 for the case of an air path Michelson inter-ferometer. The beam splitter is shown as a partially-reflective, partially-transmissive mirror. It sends oneportion of the output beam from the laser upward to thefixed mirror where it is reflected back to the beamsplitter, where it is then partially transmitted to theoptical detector and partially reflected back towardthe laaer. The other portion of the laser output beampasses through the beam aplitter, 1S reflected fromthe movable mirror to be partially reflected to theoptical detector and partially transmitted back towardthe laser. If the difference in the the path lengthsback and forth to the fixed mirror and to the movable

4-1

mirror is less than the coherence length of the laser,the two beams transmitted to the detector can be madeto interfere with one another. The detector outputwill go from a maximum to a minimum and back to a maxi-mum each time the movable mirror is displaced by onehalf the optical wavelength. With this technique, itis ossible to detect

?10- urn, e.g. 0.63 xlight.

mirror displacements as small as10-13 m, for a He-Ne laser red

LASER TRANSDUCER

SPLITTER wFig. 4.1 The principle of the Michelson interfer-

ometer.

4.1.1.3 The Mach-Zehnder Interferometer

The Mach-Zehnder interferometer configurationis shown in Fig. 4.2. The laser output beam is split

BEAM

“’’R’-

1 , ,MOVABLE

LASER I “ ‘1BEAM

SPLITTER

Fig. 4.2 The principle of the Mack-Zehnder interfer-ometer.

by the lower beam splitter. After traveling the upperand lower optical paths the two beams are recombinedso that they may interfere with each other at the opti-cal detector. This arrangement may also be employed to

detect displacements of the movable mirror as small as10-13 m. l%is configuration has the advantage thatlittle or no light is fed directly back into the laser.This is in contrast to the Michelson configuration. Amore detailed description of how such feedback can leadto laser instability and noise is contained in Section4.2. It should be noted that there are two other beamsnot shown explicitly in Fig. 4.2, that travel upwardfrom the second beam splitter, i.e. a reflected portionof the upper horizontal beam and a transmitted portionof the righthand vertical beam. These could be fed toanother optical detector to yield a second output sig-nal , which may be employed to advantage in certain ap-plications.

4.1.1.4 The

Theshown in Fig.

Sagnac Interferometer

Sagnac interferometric configuration is4.3. With this arrangement, the two por-

II II) 1 11/ I A

I LASER

Fig. 4.3 The principle of the Sagnac interferometer.

tions of the laser’s output beam are sent in oppositedirections around the closed path formed by the beamsplitter and the two mirrors. They are then recombinedto be sent on to the photodetector and also back towardthe laser. If any of the mirrors is displaced perpen-dicular to its reflecting surface, both path lengthswould be changed by the same amount and there shouldbe no detectable change in the interference processat the photodetector. On the other hand, if the tableon which the interferometer is mounted were set into,say clockwise, rotation about an axis perpendicularto the plane of the beams, the beam traveling clock-wiae, i.e. In the direction of rotation, would bedelayed with respect to the counterclockwise travelingbeam. The clockwise beam has to “catch up” to the endmoving in the same direction. The counterclockwise beamruns into the end moving in the opposite direction.Thus, the Sagnac interferometer may be employed as asensitive rotation detector and, in principal, it is thebasis for the design of the ring laser gyroscope cur-rently in use in a number of inertial guidance systems.

4.1.

tion4.4.

.5 The Fabry-Perot Interferometer

The fourth type of inter ferometric conf igura-the Fabry-Perot interferometer, is shown In Fig.It consists of two parallel, partially transmis-

4-2

—

TRANSDUCER

1 tFIXED MOVABLE

MIRROR MIRROR

Fig. 4.4 The principle of the Fabry-Perot interfero-meter.

sive mirrors. The reflectivity of these mirrors usual-ly is quite high, e.g. 95% or even higher. Assumingthat the reflectivity (reflection coefficient) is 95%,at any instant 95% of the output light from the lasersource will be reflected back toward the laser and 5%will be transmitted into the Interferometer cavity.When this portion of the incident light reaches theright-hand mirror, 95% of it will be reflected backtoward the left-hand mirror and 5% will be transmittedthrough to the detector. This will combine with lightthat has been reflected back and forth successively anincreasing number of times between the two mirrors.Neglecting losses other than the 5% transmission (ateach interface), each successive output beam intensitywill be reduced from the previous one by the factor(0.95)2 = 0.9025. Assuming that the laser has a coher-ence lenzth manv times the distance between the twomirrors, the optical signal intensity incident on thedetector may be found by forming the vector sum of theelectric fields of the various transmitted beams.

4.1.1.6 Interferometer Sensitivity

The sensitivity of various interferometers isshown graphically in Fig. 4.5. Consider first, whatoccurs in the first three type of interferometers thatwere considered earlier. For the Michelson, Mach-Zehn-der, and Sagnac configurations, two separate opticalbeams are combined at the sensitive interface of thephotodetector. As indicated in the upper left, the

~1 and 22 which are assumed to be of equal magnitudewo electrical fields are represented by the vectors

and linearly polarized in the same direction. The op-tical intensit

zis proportional to the square of their

vector sum, E ( 8 ), which is at its maximum when thetemporal and spatial relative phase angle between thetwo vectors is zero. If the length of one of the in-terferometer paths changes the phase angle varies, andE2( e ) and the intensity vary as indicated in the graphin the upper right in Fig. 4.5. , i.e. , the intensitydrops to zero as 13 increases from O to n radians, vary-ing as cos e. For further increases in e, E2( e) oscil-lates from zero to its maximum and back to zero againeach time 13 varies by 2T radians.

The corresponding diagrams for the Fabry-Perot interferometer are shown in the lower portion ofFig. 4.5. As pointed out earlier in this case, thereis a set of electrical field vectors, in principle in-finite in number, each successive one down from theprevious by a factor R2, where R is the amplitude re-flection coefficient. When the mirror separation issome integral number of half wavelengths, all of thesevectors are in phase and the output intensity is at amaximum. When the separation is increased slightly,each successive vector is shifted with respect to theprevious one by the same angle. By continuing the vec-

tor addition indefinitely, as indicated in the lowerleft, one can easily show that E2(13) in this case is asharply peaked function with maxims at = O, Zm, 411,...and s. forth; E2(e) rapidly decreases and remains CIOSeto zero for values of f3 only slightly different from O,2n, 41r,... etc., as indicated in the vector diagram atthe lower center in Fig. 4.5c. Thus, in the vicinityof its maxima, the Fabry-Perot interferometer is an ex-tremely sensitive position and length measuring device.It is in fact, one of the most sensitive displacementmeasuring devices available to modern science.

A) MICHELSON, MACH-ZEHNDER AND SAGNAC

RELATIVE PHASE SHIFT (RADIANS)B) FA6Ry-pEROT

AEl > ~E’[@),

r

DISPLACEMENT- O.25 05 0.75 I MICRON

Fig. 4.5

4.1.2

have been

The sensitivity of various typea of inter-ferometers as a function of relative phasedifference between two interfering light-wavea.

Fiberoptic Intenaity Interferometer

Up to this point, the various interferometersdepicted aa they exist in the typical optics

laboratory, with air paths and lumped optical devicessuch as beam splitters and mirrora. Their extremelyhigh displacement sensitivity has been used to measureatrain and streas. In addition, they also have a veryhigh dynamic range. This will be brought out in moredetail in later discussion. If the many advantagesof the use of fiberoptic, electrooptics, and integrat-

ed-optics are added, one can conceive of configurationsand systems that are capable of revolutionizing sensortechnology.

By employing single-mode optical fibers forthe interferometer paths, the rather stringent limita-tion on their length is immediately removed. Pathlengths of the order of a kilometer are easy to achieveand are being used in practice. Extremely small, long-life, solid-state laaers and detectors that are capableof being used in hostile environments are becomingavailable. Elements such as etched or lapped fiber-to-fiber couplers and their integrated-optic counterpartare being developed and tested. By incorporating items

4-3

that are currently available, it is already possible toconstruct relatively small-sized, highly-stable, andquite rugged interferometric fiberoptic sensors thatare capable of withstanding the rigors of many field-type applications.

Sketches outlining “all fiber” configurationsof the four different types of interferometers areshown in Fig. 4.6. In the Mach-Zehnder fiberoptic in-

A) MICHELSON

3dB COUPLER

=;:’’:;sRTRANSDUCER

B) MACH-ZEHNDER

f \

5’=i!4._-!=-!’=-C) SAGNAC

ElLASER

DETECTOR

D) FABRY-PEROT

LASER - 1 a!- DETECTOR

\: ‘/PARTIAL TRANSMITTING MIRRORS

Fig. 4.6 The configuration of various types of fi-beroptic interferometera.

terferometer shown in Fig. 4.6b, the two beam splittersare replaced with two etched or lapped 3-db couplersthat divide the laser output beam into two equal por-tions and they also recombine the light that haa tra-versed the two optical paths. It is possible to butt-couple the laser output beam directly into the fiberand to similarly couple the output fibers directly intothe two photodetectors. Thus, between aource and de-tectors, the interferometera consiats only of fiberelementa. By combining integrated circuit techniqueswith current electrooptic capabilities, all of the otherelements, including the laser, detectors, and signalprocessor, could be packaged in a single miniature chipto which the fibers will be butt-coupled. Though thedevice is not an off-the-shelf item today, there islittle doubt that they will be readily available in thenot too distant future.

4.1.3 Polarization in Fiberoptic Sensors

Earlier in this discussion of interferometersit was mentioned, but not especially emphasized, that

the fiber interferometer should employ singlemodefibers. In this case, the lightwaves injected into eacharm of the interferometer would propagate at a uniquevelocity. In fact, the so-called singlemode fibers arereally at least two-mode fibers in the sense that thereare two different states of optical polarization thatcan be propagated, i.e. the electric field vector canbe resolved into two mutually perpendicular componentthat are perpendicular to the axis of the fiber. Inan ideal, straight, imperfection-free fiber with circu-lar symmetry, the propagation velocity is independentof the direction of polarization. Polarized light in-jected into such a fiber would maintain ita directionof polarization. Thus, in an interferometer applica-tion, one could have available two similarly polarizedoptical beams that can produce the optimum interferenceeffects. That ia, if their intensities are equal, theirelectric field vectora can interfere destructively andthereby completely cancel. This can occur only forbeams of the same polarization.

In reality, however, ideal fibers with per-fect symmetry do not exist. The complications thatthis introduces can be illustrated by considering afiber with an elliptical core, as ahown in Fig. 4.7.In this case, there will be two preferred directionof polarization, those along the major and along theminor axes of the elliptical croas section aa ahown bya and b along the x and y axes in Fig. 4.7.

t Y

-------——-—-——- ——z

\

I x\

Fig. 4.7 b optical fiber with an elliptical crosssection.

Linearly polarized light injected into thefiber with its direction of polarization at some angleother than along the x or y axes will propagate in twoaeparate.modea, the ao-called HE 11 and HE 11 modea,

~ Such athat travel at alightly different velocitie .fiber is aaid to have a modal birefringence, B, definedby:

B= (~-~)x/211 (4.1)

where the two 6’s are the propagation constanta of thetwo polarization modes and i is the wavelength in avacuum. Under this condition, the direction of polar-ization will continuously change along the length ofthe fiber. Even when light that is polarized alongone of the two major axes is injected into a fiberthere will be some coupling into the other mode due toimperfections in the core-cladding interface, index ofrefraction fluctuations, and other mechanisms. Thua,both static and dynamic changes in polarization alongthe length of the fiber may occur.

The occurrence of such changes of polariza-

4-

tion may be observed in the laboratory in the followingsituation. Referring to Fig. 4.8, imagine a beam oflinearly polarized light injected into an elliptically-cored “two-mode” fiber in such a way that the inputenergy is aplit equally between the HEIIX and HEIIYmodes. The modal velocities are different thereforethe polarization state will change continuously alongthe length of the fiber, aa shown at the left in Fig.4.8. The HEIIX and HE1lY modes are linearly polarizedalong the X and Y axea, respectively, and at each posi-tion, z, along the axis of the fiber the state of polar-iza~ion is *determined by the time varying vector sumof Ex and ‘Y” Beginning at some point (a) where thetwo modes are in phase, the polarization state willchange from linear polarization at (a) to circularpolarization at (b); back to linear at (c), rotated,however, by 90” from its direction at (a); to circularat (d), but in the opposite direction from that at (b);back to linear at (e), just as at (a); and ao forthdown the length of the ”f~ber.

BEAT LENGTH L=;

(a)

(b)

(c)

(d)

(e)

Fig. 4.8

OBSERVER

@(z) =(px–py)z=o

—

The effecta of birefringence, 6, of polar-ized light in an optical fiber.

In this situation, if the light intensity inthe core Is high enough so that the core-to-claddingscattered light ia visible to the naked eye in a dark-ened room, one may obaerve an apparent cyclic variationin the intensity of the acattered light along thelength of the fiber, with the darker region beingspaced a distance, L, apart, as shown at the right inFig. 4.8. The darker regions correspond to aections ofthe fiber from which only a small amount of light isacattered towarda the eye of the obaerver. These cor-respond to regions where the reaultant electric fieldvector in the core ia parallel to the line of view, sothat, from a classical electromagnetic (E&M) viewpoint,the radiation pattern of the oscillating electric vec-tor (dipole) has a minimum in this direction. As thepolarization state changea continuously in going from(a) to (c) the component of the * vector perpendicularto the line of view increases and, therefore, thelight scattered toward the viewer’s eye alao increas-es, reaching a maximum at (c). Due to a similar pro-cesa, thea minimum

ponds to2n radian

scattered light appears to decrease back toin the section of fiber from (c) to (e).

The distance, L, between two minima corres-a one wavelength relative shift, i.e., aphase ahift, between the HEllx and the HEIIY

4

modes. Since at point (a) the two electric fields areassumed to be in phase, the relative phase angle o (Az)at some distance Az displaced from (a) la given by

O(AZ) = (Bx - BY)Az (4.2)

Thus at (b) ~ =m/2 and at (c) @c = II and ao forth. At(e) where Az = L:

o(L) = 2T (4.3)

= (M-BY)L (4.4)

Earlier in Eq. (4.1) the birefringence, B, was definedas:

B = (BX - BY)I(2TIA) (4.5)

So that for a two-mode fiber that has, at a given wave-length, A, a birefringence, B, one obtaina:

L = h/B (4.6)

where L la defined as the beat length.

Over the distance, L, the polarization stateof light propagated in a two-mode fiber may pasa throughthe entire cycle ahown at the left in 4.8. In terma ofthis process there are some applications where it isdeairable to have a fiber with a long beat length, orsmall birefringence, B, and others for which a shortbeat length, or large birefringence, is preferable.

For example, in the deaign of an opticalfiber electric current aensor employing the Faraday ef-fect as the transduction mechanism, a relatively ahortfiber element may be employed and a long beat length,L, is preferable. When attempting to detect magneti-cally-induced birefringence, any slight changes in alarge inherent birefringence, B, i.e., small L, might

maak the polarization changea induced by the magneticfielda associated with the electric current under meas-urement.

In certain applications of interferometric-type sensora, “two-mode” fibers with high birefringence,and short beat lengtha can be uaed to advantage. Asalready indicated, the output beams from the two pathaof the interferometer not only must be equal in ampli-tude but alao polarized in the same direction if theyare to totally cancel one another when they are out ofphaae by~ radians. In many interferometer sensor ap-plications fiber path lengtha of aeveral tens to aev-eral hundreds of metera are employed. It is irnpoaaibleto draw perfect fibers without variations and fluctua-tions in core dimensions and refractive indices, andwithout core-cladding interface ripplea. Therefore,even when the direction of polarization of the injectedlight la along one of the preferred axes in an ellipti-cal fiber, there will be at least random coupling dueto auch perturbations. Thus, as the propagation dis-tance increases, light originally in the HEIIX mode, iatransferred into the HE1lY mnde. If the birefringence,B, is different from zero, (even if it only fluctuates),there will be some changes in the direction of polari-zation and theae could reault in a reduction in the de-tection sensitivity of the interferometer.

One method of improving detection sensitivityis to employ fibers that have high birefringence andshort beat lengtha. In this case, due to the large dif-ference in the electric field profilea associated withthe HE1lX and HE ~y modes,

1the probability that a given

perturbation wil cauae a transition between modea la

4-5

much lower than in the case of a fiber with amall bire-fringence, B. In this senae, a high B fiber is a polar-ization-maintaining fiber and therefore may be uaed toadvantage in Interferometric-type senaors.

One way in which a high-birefringence fibermay be made is shown in Fig. 4.9. At the left an

/“n\~] (,3J) ~cQER

IDEAL FIBER \ /

PREFORM

Fig. 4.9 The production of high birefringence opti-cal fibera.

idealized fiber having a rectangular core and claddingstructure is shown. Ita bimodal structure can be rep-represented as the sum of two planar waveguide modes,one where the height of the core croas section is thedetermining factor and the other where the length ofthe core croaa aection la the determining factor. Thesemodes would have substantially different propagationconstants and the B value would be large.

Several approaches have been taken to producefibers that approximate this ideal atructure. Onetechnique is shown at the center of Fig. 4.9. A pre-form is produced consisting of a circular core and atwo-layered circular cladding. The dotted line in thefigure la the outline of its original outer circumfer-ence. Large semi-circular segments of the outer clad-ding along the length of the preform are removed aaindicated and then two additional slots are cut toexpoae a section of the inner cladding. Thia elementis then heated until, under the action of surface ten-sion, it returns to a circular croaa section. The coreand inner cladding each aasume an elliptical ahape.Fibera are then pulled from this modified preform. Thereaulting fibers have relatively large birefringence, B.

4.2 PHASE AND INTENSITY DETECTION

4.2.1 Phase Detection

As will be ahown, phaae modulation will beconverted to amplitude modulation prior to detection.Thus, it is useful to first conaider the procesa in-volved in amplitude modulation. An optical source in-put, Iin, into an intensity-type aenaor la ahown inFig. 4.10. A graph of the optical input to the sensorversus time is shown at the bottom left. In the aen-sor, a baseband input signal, Sb, amplitude modulateathe optical aource input, Iin, to produce the outputsignal from the sensor aa ahown in the graph at thebottom center. Finally, the amplitude-modulated opti-cal output signal from the aenaor is photodetected re-sulting in an amplitude-modulated electrical outputaignal from the photodetector aa ahown at top and bot-tom right of Fig. 4.10. Phaae modulation cannot bedirectly detected due to the fact that the light fre-quency is approximately 1014 Hz. Photodetectors areunable to respond to such high frequencies, i.e., they

cannot follow the inatantaneoua valuea of such high-frequency variations. Thus , in order to accomplishphase detection, an interferometric technique must beuaed to convert the phase modulation to amplitude modu-lation prior to detection.

sb

IINt

‘OUTOPTICAL

SENSOROPTICAL

SOURCE DETECTOR‘OUT

ikiki&T IME TIME TIME

Fig. 4.10 Input-output relations in an intenaity-typefiberoptic senaor.

The phaae angle, $, measured with referenceto the plane of entry into a fiber, of a lightwave ofwavelength A in a fiber of length L ia given by:

4 = 2nL/i = 2mIlL/lo (4.7)

where A. la the wavelength of light in vacuum and nl lathe refractive index of the fiber core. If L and X. areexpresaed in the same units, $ will be in radians. Ifthe fiber undergoes a change in length, AL, relative tothe fixed plane of entry, the phase angle at the endplane of the fiber becomes:

$+A41=2ml(L+AL)/~ (4.8)

These two caaea are shown in Fig. 4.11. An assumption

o L

+0 t?

+= 27r LENGTH 2%nLFIBER .— 1

WAVELENGTH A ICORE I

1

i0

+0 -A++++A~= 2un—(L+ AL)

A

Fig. 4.11 Phase change of a lightwave through an op-tical fiber of original length L that hasbeen stretched by a length AL.

4-6

is made here that the value of nl does not changethroughout the fiber during its change in length. Whilethis is not true, it will be approximately true in manyof the caaes to be considered later.

Consider the situation in which there are twooptical fibers, one located in each of the two arms ofan interferometer. A lightwave is simultaneously intro-duced into the left ends of these two fibera, initiallyof the same length or differing in length by an inte-gral multiple of 2TT rad. Assume the upper fiber in Fig.4.11. is the reference fiber. Consider the case inwhich the output of the two fibers is initially in phaseand when combined interfere constructively. If thelength of the lower fiber increases due to an appliedstress or a thermal change, the output intenaity of theinterferometer will decrease, reaching a minimum whenthe length of the lower fiber haa increased by A/2,i.e., T rad. At this point if the lower fiber contin-uea to change, then the output amplitude will increase,returning to ita maximum value when the length of thelower fiber has increased by another i/2, i.e., m rad.The reaulting current out of a photodetector placed atthe end of the fibera is shown in the upper curve ofFig. 4.12. The ordinate is the photodetector current

lro+ZD‘--–-–– ‘- ‘MAX

:+~~

SE~ > .- –-– - - - - - - - - - - - TMINOv

30 ~2% 37r

L+(RAOIANS)

A+4RAOIANS)

● PHASE DRIFT CAUSES PtiOTO -DETECTOR CURRENT (i) TO VARY❑ ETWEEN TM,N AND IMAX (FADING)

● PHASE SENSITIVITY -d,ld(A.$)

● MAXIMUM SENSITIVITY FORA+=V2 ,3v~

● V2 PHASE BIAS REIIJIREO FOR

MAXIMUM SENSITIVITY (QUADRATURECONDITION)

Fig. 4.12 Photodetector output current and its deri-vative resulting from lightwave phase-change fiberoptic sensor output.

and the abscissa is the difference in phase between thelightwaves in the two arms. This output ia typical ofthe effect of a phaae drift (shift) aaaociated with thereturn to thermal equilibrium following a step functionincrease in temperature. In general, such oscillationsare undesirable especially when the signal being meas-ured produces phase changea many orders of magnitudesmaller. A case where such oscillations are a measureof the signal being detected is described below.

A simple technique for meaauring the rate ofchange of presaure for large presaure changes ia ahownin Fig. 4.13. The sensing element consista of a lengthof fiber, L, tightly (prestressed) wound on a mandrelof a compliant material such aa Teflonc. The pressuremay be applied either to the outside of the fiber-mandrel combination or, for the caae of a hollow man-drel to the inside. Aa the length of fiber in the sen-aing arm changes the output of the photodetector willsweep through maxima and minima as ahown by the uppercurve in Fig. 4.12. The time rate of change of pressurecan be related to the frequency of oscillation in aatraight forward manner. The number of oscillations perunit time is proportional to the change in fiber lengthper unit time, where the change in length is expreased

as a number of wavelengths. An expression for the fre-quency can therefore be obtained by dividing the changein the fiber length per unit time by the wavelength oflight. This is given by the expression:

f= (nl/Ao)(dL/dt) (4.9)

Where lo/nl is the wavelength in the fiber core.

From the expression for the volume of themandrel, V = rr2D, it follows that:

~V/V = 2Ar/r + AD/D (4.10)

where r and D are the radius and length of the mandrelrespectively. For hydrostatic pressure AD/D . ~r/r andEq. (4.10) becomes:

AV/V = 3Ar/r. (4.11)

The compreaaibility, K = (1/V)(dV/dP), of the mandrelcan be written:

K = (3/r)(dr/dP). (4.12)

Since for a compliant mandrel, the change in fiberlength is cauaed primarily by the change in r, whereL = 2nNr, it follows that:

(1/L)(dL/dp) = (1/r)(dr/dP) (4.13)

and substituting Eq. (4.13) into Eq. (4.12) yields:

K = (3/L)(dL/dP). (4.14)

Letting:

dL/dP = (dL/dt)(dt/dP) (4.15)

in Eq. (4.14) and solving for (dP/dt) results in:

dP/dt = (LK/3)/(dL/dt). (4.16)

Finally, substituting Eq. (4.9) into Eq. (4.16) yieldathe deaired expression for the time rate of change ofpressure in terms of the frequency of oacillationa:

dPldt = (3Ao/KLnl)f. (4.17)

The quantity on the right multiplying f is the acalefactor. Since the length of fiber, L, is very muchgreater than the expected change in length, the scalefactor remains approximately constant. (A stress of100 Kpsi is required to produce a one percent change infiber length.) For large changea in pressure the valuesof Kand nl also vary, but in oppoaite directions. Thescale factor in Eq. (4.17) can be changed by employinga mandrel exhibiting a different sensitivity. In gen-eral, however, the largest changea in acale factor canbe accomplished by changing the length of fiber. Caremust be taken to inaure that the mandrel doea not exhi-bit resonant frequencies which are excited by trans-ients associated with the time rate of change of pres-sure. Such resonances may constitute the upper limitof measurements.

Choosing ~K .3.6 x ;:-iT’cm3)d;:”;;e&= 0.85 X 10

Si02, and for Teflon?

dP/dt = 4.85 x 105 f/L (pascala/aec). (4.18)

l%us for 1 m < L < 100 m and 100 Hz < f < 10 kHz, thetime rate of change of pressure detected will vary be-tween 5 x 105 palaec and 5 x 109 pa/see (5 atmos/sec

4-

to 5 x 104 atmoslsec). Assuming the maximum countingerror is one cycle, the maximum error will range from1% at the loweat rate of change to 10-4% at the high-est. The time rate of change of pressure versus fre-quency is given in Fig. 4.14 for various lengths of fi-ber. For lengths as short aa 0.1 m a significant errorwill ariae due to the uncertainty in the number ofturns. This source of error will decrease as theber of turna increases.

PRESSURE APPLIEDBC TO MANDRELTO

LASERn

)

CHANGE THELENGTH OF FIBER

I

R SENSOR

59 ‘ANDRE’1!BC

L# u PHOTODETECTORS

num-

Fig. 4.13 A homodyne Mach-Zehnder-type interferometerdetection aystem.

,.3

,.2 -

~

co

~

~

= 100 -av

1(J’

Icrz,.2 103 104

OUTPUT FREQUENCY (Iiz)

Fig. 4.14 Relation between time rate of change ofpressure and frequency for varioua lengthsof optical fiber.

The above derivation assumed hydrostaticpressure. Thua, the change in preasure acrosa the sen-sor muat be smell compared to the rate of change beingmeasured. For a senaor whose dimension along the direc-tion of propagation ia 3 cm, and assuming the velocityof propagation for sound at high pressure or for a shockwave to be 3000 mlaec, the pressure differential acroasthe sensing element will be 0.5 atmos, or one part in105 of the pressure change being measured.

7

Next consider the other extreme: the detec-tion of changes in length (or more exactly, phase) verymuch smaller than a wavelength, such as 10-6 radians.Any large amplitude drift (change) greatly increasesthe difficulty of measuring small changes. The signalto be considered will appear as a small amplitude per-turbation as was shown on the upper curve in Fig. 4.15.The sensitivity to phase changes varies as the slopeof this curve. Thus, the lower curve, obtained by tak-ing the derivative of the photodetector output withrespect to$ is the phase sensitivity for amall ampli-tude changes. The maximum sensitivity occurs for oddmultiples of T/2 while zero sensitivity occurs for evenmultiples of n/2. This is shown in Fig. 4.15. Here thephotodiode current is plotted against the bias (phase)angle. In order to demonstrate the sensitivity, a cw(sinusoidal) signal of amplitude ~ 10” (electrical de-grees) is superimposed about a bias (quiescent or op-

----=-.—.—I

I

+CURRENT OUT

5Klxa I

I >\U8

I PHASE VARIATION II

s61L

-20 0 20 40 60 80

BIAS ANGLE(”)

Fig. 4.15 Sensitivity of fiberopticat O“ and 90° bias angle.

100 120 140

homodyne sensor

crating) point at O“ and at 90”. The amplitude of theresulting output current is obtained by projecting thephase oscillation (input signal) upward on to the solidcurve graphically and plotting the resulting output cur-rent about a horizontal line as is normally done graph-ically with any transfer function. At 90° the resultingcurrent is large and of the same frequency as the inputsignal. At O“ bias however the amplitude of the photo-detector current is small and exhibits a frequency twicethe excitation frequency because oscillation is on bothsides of the maximum. Thus, consider such a signal in-itially at the 90” bias point. Now for the magnitude ofinput signal shown in Fig. 4.15, if the 90” relativephase between the two arms of the interferometer driftstoward the 0° point, the amplitude of the photodetectorcurrent would decrease, and at leas than 10° biaa asecond harmonic would appear. The current amplitudewould become minimum at 0° bias at which point the fun-damental component will have become zero with only asmall second harmonic left. This process is referred toas fading. The 90” bias condition is known as quadra-ture. l%is mode of detection is called homodyne detec-tion.

4.2.2 Homodyne Detection Applications

As pointed out in the discussion above, homo-dyne detection requires quadrature operation and in ad-dition some means of compensating for large amplitude

4-8

drift. In addition laser noise reduction will be shownto be necessary.

A schematic of the Mach-Zehnder fiberopticinterferometer using phase-locked homodyne detection isshown in Fig. 4.16. The light in the laser beam is

O U T P U T

S I G N A L“4+ 3dS COUPLER

REFERENCE ARM/

SENSING ARM

HIGH PASSF ILTE R $p K(

-SIGNAL

LOW PASS I SIGNAL & NOISE

FILTER 3CU3COUPLER

ePHOTODIODES

AMPLIFIER& SUMMER

Fig. 4.16 A Mach-Zehnder fiberoptic interferometeremploying phase-locked homodyne detection.

split by the 3-dB coupler into the two arms of the in-terferometer. The arm on the right is taken to be thesignal arm and the arm on the left is taken to be thereference arm. The latter contains the phase shifterdescribed below. The light through the two arms is re-combined by the lower 3-dB coupler that converts thephase modulation to an intensity modulation. The twooptical outputs of the 3-dB coupler are each photode-tected. The electrical outputs of the two photodetec-tors are fed into a differential amplifier. It in turnfeeds the compensator circuit. The compensator circuitprovides an output signal, the signal required for thephase shifter, and a reset signal. A detailed discus-sion is given in the next subsection.

There are many types of laser noise, such asphase noise, amplitude noise, and noise due to multi-mode and satellite mode operation. This is especiallyimportant when the source is a diode laser that isclosely coupled to a fiber.

4.2.3 Phase Noise

The output noise of the interferometer in dBVas a function of path length difference between the twoarms of the interferometer expressed in millimeters isshown in Fig. 4.17. The system noise determines theminimum detectable phaae shift. The minimum detectablephase shift, measured in a 1 Hz bandwidth, is shownplotted in radians using the ordinate scale on theright in Fig. 4.17 (see Ref. 1 in Subsection 4.2.8).Experimental data is given for 50 Hz, 500 Hz and 2 kHz.The interferometer was operated in quadrature. On thelog acales used, a straight line plot of decreasingnoise at each frequency is obtained as the path lengthis reduced. Notice that varying the path length from 1mm to 1000 mm, that is, to 1 meter, results in a 60 dBincrease in output noise. The curves shown terminateat a 1 mm path-length difference, but data points cor-responding to a 0.1 mm path difference are shown forall 3 frequencies. As can be seen, little further re-duction in output noiae is achieved by decreasing thepath-length difference from 1 to 0.1 mm. Thus, if thearms of the interferometer are matched to within 1 mm,phase shifts of 10-6 radians can be detected at 2 kHz.Attempts at reducing the path length difference to lessthan 1 mm would be futile. This is due to the fact thatfor an interferometer whose arms contain as much as a

100 meters of fiber, length changes on the order of 0.1mm can be expected as a result of changes in tempera-ture, presaure, tension, and other environmental condi-tions.

I I01 1 10 100 1000

PATH LENGTH DIFFERENCE (mm)

Fig. 4.17 Variation of homodyne interferometer outputnoise as a function of sensing arm pathlength difference for several output fre-quencies.

After A. Dandridge, et al., Appl. Phys. Lett. ~, 77(1981)

4.2.4 Amplitude Noise

Common mode rejection refers to a method forthe elimination of laser amplitude noise. Expressionsfor the optical intensity at the two output ports ofthe lower 3-dB coupler that was shown in Fig. 4.16 are:

11 = (1/2)(1 + ~sin~st) (4.19)

and

12 = (1/2)(1 - ~sinust) (4.20)

where I is the output optical intensity (power) of thelaser minus the various insertion and fiber absorptionlosses. Aa is the amplitude of the phase shift produc-ed by a signal of angular frequency us. Conservationof energy dictates the plus and minus signs in Eqs.(4.19) and (4.20) respectively. Summing Eqs. (4.19)and (4.20) yields I as required. Multiplying Eqs. (4.19)and (4.20) by 1 + AI/I where AI/I is an amplitude fluc-tuation whose ma nitude is the same order of magnitudeas As, e.g. 10-5 or 10-6, yields:

211 = I + AI + IAssinost (4.21)

and

212 = I + AI - IAssin@st (4.22)

where higher order terms in the infinitesimals AI/I andAs are neglected. Subtracting Eq. (4.22) fromEq. (4.21)results in the expression:

11 - 12 = IAa sinost (4.23)

Thus, the fluctuation in laser optical output amplitudeis eliminated. The subtraction is actually accomplish-

4-9

ed electrically in the differential amplifier follow-ing the photodetector as was shown in Fig. 4.7.

Experimental verification of common mode re-jection is shown in Fig. 4.18 (see Ref. 2 in Subsection

6-aII

~ 10.0 ~k OUTPUT FROM ONE PORTFmu(nu 1.0 -ILwda 01 -!3 OUTPUT OF BOTH PORTSu

USING COMMON-MODE REJECTION/ha

Fig. 4.18 Minimum detectable phase shift versus fre-

quency in a fiberoptic homodyne interfero-metric sensor using common-mode rejectionof laser amplitude noise.

After Dandridge and Tveten, Appl. Phys. Lett. ~, 2337(1981).

4.2.8). The minimum detectable phase shift, expressed inmicroradians, is plotted versus frequency. The squaresrepresent the output from a single port of the interfer-ometer. The solid line is the average of these points.The circles are the data obtained when the output fromboth of the ports of the interferometer are detectedand the different signals taken. By comparing theseresults it is seen that an order of magnitude decreasein the minimum detectable phase shift is achieved atlow frequency. At frequencies above 1 kHz a minimum de-tectable phase shift of 0.1 urad (10-7 radians) is ac-complished. This is representative of the kind of sen-sitivity that canbe achieved when common mode rejec-tion is employed and the arms of the interferometer arematched to within 1 mm as was the case in this experi-ment. Laser noise due to satellite modes and multimodeoperation was also eliminated.

4.2.5 Satellite Modea and Multimode Operation

The influence of various amounts of opticalfeedback on the modal output of a Hitachic HLP 1400diode laser is shown by the output spectrum of thelaser plotted for varioua conditions of optical feed-back as shown in Fig. 4.19 (see Ref. 3 in Subsection4.2.8). Spectrum (a) is for the free running laser witha spectral width of 5 MHz. The spectra (b), (c), and(d) illustrate the effect of increasing amounts of feed-back (from 0.04% to 1.5%). Notice that for spectra (b)and (c) the horizontal scale remains the same (i.e.,from -0.2 to +0.2 A) but for spectrum (d) the scale haschanged, going from -6.0 to +6.0 A. The second andthird curves correspond to 0.04% and 0.06% feedback.Here satellite modes appear and increaae as the amountof feedback increases. Such satellite modes arise asthe result of coupling two resonant cavities: one thelaser itself and the other the resonant cavity formedby the length of fiber from the laser to the primaryreflection. Effects due to optical feedbacks of up to0.06% are eliminated when the interferometer lengthsare matched to within lmm.

(a)

&

AFREE RUNNING

Av = 5MHZ

(c)

(b) I

11u0.2 0 0.2 0.2 0 0.2

A ASATELLITE MODES

Av = 0.02GHz Av= .12GHz0.04% 0.06%

FEEDBACK FEEDBACK

(

606

AMULTIMODES

Av = 5GHZ

1.5%FEEDBACK

Fig. 4.19 Influence of optical feedback on the modaloutput of a Hitachi HLP 1400 diode laser.

Adapted from R. Miles et al., Appl. Phys. Lett. ~,990 (1980).

Spectrum (d) shows the effect of 1.5% feed-back. Multimode laser operation results. In order toeliminate this effect, the back reflections into thelaser must be maintained below approximately 0.06%.This is achievable with care. To accomplish this, itis necessary to assure that reflections from the endof the fiber are avoided. This requires the use ofindex-matching liquid between the laser and the fiberand furthermore the end of the fiber must be cut at aslight angle. All splices and couplers have to becarefully fabricated in order to reduce insertion loss.In the discussion of connections, it was shown thatfiber misalignment would lead to insertion loss. Thesesame misalignments will also lead to undesirable re-flections.

4.2.6 Phase-Locked Loop Operation

The circuitry required to provide and insurequadrature operation in the presence of low frequencydrift is shown schematically in Fig. 4.20 (see Ref. 4

UNBIASEDTWO STAGE INTEGRATOR,

PHOTODIODESAMPLIFIER.

CIRCUIT

M / I

RESET

KO

- /)+“+\ TO PZT PHASE SHIFTER

J L 1

w/KD

/DIFFERENTIALAMPLIFIER FOR

COMMON MODEREJECTION t

AMPLIFIER, HIGH PASS..,FILTER. CUT OFFAT

LOW FREQUENCYLIMIT OF SIGNAL RANGE

BANDPASSOUTPUT

Fig. 4.20 A phase-locked loopCuit.

homodyne detection cir-

in Subsection 4.2.8). TWO photodiodea are shown on theleft. The photodiodes are operated in an unbiased con-dition in order to eliminate dark current noise. Their

4-10

outputs are combined in a differential amplifier thatprovides common-mode rejection as well as amplifica-tion. This is followed by two stages of integrationthat provide additional amplification. These two inte-grator-amplifiers pass all signals from DC up to thehigheat frequency of interest. The output of the twostage integrator-amplifier is applied to a phase shift-er located in the reference arm of. the interferometer.The phase shifter consists of either a lead zirconate-lead titanate (PZT) cylinder around which the fiber inthe reference arm is rather tightly wound or a sectionof polyvinylidene-floride (PVDF)-jacketed fiber. BothPZT and PVDF are piezoelectric materials. The outputof the integrator-amplifier is just equal to the lowfrequency noise and the signal of interest. The effectthen is to produce a phase ahift in the reference armequal to that in the sensing anm, causing the interfero-meter to remain balanced, i.e., to phase-lock the sys-tem. If the phase were exactly locked there would beno output signal from the interferometer. However,there must be an error signal at the photodetectors inorder to have a feedback signal. The amplification inthe feedback circuit thus increaaes the error signalfrom the interferometer back up to the level of thesignal being detected. If the system is initially ata bias (operating or quiescent) point away from quadra-ture there is insuffient output from the interferometerfor the compensation circuit and the system till tendto drift toward an increasing error signal and there-fore toward quadrature.

The signal out of the compensating circuit isalao fed through a high-pass filter that has its lowfrequency limit set at the lowest frequency of interest.Therefore, the resulting output is a band of frequen-cies corresponding to the frequency range of interest.This constitutes the output of the interferometric sen-sor.

Operational amplifiers (OPAMPS) are used inthe feedback circuit and combined metal oxide semicon-ductor (CMOS) components in the reset circuit. Thelevels of voltage that can be applied by these circuitsto the phase shifter are the order of + 10 volts. Onthe other hand, the range that the ph~se shifter canaccommodate ia hundreds or thousands of volts. Furthe-rmore, in many cases the amplitude of the phase driftresulting from temperatuze or pressure changes is muchlarger than the phase shift that would be generated byapplying ~ 10 volts to the phase shifter. Thus, it isnecesaary to keep track of how much voltage has beenapplied to the phase shifter and if the limit of thecircuit begins to be reached it is necessary to rapidlyreset the circuits back to the initial condition fromwhich point it can start over. This is the purpose ofthe reset circuit indicated in Fig. 4.20. The phaaechange associated with a large amplitude slow drift iscompensated by a number of saw toothed-like amall ampli-tude phase changes. Care must be taken to minimize thenoise introduced during the reset process.

The upper frequency at which a measurementcan be made is limited by the resonant frequency in thephase shifter itself. Phase-locked loop homodyne de-tection is particularly useful for frequencies below10 kHz. On the other hand, for casea where it is de-sired to make measurements at higher frequencies, sayfrom a few kHz up to nearly a megahertz, heterodynedetection may be desirable.

4.2.7 Heterodyne Detection

Heterodyne detection is relatively insensi-

tive to optical intensity fluctuations and low frequen-

cy noise. Phase trackers and the associated circuitsare not required. An interferometer employing hetero-dyne detection is ahown in Fig. 4.21. The aystem dif-

r UJO+ SolMHz aLINEARFMDISCRIMINATOR

‘A

OU;PUT

Fig. 4.21 A interferornetric fiberoptic senaor employ-ing heterodyne detection.

fers from the usual heterodyne syatem in that uae ismade of two Bragg cells. The firat cell also servesas a 3-dB coupler. By placing a star coupler (or plait-ed 3-dB fiber coupler) at points A and B it should bepossible for a single diode laser and one pair of Braggcells to serve as the optical source for several dozenaenaors. For the Bragg frequencies indicated in Fig.4.21, bulk Bragg cells are required. In thia caae GRINrods must be used to focus the light in and out of thefiber. If surface acoustic wave (SAW) Bragg cella areemployed, they must be operated at approximately 600klllz (with a difference of 100 kHz). If the lowest sig-nal frequency of interest is fs, the oscillator mustexhibit phase noise less than -120 dB/Hz at an offsetof fs from the carrier frequency. The plot of singlesideband phase noise versus displacement from the car-rier frequency for two oscillators is shown in Fig.4.22. The curve that corresponds to 600 MHz shows that

5u -70

u~ -80$1 -90w~ -1oo

z -110

nz -120<flj -130Qm -140y -150a~ -160m

I

60-100 MHz

1 , ! !

101 102 ,03 ,04 105 ,.6

FREQUENCY REMOVED FROM CARRIER

Fig. 4.22 Typical single-sideband phaae noise measur-ed relative to the carrier in a 1 Hz band-width in a fiberoptic interferornetricheterodyne sensor using fixed-frequencycrystal osallators as shown in Fig. 4.12.

4-11

the aingle-sideband phaae noiae intercepts the 120 dBlevel at about 1 kHz. The acoustooptic modulator driverequirement is approximately +33 dBm. Asauming an out-put of +10 dBm from the oscillator the amplifier shownmust provide 23 dBm of gain.

The maximum optical power that a channel wave-guide will handle is about 120 uW. One pair of Braggmodulators configured as shown in Fig 4.21 could supplyseveral sensors. However, with only 120 pW into thefirst Bragg cell it would not be possible to providesufficient optical intensity to the detectors to insurequantum-limited operation for more than four sensors.Thua, for the operation of several dozen senaors from aaingle laser and one pair of bulk Bragg cells, hetero-dyne detection must be uaed.

The difference frequency constitutes a heter-odyne frequency of 100 kHz for the heterodyne detectionconfiguration shown in Fig. 4.21. This permits the useof low-frequency, low-noise electronic circuits, suchas low-noise amplifiers and FM discriminators. Sinceheterodyne detection is relatively insensitive to opti-cal intensity fluctuation and low frequency noise,phase tracker circuits are not required. As in thecase of homodyne detection, there may be a need forpolarization-preserving fiber in order to prevent sig-nal loss. Also, Bragg cells that are highly atable re-lative to each other, are required. Finally, in hetero-dyne detection, aa in homodyne detection, optical feed-back into the diode laser greatly increases the laaernoise. Thus it is necessary to employ the aame precau-tions as were indicated above for homodyne detection.

A number of other detection schemes have beensuggested and are currently being considered. Theseinclude simple homodyning employing a 3 x 3 coupler inplace of the input coupler (see Ref. 5 in Subsection4.2.8). It can be ahown that this resulta in an operat-ing condition very close to quadrature. Syntheticheterodyne operation is another. A high frequency dith-er is employed on the phase stretcher. The output ofsuch an interferometer can be shown to exhibit the char-acteristics of a heterodyne system.

In view of the significant effort being ap-plied to the detection problem further improvements canbe expected; however, such effort la also an indicationthat the optimal detection acheme haa not been achieved.Numerous trade-offs are required. Theae include fre-quency range, sensitivity, dynamic range, cost, and com-plexity of the detection circuitry.

4.2.8 References

1.

2.

3.

4.

5.

A. Dandridge, A. Tveten, R. Miles, D. Jackson, andT. Giallorenzi, “Single-Mode Diode Laser PhaaeNoise”, Appl. Phya. Lett. 38, 77 (1981).—

A. Dandridge and A. Tveten, “Noise Reduction inFiber-Optic Interferometer Systems”, Appl. Opt.20-, 2337 (1981).

R. Miles, A. Dandridge, A. Tveten, H. Taylor, andT. Giallorenzi, “Feedback-Induced Line Broadeningin Cw Channel-Substrate Planar Laser Diodes”, Appl.Physica. Lett. 37, 990 (1980).—

K. Fritsch and G. Adamovsky, “Simple Circuit forFeedback Stabilization of a Singlemode OpticalFiber Interferometer”, Rev. Sci. Instrum. ~, 996(1981).

S. Sheem, “Fiber-Optic Gyroscope with [3x3] Direc-tional Coupler”, Appl. Phys. Lett. 37, 869 (1980).—

4.3 INTEGRATED OPTICAL CIRCUITS (IOCS)

The optical counterpart of the field of inte-grated electronics is the field of integrated optics.However, though integrated optical circuita have beenmade, they are for the moat part not commerciallyavailable. They are the subject of extensive researchand development efforta at a large number of laborator-ies. The goal of these efforts is to commercially fab-ricate in large quantities these miniaturized deviceswith interconnected waveguides all on a single sub-strate. The generation, detection, propagation, modu-lation, switching, and coupling of light on such sub-strates have been accomplished. Techniques for thefabrication of substrates and the production of thehigh resolution material distribution patterns requiredfor these integrated optical circuits exist. Mostintegrated optical circuits and associated deviceaoperate in a singlemode, therefore they are compatiblewith singlemode optical fibers. In essence most LEDs,diode lasers, and photodiodea are integrated opticdevices. Integrated optical circuits are consideredhere because they are a part of second generation fiber-optic sensor technology.

The waveguides used in integrated opticalcircuits are usually of two types namely planar films,that confine the light wavea in the vertical direction,and planar strips, (channels) that confine lightwavesin two dimensions. In both caaea, the waveguides aremade of a higher refractive index than the surroundingmaterial. Light is trapped in the layer or channel inmuch the same way that it is trapped in the core of anoptical fiber. These planar waveguides can be formedby sputtering glass on a substrate of lower refractiveindex. A very uaeful type of channel waveguide can beformed by evaporating titanium (Ti) onto lithium ni-obate (LiNb03) or lithium tantalate in the desiredwaveguide patterns, and diffusing the Ti into the aub-strate thus forming a channel of higher refractive in-dex. This is shown in Fig. 4.23. The attenuation in

“’’”’””-rLiNb03

&

SUBSTRATE

OPTICAL “1n2

CHANNELnl>nz

Si02_

n1>n2>n3

ELECTRODES—

(A) TITANIUM STRIPON LiNb03SUBSTRATE

(B) TITANIUM DIFFUSEDATHIGH T INTO SUBSTRATEFORMING CHANNELWAVEGUIDE

(C) PROTECTIVE LAYEROFSi02 SPUTTEREDON SURFACE

(D) ELECTRODES APPLIED

Fig. 4.23 Steps in the fabrication of a channel wave-guide.

auch channels is typically 1 dB/cm. A protective layerof silicon dioxide (Si02) ia often sputtered on top inorder to protect the surface. Electrodes may be deposit-ed on the Si02.

4-1

Coupling a fiber to an integrated optic chan-nel has been accomplished as shown in Fig. 4.24. The

1 v “’SILICONSINGLE-MODE FIBEti

IN ALIGNMENTV-GROOVES IN SILICON

Fig. 4.24 An optical fiber pigtailed to a lithiumniobate (LiNb03) fiberoptic chip.

fiber is aligned and epoxied in an etched silicon (Si)V-groove. The fiber end and the Si edge are polishedand butted against the polished edge of LiNb03. Index-matching liquid is used between the fiber and substrateends. Similar techniques are uaed to couple diodelasers and photodetectors to the substrate. The dimen-sions of channel waveguides are close to those of bothainglemode fiber corea and the radiating areas of stripegeometry diode lasers. For stripe geometry, the longdimension of the channel should be oriented perpendicu-lar to the long dimension of the radiating area of thediode. Insertion leases as low as a few dB can beachieved.

Channel-to-channel couplers can be formed onthe integrated optical circuit aubstrate by parallelingtwo channels in cloae proximity to each other for asufficient distance to achieve the desired couplingratio. The coupling length is defined as the distancerequired for complete power transfer to occur. Thelength required to achieve a apecified coupling ratiodepends on the separation between channels and the re-fractive indices of the channels and subatrate. Therefractive index of LiNb03 ia a linear function of theapplied electric field. This is known aa the Pockelseffect. Thus, if electrodes are applied as shown inFig. 4.25, the refractive index can be varied and thelight can be awitched to the other of the two outputports of the coupler. The direction of the electricfield is oriented oppositely in the two channels result-ing in equal and opposite refractive index changes.When the proper value of voltage is applied, the coupl-ing length is made ahorter and the light will exit fromthe same fiber it entered. When the voltage is not ap-plied, the coupling length is longer and the light willemerge from both ports. The exit channels from thisswitch may be combined to form the Mach-Zehnder inter-ferometer shown in Fig. 4.26. The result is an electro-optic intensity modulator. When the light wavea recom-bine they excite the fundamental mode of the exit chan-nel. When they arrive out of phase they tend to excitethe aecond mode but the second mode can’t propagate inthe singlemode channel, therefore it radiatea.

An acoustooptic modulator (Bragg Cell) isahown in Fig. 4.27. The interdigited ultrasonic trans-ducer is shown at the bottom. The surface acoustic wave

2

sets up periodic spatial fluctuations in the refractiveindex of the waveguide. These act as phase gratingsdeflecting a portion of the lightwave incident perpen-dicular to the resulting grating. The lightwave thatpasses straight through the grating exits with its fre-quency unchanged, while the diffracted ray has its fre-quency shifted by an amount equal to the acoustic fre-quency, e.g., 500 MHz. Such Bragg cells can be usedfor optical heterodyning.

nl—An n, +dn

+ l-l+

ELECTRODES ( n. > LiNb03

+h - , , /s.BsTRATE

WAVEGUIDE

INCIDENT BEAMJ

Fig. 4.25 A Pockels effect electrooptic binary switchmounted on a lithium miobate substrate.

MODULATED LIGHT OUTA ,-

OP

POLARIZ

Fig. 4.26 A Mach-Zehnder interferornetric electroopticintensity modulator mounted on a lithiumniobate (LiNb03) substrate chip.

4-13

ACOUSTIC ABSORBERFREQUENCY

I SHIFTED BEAM

ACOUSTICSURFACE WAVE —–—=

LIGHT-—

INCIDENT——.

/’UNDIFFRACTED

/ BEAMOPTICAL FIBER

/’

/ ‘ E3--INTERDIGITED

CHANNEL TRANSDUCERWAVEGUIDE

ACOUSTIC ABSORBER

Fig. 4.27 A Bragg cell integrated acoustic modulatorin which an interdigital transducer is usedfor frequency shifting in accordance withan electrical input signal that develops anultrasonic wave in a bifurcated opticalwaveguide.

Technology exists for integrating an array ofchannel couplers connected to an array of photodiodeswith charge-coupled device readout all on a single sub-strate. Using flip-chip techniques (mounting the chipface down) multiple fiber pigtails can be attached toa single chip. Such integrated devices promise to sig-nificantly reduce the size and cost of arrays of opti-cal sensors.

CHAPTER 5

FIBEROPTIC SENSORS AND COMPONENTS

5.1 PHASE MODULATED FIBEROPTIC SENSORS

5.1.1 General

A large variety of phase-modulated fiberopticsensors have been demonstrated, including acoustic,electric, magnetic, rate of rotation, acceleration,electric current, trace vapor, pressure, and tempera-ture sensors. They are being applied to hydrophores,magnetometers, gyroscopes, accelerometers, and otherdevices. These devices exhibit numerous advantages,the most important of which are geometric flexibility,immunity to electromagnetic interference (EMI) andelectromagnetic pulses (EMP), large bandwidth, andgreat sensitivity i.e., ability to detect extremely lowsignal levels and small signal level changes. Phaseshifts as small as 10-7 radians have been detected (SeeRef. 1 in Subsection 5.1.7 at the end of this section).For a wavelength of 0.83 microns, this is equivalent toa length of approximately 10-14 meters, correspondingto the size of an atomic nucleus. Transduction, i.e.phase shifting, occurs as a lightwave travels through-out the sensing length of the optical fiber. Coherentlight sources, singlemode fiber, and relatively complexoptical and electronic circuitry are required.

Considershown in Fig. 5.1.

the Mach-Zehnder interferometerPhase-locked loop homodyne

LASER

detec-

m“:oDEsFig. 5.1 A phase-locked loop Mach-Zehnder-type homo-

dyne-detection interferometer that cnnvertsphase modulationmodulation.

tion, which is especiallybetween 10 Hz and 20kHz, ismode fiber-ui~tailed diode

to intensity (amplitude)

suitable for frequenciesshown. Light from a single-laser is divided eaually

between the” ~ms of the interferometer using a ‘solidstate 3-dB fiber coupler. The sensing portion of thesensor arm is designed to respond to the field to bemeasured while the remainder of the sensing and refer-ence arms are insensitive. The two beams of light

5-1

that have traveled independently through the two armsare recombined by a second 3-dB coupler that convertsthe phase-modulation to an intensity-modulation. Theamplifiers and summing circuits combine the electricalsignals from the photodiodes, one for each of the twooutput optical ports from the 3-dB coupler, in such amanner as to reject common mode noise, e.g., laseramplitude fluctuations. An integrator completes thephase-locked loop. The output signal is filtered toeliminate low frequency noise. In an alternate ar-rangement, both arms of the interferometer have a por-tion that is sensitive to the field being measured.These portions are spatially separated and thereforethe combination is sensitive to the gradient of thefield being measured. Using a homodyne detectionscheme in a phase-locked loop configuration, phaseshifts as small as 10-7 radians have been measured atfrequencies above 1 kHz. The phase shifter in the refer-ence arm is used as part of the phase-locked loop. Thephase shifter can be fabricated by winding the fiberaround a PZT stretcher or by applying a piezopolymerjacket on part of the fiber. In either case, the outputof the amplifier/integrator circuit is applied to thephase shifter causing a phase modulation in the refer-ence arm of the interferometer equal to that in thesensing arm. With this arrangement, the phase relationbetween the two arms of the interferometer is lockedat the point of maximum sensitivity. This is known asquadrature operation.

Various fiberoptic sensnr configurations areshown in Fig. 5.2. A planar arrangement is shown in

SPATIAL SHADING

aGRADlENT

Fig. 5.2 Optical fiber configurations used in fiber-optic sensors.

the upper left. The linear array of spiral wound sen-sors in the lower left is suitable for beam forming.A spatially shaded element, such as in the upper right,where the spacings between windings vary according toa Gaussian distribution, possess a beam pattern exhi-biting greatly reduced side lobes. Finally, the grad-

ient configuration in the lower right is produced byutilizing both arms of the interferometer aa spatiallyseparated sensors.

5.1.2 Fiberoptic Acoustic Sensors

5.1.2.1 Acoustic Pressure Sensors

Extending the discussion for an acoustic sen-sor in Subsection 4.2.1 and considering Eqa. (4.7) and(4.8), the pressure variations associated with a soundwave produce phase fluctuations given by:

A$ = kA(nL) = k(nAL + LAn) (5.1)

A$ = kL(nAL/L + An) (5.2)

where AL/L is the axial strain, S11; k is the wave num-

ber; n is the refractive index of the core; and An isgiven by:

An = -(n3/2)[(Pll + P12)S12 + P12S11] (5.3)

where Pll and P12 are the Pockel’s coefficients and S12is the radial strain. A constant volume assumptionyields the relation S12 = -S11/2. This assumption isvalid only for a material whose Poisson’s ratio is closeto 0.5. It is also quite good for the polyester jacketmaterial Hytrelc, but not as good for fused silica.These materials exhibit values of Poisson’s ratio equalto 0.483 and 0.17 respectively. More exact treatmentssre given in Refs. 2, 3, and 4 in Subsection 5.1.7.Substituting these relations into Eq. (5.3) yields:

A$ = kLn[l+(n2/4)(Pll - p12)]Sll (5.4)

In fused silica Pll = 0.12, P12 = 0.27 and n = 1.46.Substituting into Eq. (5.4) results in:

A$ = 0.92kLnSll (5.5)

For an isotropic material:

AL/L = Av/3v :(1/3V)(~V/aP)AP (5.6)

where AL/L = S11 is the axial strain, V iS the volume,P is the applied pressure and (1/V)(aV/ap) iS the com-

pressibility, K. Thus:

S1l = (1/3)KAP (5.7)

With Kaa the wave number, Eq. (4.7) in Subjection 4.2.1reduces to $ = kLn. Using this and combining Eqs. (5.5)and (5.7) results in:

A@/@AP = 0.307K (5.8)

The compressibilities of silica and the pol~~ester Hytrelc are 2.7 x 10-11 and 2.67 x 10-10 pascalsrespectively, leading to:

A$/$AP = 8.3 x 10-12 pascal-l

for bare optical fiber and:

A$/$AP = 8.2 x 10-11 pascal-l

for Hytrelc jacketed optical fiber. Experimental valuesof A$/$AP, shown in Fig. 5.3, (See Ref. 5 in Subsection5.1.7) are 4.5 x 10-12 and 1.0 x 10-10 pascal-l respec-tively. The calculated and measured values agree towithin 18% for Hytrelc and a factor of two for fusedsilica. These are quite reasonable agreements espec-ially for Hytrelc where the constant volume assumption

5-2

is more nearly valid. Thus, the phase of a lightwavein Hytrelc-jacketed optical fiber, where the croas sec-tional area of the Hytrelc is much greater than thatof the fused silica, responds to pressure according tothe Hytrelc compressibility. While the results shownin Fig. 5.3 are for jacketed optical fibers, similarresults are obtained when bare optical fiber is woundtightly on a Hytrelc or similar mandrel. In eithercase, the more compressible plastic (either jacketor mandrel), when subjected to fluctuating pressure,carries (atretches or compresses) the optical fiberalong with it.

J

PIJSTICCOAT(lmm)

❑ DD ❑ ODDDU ❑

PLASTIC COAT (O.4 mm)00

Ooooo(looooooooo(x o 0 0

1~lo -In

Q$ SARE

$ ALUMINUM COAT< AAAAAAAAAAA A A 6 A A

1 1 , 1 1 1 10.2 0.4 O.b 0.8 10 12 1.4 16

FREQUENCY (kHz)

Fig. 5.3 Acoustic sensitivity vs frequency for vari-ous typea of optical fiber jacketing.

Adapted from Lagakos et al., Opt. Soc. Am. ~, 460(1982).

The discussion above is valid for the mandrel-wound or thick-jacketed fibers. For thinner jackets,the phase sensitivity is a more complicated functionof the elastic moduli. A low Poisson’s ratio will re-sult in the thick-jacketed limit being approached withthinner jackets. Baaed on the criteria of large com-pressibility and low Poisson’s ratio, Teflonc appearato be an optimum material. In order to demonstrate theeffect of increasing jacket thickness. Ea. (5.2) is re-written as:

A$ = kLn(AL/L + An/n)

= kLN[(l/L)aL/aP +

and therefore, since $ = kLn as

A$/$AP = (1/L)aL/aP +

(1/n)an/aP]AP

indicated above:

(1/n)an/aP)(5.9)

‘CL,Z + Cn,z+cn,r

where CL z corresponds to the first term in the brackets

and the 2n,z and cn,r correspond to the fiber axial andtransverse components of the second term in the brack-ets. The last two terma are both associated with thepressure-dependence of the refractive index, n. Thevarious values of the three components of A$/$AP areshown in Fig. 5.4 (see Ref. 4 in Subsection 5.1.7). Ascan be seen, the thick-jacketed fiber results were ob-tained for a jacket thickness of approximately 600Pm.

A

oem

t0prftcprt

F

cssN

a

--~ I I T I I I I I1! 20 –~ c n.z9

10‘0= ~ n,r% 0.0 ~— -–– –– ––––––––--–- - - - -

*g –10

z –20>

~ –W

%“ –40

$~ -50 -

< –so I I I I I I

100 2(Y2 300 400 500 600

HYTREL THICKNESS (pm)

Fig. 5.4 The components of the per-unit phase changeof a lightwave in a Hytrelc-jacketed fiberper pascal as a function of jacket thick-ness.

fter Lagakos and Bucaro, Appl. Opt. ~, 2717 (1981).

In order to calculate the pressure sensitivityf one meter of Hytrelc-jacketed fiber, consider thexperimental results that were given in Fig. 5.3. The

is 10-~0 pascal-l.easured value of A /@jAP, corresponding to a l-mm plas-tic jacket Solving fOr A$/~ andaking L = 100 cm, n = 1.5, k = 7.4 x 104/cm (for A =.85 microns) yields aA$/$of 10-6 radians for 10Q3ascals. Thus, 103 micropascals produces a one micro-adian phase shift. The pressure sensitivity per meteror this case is 60 dB re 1 micropascal. Increasinghe length of optical fiber to 10 and 100 meters in-reases the pressure sensitivity to 40 dB re 1 micro-ascal and 20 dB re 1 micropascal respectively. Theseesults are only 5 dB greater than the quantum limitedheoretical results shown in Fig. 5.5. Included for

~ \ \— t \ H56EOUIV \

d~ 30 cOATEDFIBE’R 115fiW20ml Y\Y+ I

3 5 10 2 5 100 2 5 1,000 2 5 Io,orm

F R E Q U E N C Y (H,]

ig. 5.5 Variation of acoustic energy spectrum levelas a function of frequency for two coatedfibers along with other noise levels in asea subsurface environment.

omparison in Fig. 5.5, are various ambient noises,uch as shipping, weather and seismic noiaes. Alsohown is the equivalent noise pressure of the U.S.avy’s H56 hydrophore.

The effect of jacketing optical fiber withluminum (measured experimentally) is to reduce the

5-3

value of A~$AP below that of fused silica, as was shownin Fig. 5.3. Theoretical results are shown in Fig. 5.6

--1-a I T I r I I I I

% 0.5 –:

y0.0 -

:

3–0.5 —

~

:–10 -

5~ –15 — CALCIUM ALUMINATE GuSS

Gz# –2.0 —

g: –~,5 -

$

<0 20 40 60 SO 100 120 140

COATING THICKNESS (pm)

Fig. 5.6 Acoustic response (phase shift of a light-wave) in an optical fiber as a function ofcoating thickness.

After Lagakos et al., Opt. Lett. ~, 460 (1982).

(See Ref. 6 in Subsection 5.1.7) for jackets of nickel,calcium aluminate glass, and aluminum. A nickel jacketas thin as 10 microns should reduce the acoustic sensi-tivity of silica fiber to zero; however, the thicknessis critical. On the other hand, a 90-micron jacket ofaluminum is required for zero acoustic sensitivity butthe thickness is much less critical. The variation of‘L,z~ ‘n,z~ cn,r, and A$/@P versus the thickness ofthe the aluminum jacket are shown in Fig. 5.7 (See Ref.5 in Subsection 5.1.7).

4,

--I 2 -z:c1 E n,z

y 0 -––––––––––––-––-----–0

---——g

%* –2 -~

o 20 40 60 80 100 120 140ALUMINUM THICKNESS (pm)

Fig. 5.7 Pressure components per unit sensitivityper unit pressure as a function of aluminumjacket thickness on an optical fiber.

After Lagakoa and Bucaro, Appl. Opt. 20, 2719 (1981).—

5.1.2.2

mined by

Pressure Gradient Sensors

The direction of a sound source can be deter-using either an array of omnidirectional sen-

sors or a pressure gradient sensor. Sensor arrays willbe considered in Chapter 6. Pressure gradient hydro-phores sense the pressure at two closely spaced points.The distance between sensors, S, iS typically much lessthan the wavelength of sound, k, in the propagationmedium, namely water in the calculations that follow.A pressure gradient measurement can be accomplished bymeans of either two distinct sensors, one at each point,or by a single senaor apanning the distance between thetwo points. Both types of sensora will be consideredhere.

Since the output signal from a pressure-grad-ient hydrophore is proportional to the preasure grad-ient, ita reaponse ia proportional to the particle velo-city. Such sensors are therefore often called particlevelocity hydrophores. This is an advantage when operat-ing near a pressure releaae aurface where the particlevelocity almost doublea and the pressure itself goes tozero. The tendency to reapond to particle velocityrenders them more aensitive to flow noiae than omni-directional hydrophores. Thia follows because particlevelocity fluctuations associated with flow are oftenmuch greater than the particle velocity oscillationsassociated with the acoustic signal being measured.Consider the sine wave shown in Fig. 5.8 where the

PA- -I

P

Fig. 5.8 The pressure distribution aa a function ofdistance from the zero-preasure point of asingle pressure wave.

instantaneous acoustic preasure, P, is given by:

p = pAsiI’i (2~/ka)x (5.10)

where pA is the acoustic amplitude, as is the soundwavelength, and x is distance in the same units as ~.The pressure amplitude at x = O and x = S (S <<~) areO and 21rPAS respectively (for small y, siny=y). If oneaensor (or sensing end) iS at x = O and the other at x= S, then the pressure difference to be measured is:

P~n = (2TpA/~s)S (5.11)

At 100 Hz, a gradient aenaor element 10 cm long willdetect a preasure P~n = -27.5 dB re pA. The value ofPdn referred to PA variea 20 dB per decade thua, at10 Hz the value of Pmin which must be detected is -47.5dB re PA. The large acoustic senaltivlty achievablewith fiberoptic acouatic aensors make them especiallydesirable for this application. The variation of P~nwith frequency is shown in Fig. 5.9 for 118 meters and373 meters of optical fiber in each case wound on two2.5 cm diameter Teflonc mandrels spaced 8 cm apart.

5-4

Fig. 5.9

100

90

80HEAVY RAIN

70

60

50

40

SS2 W I N D

30 S P E E D

10 KTS

20

\

13 5 ID 2 5 100 2 5 1,000 2 5 10,000

FREOUENCY (Hz)

V a r i a t i o n of the acouatic energy spectrumlevel aa a function of frequency for a fi-beroptic presaure-gradient hydrophore withother noise levels in a sea subsurface en-vironment.

The calculated reaults shown in Fig. 5.9 isfor the case of the aound wave propagating parallel tothe line joining the two sensors. The sensitivity ofa Preasure gradient sensor to a sound wave propagatingperpendicular to this direction ia zero because bothsensors are then aubjected to the aame pressure. Thedirectivity is dipole-like aa shown in Fig. 5.10(a).The cardioid directional responae shown in Fig. 5.10(b)can be obtained by combining the dipole output withthat of an omnidirectional hydrophore with sensitivityequal to that exhibited by the dipole at e = OO. The

(a) (b)

DIPOLE CARDIOIDPRESSURE GRADIENT PRESSURE GRADIENT

Fig. 5.10 Sensitivity directivity patterna for prea-sure gradient aensors.

cardioid directivity pattern is not drawn to the samescale as the dipole pattern.

For the extended element pressure gradientsensor, consider a neutrally bouyant cylinder of length,s, spanning the distance between the two sensing points.If this cylinder is oriented with ita axis parallel tothe direction of sound propagation, it will experiencea force, F = A(P2 - PI) where A ia the area of the endface, and P1 and P2 are the presaures at the two ends.Pmin in Eq. (5.11) is equal to P2 - Pl, thus:

F=AP~n=mamin (5.12)

and combining with Eq. (5.11) yields:

(5.13)

Since neutral bouyancy is required, m/AS = maaa per unitvolume = 1 and Eq. (5.13) becomes:

tin = (2T/k~)pA (5.14)

Thus, once the sound frequency (wavelength, 1s) andpressure level are chosen, the acceleration can bedetermined. For f = 100 Hz (As = 1460 cm) and PA = 50dB re 1 micropascal, corresponding to the 118-met r

-3curve that waa shown in Fig.(1.6 gal).

= 1.67 X 10 gThis requires an5;1;r~%Ny sensitive ac-

celerometer. The two-fiber accelerometer describedbelow exhibits the required sensitivity.

5.1.3 Fiberoptic Magnetic Sensors

Yariv and Winsor (See Ref. 7) suggested thatan optical fiber could be used to measure the changein length of a magnetostrictive material subjected toa magnetic field. The resulting optical phase changeis linearly related to the magnetic field. Jarzynski,et.al. (See Ref. 8 in Subsection 5.1.7) developed ex-pressions for the strain induced in a magnetostrictive-ly-jacketed fiber subjected to a weak axial magneticfield. These expressions were obtained as a functionof jacket thickness for a variety of magnetostrictivematerials as shown in Fig. 5.11. The magnetooptic

70-1*j

aXO

t 4.5% CO.95.5% Ni10.0

8.0 -

2V-PERMENDUR6.0 -

4.0 -

2.0 -

I , , # 1 # 1 , 1

0 5 IO 15 20 25 30 35 40

METAL JACKET THICKNESS (pm)

Fig. 5.11 Magnetic sensitivity of magnetostrictivemetal-jacketed optical fiber as a functionof jacket thickness for various magneto-strictive metals.

Adapted from J. Jarzynski et al., Appl. Opt. ~, 3746(1980).

coupling coefficient as shown in Fig. 5.12 was measuredfor nickel by Cole, et.al. (See Ref. 9 in Subsection5.1.7) using a nickel cylinder around which the opticalfiber in one arm of the interferometer was wound asshown in Fig. 5.13). The relevant theory has been com-pared with magnetooptical experimental data taken atlow frequency (< 1 kHz) and msgnetomechanical datataken at frequencies greater than several tens of kilo-hertz. Thia study demonstrated that the piezomagneticatrain coefficient remains constant from low frequencyup to the frequency at which eddy currents become im-portant. Therefore, the low frequency measurement re-aults may be uaed to design magnetic sensors that willoperate at high frequencies, i.e., to the eddy currentlimit.

5-5

J10 100 1,000 10,000

FREQUENCY (HZ)

Fig. 5.12 The magnetooptic coupling coefficient ver-sus frequency for an optical fiberwoundnickel toroid with walls 0.038 cm thick.

After J. Cole et al., Opt. Lett. ~, 216 (1981).

\ /-WINDING.

-TOROIDALWINDING

HOUSING

Fig. 5.13 Optical fiber wound on a magnetostrictivenickel toroid (wall thickneas 0.038 cm) foruse in meaauring the magnetooptic couplingcoefficient.

After J. Cole et al., Opt. Lett. ~, 216 (1981).

Magnetoatrictive materials have been used ex-tensively as acoustic transducers for the production ordetection of sound. In the preaent application thesemateriala are used to detect magnetic fields by measur-ing the reaulting atrain produced. The most atraightforward and sensitive technique for such measurementsinvolvea uaing an optical fiber in one arm of a Mach-Zehnder interferometer. The fiber is either jacketedwith the magnetostrictive material or wound around amagnetostrictive mandrel. The resulting change in op-tical path is due to changes in both the refractiveindex and the length of the optical fiber core. Thisleads to a phase ahift A+ given by Eq. (5.5) in Subsec-tion 5.1.2.1. An expression for S11 can be obtainedfrom the effective piezomagnetic strain constant dT de-fined by the expression:

dT = 4n(3S11/aH)T (5.15)

where T is the streaa. Integrating this expressionyields:

Sll = (1/41r) a ‘b dTdH (5.16)

where the limits a and b are Ho-Hi/2 and Ho+H1/2, re-spectively, H. is the dc bias field choaen to ~ximizedT, and HI is a small excursion about that point. For

nickel H. = 3.6 oersteds and for a small excursi n-8about the maximum, dT r~~ains constant at 8 x 10 .

Therefore, S1l = 6.4 x 10 HI and:

@/kLHl = 8.6 X 10 -7 oersteda -1 (5.17)

is the magnetooptic coupling coefficient. This agreeaquite well with the value of coupling coefficient be-tween 7 and 8 x 10-7 measured by Cole et.al. (See Fig.5.12 and Ref. 9 in Subsection 5.1.7). The value of dTused in Eq. (5.16) was measured at approximately 30 kHzand has been shown to be valid up to the frequency atwhich eddy current limitations occur.

Using the measured magnetooptic coupling co-efficient shown in Fig. 5.12, the minimum detectablemagnetic field (oersteds) per meter of nickel-jacketedoptical fiber can be calculated. From Fig. 5.12, forA$ = 7.5 x 10I7 kLH, and using k = 7.4 x 10-4 (for 0.85micron optical radiation), L = 102 cm, and 10-6 radiansminimum detectable phase shift, the minimum detectablemagnetic field for 1 meter of nickel-jacketed opticalfiber is 1.8 x 10-7 oersteds (1.8 x 10-2 gamma). Re-cently a minimum detectable magnetic field of 5 x 10-9oersted per meter of fiber waa measured using opticalfiber jacketed with an amorphous magnetostrlctlve mater-ial (See Ref. 10). Extrapolating to 1 km of such me-tallic glass-jacketed fiber leads to the predictionthat magnetic fields as amall as 5 x 10-12 oersteds maybe detected by this means. On the other hand a one cmlength of such jacketed fiber should permit the meas-urement of a magnetic field as small as 5 x 10-7 oersted(0.05 gamma).

The sensitivities of pressure, magnetic, andtemperature fiberoptic sensors is summarized in Fig.5.14. The cross section configuration of the variousjacketed optical fiber is shown in the middle column.The predicted sensitivities corresponding to one mlcro-radian phase shift for one meter of jacketed fiber isshown in the last column.

SENSOR TYPES

PRESSURE

MAGNETIC

TEMPERATURE

CONFIGURATIONS

op,Geo~

Si02

LASTOMER

a SiO*,0e02SiO*

MAGNETO–STRICTIVE

SiO~

e

Si02, GeO~

METAL

FI?EDICTED PERFORMANCESA~-W-6RAD, lMETER FISER)

P~NX 60dS re #Pa

HMNZ 5xlo”90ERsTED(METALLIC GLASS)

ATMNZ FTSC”

Fig. 5.14 Fiberoptic sensor performance parameters(coefficients) for several fiber

5.1.4 Fiberoptic Electric Current Sensors

jackets.

Two techniques for measuring electric cur-rents are shown in Fig. 5.15 (See Ref. 11 in Subjection5.1.7). In the first, a section of nickel-jacketedfiber is located in the center of a solenoid energizedby the current being meaaured. By measuring the magne-

tic field intensity, the electric current is determined.

5-6

Using this technique a1o-8 A/m waa measuredto 5000 Hz.

minimum electric currentover the frequency range

of 3 x100 Hz

FIBERa

\“I

ALUMINUMFIBER TUBING

Fig. 5.15 Fiberoptic senaors for measuring electricalcurrents.

After A. Dandridge et al., Electron. Lett. ~, 524(1981).

The second technique, also shown in Fig. 5.15,depends on the resistive heating that occurs in a sec-tion of aluminum jacketed optical fiber as a result ofpassing the electric current to be measured through thejacket. Using this technique aminimum detectable elec-tric current of 1.3 x 10-5 A/m was measured at 1 Hz.

5.1.5 Fiberoptic Spectrophones

Spectrophones are used to determine the pre-aence of trace vapors by means of the acoustic signalproduced by the temperature increase associated withthe absorption by the vapor of a pulsed laser output.Conventional microphones are used to detect the acous-tic signal. The schematic of a fiberoptic spectrophone(See Ref. 12 in Subsection 5.1.7) is shown in Fig. 5.16.

339u”ItleNeLASER

06328 ”. H?NeLAsER@

Fig. 5.16 A fiberoptic spectrophone for detecting thepressence of trace vapors.

After D. Leslie et al., Electron. Lett. ~, 581 (1981).

The frequency of the excitation laser is equal to anexcitation frequency in the absorption spectrum of thetrace vapor being detected. The absorption cell con-sists of a thin walled cylinder around which is wounda fiberoptic coil to form one arm of a Mach-Zehnderinterferometer. The fiber coil serves as the micro-phone. It has the advantage of not requiring electri-

cal leads in the vicinity of the vapor. The chopperis operated at a frequency at which the acoustic aenai-tivity of the absorportion cell is high.

The light from the excitation laser excitesa characteristic absorption line in the molecular spec-trum of the vapor being detected. When the excitedmolecules return to equilibrium the temperature of thevapor Is increased resulting in a preaaure increase.By chopping (interrupting) the light at a given rate(frequency), the resultant fluctuation in preasure Isdetected as aound of the same frequency. Even moredesirable 1S to make use of a variable frequency laaeraa the excitation source. The absorption coefficientsvs. frequency of ambient atmosphere and of methanewhose concentration 1S five times ambient are shown inFigs. 5.17 and 5.18.

lo”~WAVELENGTH

Fig. 5.17 The absorption coefficient of ambient at-mosphere aa a function of wavelength.

Provide by D. Leslie, U.S. Naval Reaearch Laboratory.

ABSORBERS

TYPE (TORR)H20 14.260C02 0,251

03 2.3x lC”5N20 2.1 X1 O-4co 5.7 x10-5

II II

CH4 12’1 0-31 1

1~ II~’”i02 159627

22.9°C760 TORR

JJWAVELENGTH

Fig. 5.18 The absorption coefficient of methane gasas a function of wavelength for a concen-tration of 7.6 x 10-3 torr (5 x ambient).

Provide by D. Leslie, U.S. Naval Research Laboratory.

5.1.6 Summary

The acoustic and magnetic field sensors des-cribed above represent primary measurement devices.Other primary measurement devices include sensors to

5-7

measure strains, electric fields, temperature, accel-eration, and rate of rotation. They differ from theacoustic and magnetic senaors discussed above that relyon specialized jacketa and utilize a Mach-Zehnder inter-ferometer. The electric current and trace vapor sen-sors are secondary devices relying on the measurementof the magnetic field or the temperature in the formercase and the aound associated with the absorption oflight in the latter case.

5.1.7 References

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

5.2

D. Jackson, A. Dandridge, and S. Sheem, Opt. Lett.~, 139 (1980).

B. Budiansky, D. Drucker, G. Rino, and J. Rice,APP1. Opt. ~, 4085 (1979).

G. Hocker, Opt. Soc. Am. ~, 320 (1979).

N. Lagakos and J. Bucaro, Appl. Opt. 20, 2716(1981).

—

N. Lagakos, T. Hickman, J. Cole and J. Bucaro,Opt. Lett. ~, 443 (1981).

N. Lagakos, private communication.

A. Yariv and H. Winsor, Opt. Lett. ~, 87 (1980).

J. Jarzynski, J. Cole, J. Bucaro and C. Davia,Appl. Opt. ~, 3746 (1980).

J. Cole, N. Lagakos, J. Jarzynski, and J. Bucaro,Opt. Lett. ~, 216 (1981).

K. Koo and G. Sigel, Technical Digest, Optical Fi-ber Communication Meeting, Phoenix, Arizona (1982)p. 72.

A. Dandridge, A. Tveten, and T. Giallorenzi, Elec-tron. Lett. ~, 523 (1981).

D. Lealie, G. Trusty, A. Dandridge and T. Giallo-renzi, Electron. Lett. ~, 581 (1981).

INTENSITY MODULATED FIBEROPTIC SENSORS

5.2.1 General

The second type of fiberoptic sensor to bediacusaed is referred to as an intensity-modulated aen-sor. Ita basic configuration is sketched in block dia-gram form in Fig. 5-19. The output lightwave from an

+ l~”TOPTICAL

SENSOROPTICAL

SOURCE DETECTOR‘OUT

.

TIMETIME TIME

Fig. 5.19 A generalized intensity-type fiberopticsenaing system.

optical source of constant intensity IIN (shown at thelower left) is injected into the sensing element. Thiselement, acted on by an external force field (basebandsignal), represented in the figure as an incident ainu-soidally-varying quantity, alters the intensity of thelight transmitted through the sensor. The modulationenvelope of the output intensity, IOUT, matches that ofthe input force field (signal). In turn, the time vary-ing output optical intensity, incident on the photode-tector, similarly modulates the output voltage, eo~.

The intensity-modulation sensor shown in Fig.5.19 employs relatively simple optica and circuitry. Anincoherent optical source, such as an LED, or a high-intensity incandescent source, may be used, togetherwith multimode fibers as links between the sensing ele-ment and the source and detector. The sensor itaelftypically consists of one or two multimode fibers orsome mechanooptic, electrooptic or other atraight for-ward transduction element. Achievable sensitivities,expresaed in terms of minimum detectable displacementsfor intensity-type mechanical motion detectors, lie inthe ran e 10-10 to 10-7 m, as compared to a lower limit

fof 10-1 m achievable with interferometric type fiber-optic sensors.

5.2.2 Evanescent-Field Fiberoptic Sensor

To illustrate the various types of intenaitymodulation transduction mechanisms currently under in-vestigation, consider first the evanescent field trans-ducer (see Ref. 1 in Subsection 5.2.6) outlined in Fig.5.20. It consists of a pair of single or multimode op-

L .

OPTICALDETECTOR

d -CORE SPACINGL- INTERACTION LENGTH

Fig. 5.20 .An evanescent-field intensity-type fiber-optic sensor.

tical fibers. In the transduction element itself thecladding is reduced In thickness, or entirely removed,so that the distance, d, between the cores is smallenough to permit evanescent field coupling between thetwo fibers over some small interaction length L. Coupl-ing may be enhanced by potting the interaction responsein a fluid or flexible elastomer of refractive index,nz, the same as that of the cladding. Slight varia-tions of the spacing, d, the interaction length, L, orthe refractive index, n2, induced by the particularforce field of interest may produce substantial changesof the light coupled into the lower or pick-up fiber.Promising results have been reported on two hydrophone-type applications of this modulation mechanism. Furtherstudies are in progress.

5.2.3

shown in

Reflection Coefficient Fiberoptic Sensor

A second intensity-type fiberoptic sensor isFig. 5.21. Its operation is based on changea

5-8

OPTICALDETECTOR

I

:;cm; FIBER SENSOR

\’

C L A D D I N G ‘2

CORE

CLADDING —MIRRORED

Fig. 5.21 A critical-angle intensity-type fiberopticsensor.

After R. Phillips, Opt. Lett. ~, 318 (1980).

in the optical reflection coefficient (See Ref. 2 inSubsection 5.2.6) at the right hand tip of the fiber.Referring to the upper portion of Fig. 5.21, light in-jected into the core at the left end of the fiber ispartially reflected back along the length of the fiberand then directed to the photodetector using a beamsplitter. As indicated in the lower expanded view ofthe right end of the fiber, two reflecting facets arelapped on the end of the fiber. The lower facet iscoated so that it ia totally reflecting. By carefullycontrolling the angle of the upper facet so that thebeam in the core is incident at an angle larger thanthe critical angle, the light in the core will be par-tially transmitted into the medium of refractive indexn3 in contact with the end of the core. Slight varia-tions in n3, induced by changea of pressure or tempera-ture, for example, will change the intensity of thereflected beam. One can thus envisage a probe or cathe-ter-type presaure transducer, of active area equal tothat of the end of the core, i.e., effectively a pointpressure probe, that could be superior in many ways tosome of the more conventional types that are in usetoday.

5.2.4 Moving Grating Fiberoptic Sensor

A conceptually simple intensity-type aensoris the moving grating transducer shown in Fig. 5.22(See Ref. 3 in Subjection 5.2.6). Two fibers are sep-

MOVABLEGRATING

HFig. 5.22 A moving-grating

senaor.

STATIONARY~GRATING

1

I

I

1

nCLADDING

CORE

TODETECTOR—

CLADDING

intensity-type fiberoptic

arated by a small gap in which is placed a pair of grat-ings, consisting of a cyclic grid of totally transmis-sive and totally reflecting (opaque) parallel line ele-ments of equal width. When the gratings are moved rela-tive to one another there is a change In the transmit-ted intensity. This type of transducer has been employ-ed in a hydrophore, as sketched in Fig. 5.23. Here one

DIAPHRAGMn \ n

L

r HYDROPHORE/HOUSING

/

I , I

OPPOSED GRATING

Fig. 5.23 A moving grating intensity-type fiberopticsensor used in a hydrophore.

Adapted from W. Spillman, Appl. Opt. ~, 465 (1981).

of the gratings is shown mounted on the rigid baseplate of the housing while the other is attached to aflexible diaphragm. The diverging lightbeam from theinput fiber on the left is collimated using a shortgraded-index self-focusing (Selfocc) lens and then par-tially transmitted through the gratings as a parallel(collimated) beam that is focused into the output fiberusing a second self-focuaing (Selfocc) lens. Assumingthe two gratings each consist of 5 pm-wide grating ele-ments that are spaced 5 Bm apart, the transmitted lightintensity will vary cyclically as sketched in Fig. 5.24,passing through successive maxima each time the gratingdisplacement changes by 10 ~m. From this graph it may

1.0

0 4 8 12 16RELATIVE DISPLACEMENT (pm)

Fig. 5.24 The relative light intensity transmittedthrough a moving-grating intensity-typesensor as a function of the relative dis-placement of the movable grating.

5-9

be seen that the sensitivity will be greatest when thequiescent or bias point is set at a relative displace-ment of 2.5 pm, 7.5 pm, 12.5 pm, etc. In addition, de-creasing the width of the grating elements will in-crease the sensitivity but decrease the dynamic range.

5.2.5 Microbend Fiberoptic Sensor

The intensity-type sensors to be consideredlast are based on microbend-induced ejection of lightfrom the core of a fiber into the cladding (See Ref. 4in Subsection 5.2.6). Referring to Fig. 5.25, thetransduction element in this type of sensor consistsof a deforming device such as a pair of toothed or se-rated plates that introduce small bends in a fiber. As

F FFIBER

\I

DEFORMER

II

MODE1: E1-sin(LJt-~lz)

MODE2: E2-sin(Ut–~2z)

COUPLING CONDITION: L=—13;:132

Fig. 5.25 A microbend intensity-typeser.

fiberoptic sen-

ahowo in the figure, the distance L between adjacentteeth defines the apatial frequency of the deformer. Byincreasing the force, F, applied to the plates the am-plitude of the deformations can be increased. In theearlier brief discussion of attenuation mechanisms infibera, it was shown that random bends in fibers cancause light to be ejected from the core into the clad-ding. Thia process is illustrated in the enlargementof the deformer shown in Fig. 5.26. Rays propagating

~<................b-- ..,.. . . . . .1

—Y

PcoRE-&D= +Fig. 5.26 The deformation and reaulting coupling of

light from core to cladding that occurs ina microbend intensity-type fiberoptic sen-sor.

in a straight section of the fiber at an angle lessthan the critical angle may have their angle of inci-dence on the core-cladding interface increased by thebends and thus be partially transmitted into the clad-ding. A more detailed wave theory analysis of periodicbend-induced coupling indicates that the level of coupl-ing between modes, including non-attenuating core modesas well as attenuating core and cladding modes, isstrongest when the difference between the effectivepropagation constants of a pair of modes, (Bi - Bj), isequal to 2 /1..

A number of studies of this phenomenon havebeen conducted. For example, the system shown in Fig.5.27 was used at the Hughes Research Laboratories. As

FIBER

L I

1

EO~

DETECTOR MODE DEFORMERSTRIPPER—

Fig. 5.27 A microbend intensity-typesor system developed by theLaboratories.

fiberoptic sen-Hughes Research

indicated in the figure, light was injected into amultimode step-index fiber which was passed through adeformer element. In this case the intensity of thecore light reaching the end of the fiber was monitored.By using a helium-neon laser with a well-collimatedbeam it was possible to vary the incidence angle oflight into the fiber and thus inject light into a fair-ly well defined set of propagating core modes. On sec-tions of the cladding, just before and just after thedeformer, mode strippers were employed. These elements,which in their simplest form might consist of blackpaint applied to a few centimeters of the outer surfaceof the cladding, absorb almost all of the light thatmy be propagating in the cladding of the fiber. Theuse of cladding mode strippers first insured that onlycore light reached the section of fiber in the deformerand then that any core light ejected into the claddingby the deformer was absorbed so that it did not reachthe photodetector.

Uaing the system outlined in Fig. 5.27, theHughes’ inveatigatora measured the transmitted opticalintensity as a function of the force applied to thetransducer (microbend deformer). This was done forseveral different angles of incidence of the input lightand the reaulting data la preaented in Fig. 5.28. Aashown in that figure, when the input incidence anglewas set at 0°, i.e., for light injected along the axisof the fiber, the output intensity decreased by abouttwenty percent as the force applied to the deformer in-creaaed from O to 2 newtons. On the other hand, forlight incident at 9°, the transmitted intensity decreas-ed to approximately 40 percent of the input when theapplied force waa again increased to 2 N. In addition,the slope of the transmission intensity, I, veraus ap-plied force, F, curve was nearly conatant over the

5-1

range 0.5N < F > 1.5 N. In the latter caae, 9“ corres-ponded closely to the critical incidence angle, thusthe light waa injected mainly into the highest orderpropagating modes and therefore was more eaaily ejectedfrom the core into the cladding.

loofiT_..- ,_L1::::-,-

1 I 1 I I I I I I I I I IT – - * — - 0 - - 1

r r ——— O.ODEG .

20 - - - - - 7.ODEG 0-“---”- 8.ODEG ❑ 1

} ------- 9.0 DEG ● 4oo~

0.5 1.0 1.5FORCE N

Fig. 5.28 The percent transmission of core inputlight obtained at the output as a functionof applied force in a microbend intensity-type fiberoptic sensor.

After J. Fields, et al., J. Acouat. Soc. Am. ~, 816(1980).

Using the results of this and aimilar experi-ments, the Hughes investigatora, in cooperation withthe Physical Acouatica Branch of the U.S. Naval ReaearchLabora~ory, deaigned and teated a hydrophore employingsuch a microbend deformer asTheir first prototype unit ia

the transducer element.aketched in Fig. 5.29

/--FIBERLEADS

/DIAPH

Fig. 5.29 A microbend intenaity-type fiberoptic sen-sor hydrophore developed by the Hughes Re-search Laboratories and the U.S. Naval Re-search Laboratory.

After Fields and Cole, Appl. Opt. ~, 3265 (1980),

(See Ref. 5 in Subsection 5.2.6). One deformer platewas rigidly mounted to the cylindrical ahell of thehydrophore while the other was attached to a thin dia-pragm. In addition to the through-put fiber, a secondinactive fiber was included to insure that the deformerplates remain parallel during operation.

At this point it would be uaeful to reviewsome of the basic acoustical levels and unita of meaa-ure. Referring to Fig. 5.30, one frequently encounter-ed acoustic reference pressure level encountered in airacouatics is 0.0002 dynea/cm2. This is the accepted

o

1

TT71 NEWTONIMETER 2

~0 ~B 1 PASCAL (Pa)

1 DYNE/CENTlMETER2

AIR ACOUSTICS

IREFERENCE LEVEL –––

UNDERWATER ACOUSTICSREFERENCE LEVEL . . . . . . - 1 -

4’0.0C02 DYNEICENTIMETER220 MICRONEWTON/METER220 MICROPASCAL

26 dB

1 MlCRONEWTONfMETER21 MKROPASCAL (#Pa)

Fig. 5.30 Pressure levels and units for comparison ofunderwater acoustic pressure referencelevels.

average minimum detectable sound pressure for humans at1000 Hz. Another is the currently accepted 1 m.lcronew-ton/m2 or 1 micropascal (1 ~Pa) reference pressure forunderwater acoustics. To compare these on a decibelscale, recall first that for a pressure ratio, P1/P2,the number of decibels, N, in dB, is defined by:

N = 20 loglo P1/P2 (5.18)

Since 0.0002 dynes/cm2 is equl to 26 upa, the airacoustic reference pressure is 26 dB above the under-water reference pressure. Similarl

J’as indicated in

Fig. 5.30, a pressure of 1 dyne/cm is at a level of74 dB re 0.0002 dyne/cm2 and at a level of 100 dB re1 pPa. Finally, a pressure of 1 Pa corresponds to 120dB re 1 pPa and 20 dBre 1 dyne/cm2. The table present-ed in Fig. 5.30 is an aid in interpreting hydrophorecharacteristics and in performing comparisons presentedhere and in later sections.

Returning to the consideration of the Hughes-NRL microbend hydrophore, an experimental evaluation ofthe acoustic characteristic of their initial prototypewas conducted at NRL. As indicated in Fig. 5.31, thehydrophone was placed in an acoustic test tank and meas-urements were made of its sensitivity and frequency re-sponse over a frequency range of 200 Hz to 2000 Hz. The

H ~ MODE STRIPPER

u \

Fig. 5.31 Test arrangement and sensitivity level ofthe Hughes Research Laboratories and U.S.Naval Research Laboratory microbend inten-sity-type fiberoptic senaor hydrophore.

After Fields and Cole, APP1. Opt. ~, 3265 (1980)05.

results are shown in graphical form in the lower por–tion of the figure. The minimum detectable pressure,in a 1 Hz band and at a unity signal-to-noise ratio,was approximately 100 dB re 1 ma. The 10 dB fluctua-tions about this value were attributed to resonances inthe outer case and deformer mount. It should be possi-ble to eliminate these resonances without much difficul-ty. In addition, a significant increase in sensitivitywas achieved in later designs by employing specially-designed graded-index fibers. This was to be expectedsince the fiber employed in the initial prototype wasa readily available standard communications step-indexfiber. Such optical fiber has been designed to havelow microbend sensitivity to reduce losses due to bend-ing introduced in cabling and other field use distor-tions. By employing graded-index fibers with enhancedmicrobend effects, sensitivity increases of more than40 dB have been achieved. Thus, these improved micro-bend transducers are comparable to many of the moreconventional hydrophores currently in use.

It should be emphasized that with the micro-bend transducers discussed above, attempts are made todetect a very small change in the intensity of a rela-tively intense optical beam. This type of sensor isreferred to as a brightfield microbend transducer. Asecond type of microbend device, a so called darkfieldtransducer, was proposed initially by a group at Catho-lic University and currently is under investigation byseveral different groups. The sensor is shown in Fig.5.32. Beginning at the left, it is quite similar in

FIBER MODEDEFORMER STRIPPER

OPTICALSOURCE

Fig. 5.32 The microbend darkfield intensity-type fi-beroptic sensor system.

arrangement to the brightfield transducer up to and in-cluding the deformer. As with the brightfield trans-ducer described above, light, possibly from a broad-band incoherent source, is introduced into a multimodefiber. Care ia taken to remove cladding light prior tothe deformer. The darkfield transducer differs fromthe brightfield transducer in that the light ejectedfrom the core into the cladding is used to generate theoutput signal.

As indicated in Fig. 5.32, the Catholic Uni-versity group used a more elaborate mode-stripper onthe output section of the fiber (see Ref. 6 in Subsec-tion 5.2.6). The fiber was stripped of ita outer coat-ing and passed through a small chamber filled with arefractive-index matching fluid. A number of photode-tectors mounted in the walls of the chamber respondedto changes in the intensity of the core-to-claddingejected light. In contrast with brightfield, the dark-field case has a relatively low level of backgroundlight that is modulated by changes in displacement ofthe deformer. The degree” -of modulationlarge and thus a very high sensitivitymay be employed without overdriving it.detectable signals should, in principle,in the brightfield case. This has beenrecent studies.

may be quitephotodetectorThe minimum

be lower thanconfirmed in

1

A simplified design of the cladding lightmonitor is indicated in Fig. 5.33. The pick-up fiber

STRIPPER DEFORMER

Io-

SOURCE FIBER FIBER-FIBERCOUPLER

DETECTOR FIBER

kAI

Fig. 5.33 A darkfield microbend intensity-type fiber-optic sensor with a fiber-fiber couplerfollowing the deformer (microbender) de-veloped by the Catholic University.

is directly coupled to the outer surface of the clad-ding of the through-put fiber. Recent studies of thistechnique

darkfield

STR!-R

have ha~ p~omising results.

The design and operation of a linear array ofmicrobend sensors is shown in Fig. 5.34. Each

SOURCE FIBER

DEFORMER

\

STRIPPER DEFORMER

%T

,~fi .- .----

\ ----

K /’FIBER-FIBERCOUPLERS

)

Fig. 5.34 A series of deformers used to control theintensity of light tapped from an opticalfiber bus.

sensor is an assembly consisting of a cladding-modestripper, a microbend deformer (transducer), and a fi-ber-to-fiber coupler. Many of these assemblies may bemounted in series on a single optical fiber bus. Thecladding-mode stripper removes any residual light inthe cladding just prior to the microbend deformer. Thedeformer causes light from the core to enter the clad-ding according to the baseband (information-bearingforce, pressure, or sound) signal. Following the de-former, the coupler removes the light (baseband signal)from the claddlng and dispatches it to a photodetector.

A number of different multiplexing schemescould be used in the detection portion of the array.The moat direct, would be to feed each cladding lightpick-up fiber to a separate photodetector. Temporaland spatial averaging of a number of closely spaced

5-1

transducer outputs could also be accomplished prior tophotodetection. The optical outputs may be combinedwith appropriate time delays determined by the trans-ducer spacings and coupler fiber lengths. On the otherhand, by employing a pulse modulated optical source, itis possible to employ a single return bus fiber intowhich the optical output pulses from the various trans-ducers could be fed. Time domain multiplexing schemescould then be used to identify and process the signalfrom the individual sensors. These and other varioustypes of fiberoptic sensor arrays and the telemeteringof their outputs are discussed in detail in Chapter 6.

This brief description of various intensitytype sensors is not exhaustive. The discussion is aimedat introducing some basic concepts regarding their over-all design and behavior. Many other fiberoptic inten-sity transducers are currently under investigation suchas sensors employing fibers with temperature sensitiveabsorptive dopants, and several displacement and pres-sure transducers employing strain-induced birefringenceas an intensity transduction mechanism. All of thesehave the advantage of being much simpler in design andoperation, but they are less sensitive than interfero-metric fiberoptic sensors. Further improvements, in-cluding increases in sensitivity, are expected for theintensity-type fiberoptic sensors.

5.2.6

1.

2.

3.

4.

5.

6.

s.

R.

w.

J.J.

J.

N.R.

5.3

sensors

References

Sheem and J. Cole, Opt. Lett. ~, 322 (1979).

Phillips, Opt. Lett. ~, 318 (1980).

Spillman, Appl. Opt. ~, 465 (1981).

Fields, C. Asawa, O. Ramer, and M. Barnoski,Acoust. SOC. Am. Z, 816 (1980).

Fields and J. Cole, Appl. Opt. ~, 3265 (1980).

Lagakos, T. Litovitz, P. Macedo, R. Mohr, andMeister, Appl. Opt. ~, 167 (1981).

FIBEROPTIC LINRAR ACCELEROMETERS

The operation of interferometric fiberopticdescribed in Section 5.1 depends primarily on

phase changes associated with force-field-induced mecha-nical strains. Similarly the two-fiber optical accel-erometer described in this section makes use of thechange in fiber length due to a force resulting fromthe acceleration of a mass suspended between two fibers.The effect is to increase the tensile stress in the fi-ber in one arm of an interferometer and decrease thetensile stresa in the fiber in the other arm. The de-vice for accomplishing this is shown in Fig. 5.35. Asection of the fiber in one arm of the interferometeris attached both to the upper end of the case and tothe mass. A similar section of fiber in the other armof the interferometer is attached to the mass and tothe lower end of the case. Thus, the mass, m, is sus-pended between the two fiber sections which effectivelyserve as springs. If the accelerometer case is givenan acceleration, a, vertically upward, the upper fiberelongates by AL and the lower fiber shortens by thesame amount in providing the force F required to accel-erate the mass. This may be written as

F=2AAT=ma (5.19)

2

iii=

DIODELASER

3dB COUPLER

UPPER~1 lppoRT

lk

CASEIER

DIAPHRAGMS

LOWER SUPPORTFIBER

SIGNAL MASS

)1‘t’ /um1

ELECTRICALREBALANCE

s

3dB COUPLER

PHOTODIODES

Fig. 5.35 A two-fiber phase-change interferometricfiberoptic accelerometer.

where A is the cross sectional area of the fiber, AT isthe magnitude of the change of the tensile stress ineach fiber, and the 2 is due to the presence of two fi-bers. The resulting strain AS = .4L/L is given by:

AS = AT/Y = ma/2YA (5.20)

where Y is Young’s modulus for the fiber.

Consider next an optical beam propagating inone of*the fibers. Its phase shift, $ , in travelingthe length L, as given in Subsection 4.2.1 and Eqs.(4.7) and (4.8), is:

4 = zn~~l~o (5.21)

where h. is the optical wavelength in vacuum and n isthe fiber core’s refractive index. The’ quantity Aolnis the wavelength of the light in the fiber core. Ingeneral, the change in @ per fiber (twice this for twofibers) may be written as it was in Eq. (5.1), namely:

A+ = 2m(nAL + LAn)/Ao (5.22)

with the wave number k = 2iI/lo. For the case of a ten-sile strain, however, the AL term dominates and one maywrite:

A+ = 2nnAL/~o = 2nnLAS/lo (5.23)

Substituting into Eq. (5.23) from Eq. (5.20) and be-cause A - n(d/2)2:

A~ = 4nLma/Y~d2 (5.24)

where d is the fiber diameter.

Solving Eq. (5.24) for ~n in terms of A$~n yields:

amin = AoYd2A$tin/4nLm (5.25)

Referring to Fig. 5.35, the effective springforce F, required to displace the mass m a distance z,along the axis of the fiber, is given by:

F = -2YAz/L = -kz (5.26)

from which it follows that 2YA/L = k, where k is theeffective spring constant. However, when a mass m is

5-1

attached to a spring with a spring constant k, the re-sonant frequency is given by:

fr = (1/2n)(k/m)112. (5.27)

Thus, combining Eqs. (5.26) and (5.27) there is obtain-ed:

fr = (1/2n)(2YA/Lm)l/2 (5.28)

As above, A = m(d/2)2. To further emphasize the depen-dence of the resonant frequency, fr, on the fiber para-meters, Eq. (5.28) may be written as:

fr = [Yd2/8mLm]1/2 (5.29)

Comparing Eqs. (5.25) and (5.29) we see that the opti-cal fiber physical parameters appear in the form Yd2/Lm. Therefore, if the expression d2/Lm in Eq. (5.25)is decreased in order to decrease ~in, the valueof fr given by Eq. (5.28) is also decreased. The mini-mum detectable acceleration (a~n) and longitudinalresonant frequency are shown in Figs. 5.36 and 5.37 asfunctions of m and d. In each case the length of fibeL is taken to be one cm and the value of A

%is 10-5

radian. Alternately, if a mass of one gram ~ chosen,the mass in grams on the abscissa in both Figs. 5.36and 5.37 can be replaced by the length in centimeters.

3.0 t.

10 2.0 3.0

MASS (grams)

Fig. 5.36 The variation of sensitivity in microgramsas a function of the mass in grams in afiberoptic accelerometer for differentsizes of fibers.

10.0

- h -$ dm

-1-

.--— ------.-----

I 1 1 110 2.0 3.0

MASS(grams)

Fig. 5.37 The variation of resonant frequency as afunction of the mass in a fiberoptic accel-erometer for different sizes of fibers.

3

Referring once more to Fig. 5.35, if the massis given a transverse (cross axis) acceleration, bothoptical fibers are strained the same amount. Thus, theinterferometer remains balanced and to first order thisdevice is insensitive to transverse accelerations.Cross axis coupling will occur if simultaneously thereare components of acceleration that has componentsparallel and perpendicular to the longitudinal axis ofthe fiber. The diaphragms indicated in Fig. 5.35 areprovided to essentially eliminate cross-axis coupling.

Tveten et.al. (See Ref. 1 of Subsection 5.3.1)investigated a single fiber version of this device. Thesensitivity in radians/g versus frequency is shown inFig. 5.38 and the value of amin versus frequency inFig. 5.39.

100or

y 100 -v

: 10 -~> ~-----&l -:

~ 0.1 10 100 200 300 400 500

FREQUENCY HZ

Fig. 5.38 The sensitivity in radianslg (g = 9.8m/s2)of a single-fiber fiberoptic accelerometeras a function of frequency. The low-fre-quency theoretical sensitivity is shown bythe horizontal line.

After A. Tveten et al., Electron Lett., 16, 854 (1980),—

.-

.- 100 200 300 400;

FREQUENCY, tiz

Fig. 5.39 The minimum detectable acceleration (g =9.8m/s2) as a function of frequency for asimple single-fiber fiberoptic accelero-meter.

5.3.1 References

1. A. Tveten, A. Dandridge, C. Davis, and T. Giallor-enzi, Electron. Lett. ~, 854 (1980).

5-1

5.4 FIBEROPTIC ROTATION-Fb+TE SENSORS

5.4.1 Introduction

The measurement of rotation is of consider-able interest in a number of areaa. For example, iner-tial navigation systems as used in aircraft and space-craft depend critically on accurate inertial rotationsensors. The allowable errors in rotation sensor per-formance depend on the particular application. Typicalrequirements for aircraft navigation lie between 0.01and 0.001 degreeslhour. In terms of earth rotatiorate, flE = 15 degrees/hour, this becomes 10-3 to 10 -2

!lE. Fig. 5.40 lists several other applications of rota-tion sensors, such as surveying, where the accuratedetermination of azimuth and geodetic latitude is impor-tant (see Ref. 1, Subsection 5.4.20). In this case-6 ~ or less iS needed.performance of 10

2Geophysics

applications include t e determination of astronondcallatitude, and the monitoring of polar motion caused bywobble, rotation, precession and wandering effects (seeRef. 1, Subsection 5.4.20). A highly precise rotationsensor may be used to measure any changes in the lengthof the day and to detect torsional oscillation in theearth caused by earthquakes. Finally, ultraprecisesensors may find applications in relativity-relatedexperiments such as the determination of the preferredframe and dragging of inertial frames (see Ref. 2,Subsection 5.4.20).

●

●

●

●

NAVIGATION WQESIO –3

SURVEYINGAZIMUTH, GEODETIC LATITUDE N <10–6

flEGEOPHYSICS

ASTRONOMICAL LATITUDE S10–6POIAR MOTION (WOBBLE, NUTATION, PRECESSION,

WANDERING)LENGTH OF DAYEARTHQUAKES <10–11

RELATIVllVGLOBAL INERTIAL FRAMEDRAGGING OF INERTIAL FRAMES <10–10

Fig. 5.40 Various application areasaensors.

of rotation-rate

5.4.2 Methods of Rotation Sensing

The popular rotation sensor used over thepast few decades (Fig. 5.41) has been the mechanicalgyroscope which dependa for its operation on the highangular momentum generated by a spinning wheel or aspinning ball. The angular momentum of spinning nucleihas also been investigated for use as a rotation sensor(see Ref. 3, Subsection 5.4.20). The advent of thelaser in 1960 rekindled the interest in the use of theSagnac (see Refs. 4 and 5, Subsection 5.4.20) effectfor the sensing of inertial rotation by purely opticalmeans. The so-called ring laser “gyroscope” (see Ref.6, Subsection 5.4.20) which has been under active de-velopment for almost two decades has succeeded in ac-hieving inertial-grade performance and has recentlybeen selected for use in the new Boeing 757 and 767aeroplanes and also in other navigation systems. Morerecently the availability of low-loss single-mode fi-bers opened up a very active and very promising areaof research in fiberoptic rotation sensors also basedon the Sagnac effect (see Ref. 7, Subsection 5.4.20).

4

● ANGULAR MOMENTUM CRYOSCOPES

MECHANICAL - ROTATING WHEELIBALL

NUCLEAR - SPINNING NUCLEI

● SAGNAC EFFECT “GYROSCOPES”

E.M. WAVES

MAITER WAVES

● DISTANT-STARS TRACKERS

SIMPLE STAR TRACKERS

LONG-BASELINE STELL4R INTERFEROMETRY

Fig. 5.41 Various rotation-rate sensor devices.

5.4.3 Interest in Optical Rotation Sensors

The main advantages of optical “gyroscopes”over mechanical ones are briefly outlined in Fig. 5.42.However, it is the promise of the projected low cost ofthe optical devices that is driving their development.

● NO MOVING PARTS

● No wARM-UPTIME

● NO G-SENSITIVITY

. LARGE DYNAMIC RANGE

● DIGITAL READOUT

● LOW COST

● SMALL SIZE

● USES LIGHT

Fig- 5.42 Potential advantages of optical rotation-rate sensors (gyroscopes).

In this section we will give a brief andple derivation of the Sagnac effect in vacuum andin a medium; discuss techniques of implementing

sim-alsothe

Sagnac effect for the measurement of rotation togetherwith the fundamental limits on sensitivity in each case.The basic principle of fiberoptic rotation aensors willthen be considered with emphasis on techniques, problemareas, and recently achieved performance.

5.4.4 Sagnac Effect in a Vacuum

AH the optical rotation sensors under de-velopment are based on the Sagnac effect (ace Ref. 5,Subsection 5.4.20) which generatea an optical path dif-ference AL that is proportional to a rotation rate fl.For example, if we have a diac of radius R that isrotating with angular velocity Q, as shown in Fig. 5.43,the optical path difference AL experienced by lightpropagating along opposite directions along the peri-meter is given by:

AL = (4A/c)$l (5.30)

5-1

where A is the area enclosed by the path, i.e., A = ~R2and c ia the velocity of light in a vacuum.

The rigorous derivation of this formula isbased on the propagation of light in a rotating frame(see Ref. 5, Subsection 5.4.20) i.e., an acceleratingframe of reference, where the general theory of rela-tivity must be used to perform the calculation. How-ever, a simple way of explaining the formula in Eq.(5.30) iS given in Fig. 5.43. Again, consider the disc

% 1

D-----------

,’ .i’R,,@j 2‘1 ,,, ,’‘., ,/’

‘. ,,..- --------

{

Lcw=2mR+R~tcw= Ccwtcw

Lccw=27rR-R~tccw= Cc,-wtccw

>tcw= ~c::RRQ 2*R: tccw = Cccw + RQ

~At=tcw–tccw= ‘wR[2R~ - (Ccw - Cccw)]

Ccw ccc.

IN A VACUUM CCW=CCCW=C

~ A t = ‘TR ~ O = %() ; ~ AL= LCW– LCCW. ~C)

Fig. 5.43 A demonstration of the Sagnac relationshipsfor the vacuum case.

of radius R rotating with an angular velocity !l aboutan axis perpendicular to the plane of the disc. At agiven point on the perimeter, designated by 1 in Fig.5.43, identical photons are sent in clockwise and coun-terclockwise directions along the perimeter. If Q = o,the photons, which travel at the speed of light in avacuum, will arrive at the starting point 1 after cover-ing an identical distance 2?TR in a time t = 2nR/c. Nowin the presence of a disc rotation $2, the ccw photonwill arrive at the starting point on the disc, which isnow located at position 2, after covering a distanceLccw which iS shorter than the perimeter 2TR given by:

LCcw = 2TR - l?iltccw = cccwtccw (5.31)

where Ri2 is the tangential velocity of the disc andtccw is the time taken to cover the distance Lccw. In

addition, Lccw is also given by the product of thevelocity of light Cccw in the ccw direction and tccw.For propagation in a vacuum Cccw = C. Similarly, thephotons propagating in the cw direction experience alarger perimeter Lcw given by:

LCw = 2TR + R!ltcw = ccwtcw (5.32)

Using Eqs. (5.31)tccw as given Inbetween clockwisecomes:

At = tcw - tccw

4TR2nlc2 =

and (5.32) we can solve for tcw andFig. 5.43 so that the difference Atand counterclockwise propagation be-

. (21TR)(2Rf0/C2 =(5.33)

(4A/c2)sl

5

The path length AL traveled by light in a time At istherefore given by:

AL = cAt = (4A/c)fl (5.34)

5.4.5 Sagnac Effect in a Medium

In the case of light propagation in a medium(see Ref. 5, Subsection 5.4.20) of refractive index n,(Fig. 5.44) the velocity of propagation must take intoconsideration the relativistic addition of the velocityof light in the medium, i.e., c/n and the tangentialvelocity of the medium, i.e., Rfl so that Ccw becomes:

to first

Ccw = (c/n + R.Q)/(l + RQ/nc) =

c/n+RQ(l- l/n2 + ...)

order in VIC. Similarly Cccw,

CCCW = (c/n - IW)/(1 - RQ/nc) =

c/n-RQ(l - l/n2 + ...)

IN A MEDIUM. REFRACTIVE INDEX nc~ +RO

cCw = . ~ +RQ (l– ~)+..1+% “2

cTi- – R()

C&w = — =,–~nc

c7i- –Rfl (1-~)+

~Ccw-Cccw=2RQ (1-;)

r

(5.35)

is given by:

(5.36)

~A, ~2wR[2R &(Ccw-Cccw)l ~ 2rR12R0-2R62(l-p)jCcwcccw C2

“2

‘EE1 THESAME ASIN AVACUUM

Fig. 5.44 A demonstration of the Sagnac relationshipsfor the rotating single-loop optical fiber.

Therefore, At in a medium becomes:

At = tcw - tccw(5.37)

= 21rR[2Ro - (Ccw - cccw)l/[cc#ccwl

UPon substitution for Ccw - Cccw from above, there isobtained:

At = 21TR[2RQ - 2RQ(I - l/n2]/[c2/n2](5.38)

. 21TR(2RQ/C2) = (4A/c2)Q

which is idential to that in a vacuum. If the mediumis an optical fiber wound in a coil of N turns, then Atbecomes:

At = (4AN/c2)fl (5.39)

5-1

Thisgiven

where

corresponds to a nonreciprocal phase shift A$,by:

A$ = 2~Atc/Ao = 2rAt/(A/V)(5.40)

= (8.AN/aoC)c?

A = A./n and v = c/n are the wavelength and sc.eed“.

of light in the medium (n is the refractive index ofthe fiber core), respectively. In terms of path lengthdifference:

AL = A4A012T = (4AN/c)!l (5.41)

For a fiber of length L wound in a coil of diameter D:A = TD2/4 and N = L/nD so that:

AL = (4~/c)n = (LD/c)n (5.42)

or:

AI$ = (2TTLD/aoC)Q (5.43)

5.4.6 The Magnitude of the Sagnac Effect

In order to get a feel for the magnitude ofAL, (Fig. 5.45) assume an area A = 100 au2 and a rota-~~:~orate of 10-3 ~ (i.e., 0.015°/hr or 7 x 10-8 radl

For a single-turn fiber loop enclosing such anarea we get AL . 10-15 cm. This is not a very largeeffect considering the diameter of a hydrogen atom isabout IO-8 cm. Clearly, a large number of turns N isnecessary to increase the magnitude of AL.

A=100cm2; Q .CiE * 10-4 rad/sec

~ AL*10-12cm

W. ‘DIAMETER- OF HYDROGEN ATOM- lo-8cm

FoR n = 10-3nE = 10-7 radlsec

Fig. 5.45 Computation of the change in effective opti-cal length (Sagnac effect) in a rotatingsingle-loop of optical fiber.

5.4.7 Methods of Optical Rotation Sensin&

For the sake of completeness, Fig. 5.46 showsthe various schemes for the measurement of AL. On theextreme right is the multiturn fiber interferometermethod (see Ref. 7, Subsection 5.4.20) mentioned above.On the extreme left is the ring laser approach (seeRef. 6, Subsection 5.4.20) and in the middle is thepassive resonator approach (see Ref. 8, Subsection5.4.20). In both the active and the passive reaonatorapproach, a nonreciprocal path length difference AL dueto the Sagnac effect becomes a nonreciprocal change inthe resonance frequency, Af, of the cavity for CW andccw propagation where:

Af = (4A/ioP)$l (5.44)

6

where P is the optical perimater of tha path. In theactive resonator (i.e., ring laser) approach the cw andccw outputs of the laser have a frequency differenceAf which IS auto~tically generated when the laser issubjected to a rotation. In the case of the passiveresonator, Af has to be measured by means of lasersexternal to the cavity (see Refs. 8 and 9, Subsection5.4.20).

SAGNAC EFFECT I1

I IACTIVE APPROACH PASSIVE APPROACH

[ r {

RING LASER R E S O N A T O RII

INTERFEROMETER

~

I-7 d( AL=!$N,,

H&@=bA N,,

fcw fccwA. & -

AL

Fig. 5.46 Methods of measuring the change in effectiveoptical length ( Sagnac ef feet).

5.4.8 Fundamental Limits in Optical RotationSensors

Figs. 5.47 and 5.48 show a comparison with-out derivation of the quantum noise limit for all threecases. For the ring laser (RL) , the quantum limit comesfrom spontaneous emission in the gain (see Ref. 10, Sub-section 5.4. 20) medium and gives an uncertainty 6!l inthe measurement of Sl given by:

6% x oioP/4A)(rc/(nphT) l’2) (5.45)

● RING LASER GYRO

J-------+ +- + ~+4 4

1I1

1

! SPONTANEOUSI I

fccw fcw

, EMISSION, ,\cJ P I ‘~,)!! x — —RLG 4A ~

1

\-~:;.+.w- fccwi

fcw

● PASSIVE RESONATOR GYROt+

El PHOTONSHOT NOISE

-tI I

Fig. 5.47 Computation of quantum noise limits in fi-beroptic rotation-rate sensors.

5-1

JILc ~0/2

P H O T O N S H O T N O I S E‘jf]MFG= LD ~

Fig. 5.48 Photon shot-noise computation for a multi-turn fiberoptic gyroscope utilizing theSagnac effect.

where r. is the linewidth of the ring laser cavity withno gain; nph Is the number of photons/see in the laserbeam and T is the averaging time. For the passive res-onator (PR) case the limit is determined by photon shotnoise and is given by:

6nPR = (kop/4A)(rc/(nphTl~T )1’2) (5.46)

where q D is the quantum efficiency of the photodetector.As can be seen, the passive and active resonator ap-proaches give approximately the same limit. For themultiturn fiberoptic (FO) interferometer ( see Ref. 11,Subsection 5.4. 20) the photon shot noise limit is givenby:

M-lFo = (c/LD) (ko/2(nph~JjT )1/2) (5.47)

where nph is a number of photons/see leaving the inter-f erometer. Al these limits are compare

i-# in Fig. 5.49

for A = 100 cm ; P = 60 cm; 10 = 6 x 10 =3X1015 photons/see corresponding to 1 mW; L =c~bOn~h(i. e. ,N = L/P = 1000); rc = 300 kHz; IID = O. 3; and T = 1 sec.We notice tha the uncertainty d~ in this

-t ,Eexample is

about 5 x 10 or O. 008°/hr for all three cases.

RING LASER PASSIVE RESONATOR FIBER

c AOI 2

LD j=

~2EXAMPLE: A = 77

P = To

L = NP

= 100 cm 2 ; Ao= 6x1O cm

= 40 cm ; n ~h = 3x1015Isec = lmW

= 400 m ; T * 1 sec

rc x 300 kHz 70 = 0.3

&f)= 4.10–4QE 7XI0 “QE 5X1O–4 f)E

0.006 “/hr 0.01 “Ihr 0.008 O/hr

Fig. 5.49 Computation and comparison of the shot-noiselimits for various types of rotation-ratesensors utilizing the Sagnac ef feet.

7

5.4.9 Fiberoptic Rotation-Rate Sensors

A simple configuration of a multiturn fiber-optic rotation-rate aensor (see Ref. 7, Subsection5.4.20) is shown in Fig. 5.50. Light from a laser orsome other suitable light source ia divided into twobeams by a 50-50 (3 dB) beamsplitter and then coupledinto the two ends of a multiturn (multlloop) single-mode fiber coil. The light emerging from the two fiberends is combined by the beamsplitter and detected in aphotodetector. In the abaence of rotation, the twoemerging beams interfere either destructively or con-structively depending on the type of beamsplitter used.For a 50-50 (3 dB) lossless beamsplitter the emergingbeams, as shown in Fig. 5.50, interfere destructively.

NTURNS

d DETECTOR

L –L~cw=~NQCw c

ne,g. N=1000:A=100cm2: Q=f)E

=AL~16gcm-5A

=2X1O

A$=8mANQs10-4 RADAoc

Fig. 5.50 Computation of the phaae change for a multi-turn fiberoptic interferometric rotation-rate sensor.

However, the emerging beams that return back to thelight source interfere constructively, i.e., at the peakof a fringe. In the presence of a rotation rate $2, aAL will be generated given by:

AL = Lcw - Lccw = (4Atf/c)n = (LDIc)Q (5.48)

where A, N, L, D have been defined earlier. This ALwill therefore cause a fringe shift Az given by:

AZ = (LD/ioC)n (5.49)

or a phase shift of:

A$ = (21TWaoC) (5.50)

For A = ~D2/4 = 100 cm2 and N = L/rD = 1000 (i.e., D‘11.3 cm and Lx 355 meters) and if i. = 0.63 ~m andn= 1.5, we get a phase shift of 3.0 rad for a rotationrate of 1 rad/sec. Therefore, to detect the full earthrotation, we must measure a phase shift of 9.1 x 10-5radians and for typical navigation applicat ons (10-3~) the phase ahift reduces to about 10-{ radians.

For a given size sensor, i.e., a fixed coildiameter D, the sensitivity may be enhanced by increas-ing the length of the fiber L by adding more turns. Un-fortunately L cannot be increased indefinitely becauseof the finite attenuation of optical power in the fiber.

5-1

Typically, for a fiber attenuation rate of 1 dB/km, theoptimum length is several km.

5.4.10 Photon Shot-Noise Limit

Earlier a proof was given of a comparison ofthe basic limits to the rotation measurement using thethree techniques outlined in Fig. 5.46. In this sectionwe will derive an approximate formula for the limit ina fiberoptic rotation-rate sensor.

Fig. 5.51 shows a plot of intensity I or de-tector output current iD versus nonreciprocal phaseshift A+ . In this case, the peak intensity, due to con-structive interference, is shown centered on A$ = O fora zero rotation rate. In the presence of a rotation,A+ shifts from zero and therefore a change in detectioncurrent iD occurs. The greatest change in iD for agiven small change in A$ clearly occurs at the point onthe fringe with the maximum slope, i.e., where A$ = +~12. Therefore, by applying a fixed nonreciprocal bia~of T/2, the operating point can be maintained where thesensitivity to rotation is a maximum. In this way, anapplied rotation causes a A$ which in turn generates achange in the light intensity at the detector that isproportional to the rotation. A problem arises when the

1

&I D

,)

INTENSITY NOISE

;1 i,1,1,1-w OY?$7

) A+8(A+) - PHOTON

/N O I S E - -

8( AIP)s-= —iD/~ - iD/IT

T*LS 7r.—SIN iDm m

*OC ~=87ANBUT A@=* —QAOC

SHOT NOISE

Fig. 5.51 The optical intensity (power) or photode-tector output current as a function ofphase change and photon shot-noise computa-tion in a fiberoptic rotation-rate sensor.

intensity of the light source varies since this cannotbe distinguished from a change in intensity due to arotation. Therefore, the uncertainty in the measure-ment of a given rotation rate, i.e., a given A$, mustbe influenced by the intensity noise in the light. M-though there are many ways of compensating for intensityvariations of the light source, it is not, however,possible to reduce the effect of photon shot noise (seeRef. 12, Subsection 5.4.20) because it is a random pro-ceas. Therefore under ideal conditions the uncertaintyin the measurement of A$ ia limited only by the photonahot noise (see Ref. 12, Subsection 5.4.20). This un-certainty 6(A$) is therefore given by:

6(A$) = (photon shot noise)/(fringe alope) (5.51)

8

This is a minimum where the fringe slope is a maximum.In other words:

15(A$) z n(2eiDB) qiD .

iT(nph~DT )1’2/nph~DT(5.52)

where e iS the electron charge; B is the bandwidth ofthe detection system; nph is the number of photonsfsecfalling on the detector; ~ is the quantum efficiency ofthe detector; and T is the averaging time = l/2B. SinceEq. (5.50) iS:

A+ = 2nLD/loc

the uncertainty in the measurement of ~, i.e., 6$2, be-comes:

which :

5.4.11

may bedrift :not be

62 = Aoc&(A41)/21rLD

= (C/LD)(lo/2)/(nphtlT)l’2 = (5.53)

cio/2LD(iD/2eB)112

s the same expression given earlier.

Ideal Performance

The ideal performance of a fiberoptic “gyro”summarized as shown in Fig. 5.52. The random

s limited by photon shot noise and there shouldany aource of bias or drift in the absence of

rotation. For a given rotation, the stability of thescale factor, i.e., 2nLD/aoc, which related !2 to Ahmust be limited by the stability of L, D and ~o.

●

●

●

RANDOM DRIFT IS LIMITED BY PHOTON SHOT NOISE

NO BIAS OR DRIFT WHEN!! =0

SCALE FACTOR STABILITY IS LIMITED BY STABILITY OFL,D

ANDAO

Fig. 5.52

5.4.12

cussed in

Ideal performance features of a fiberopticrotation-rate sensor (L = coil length, D =diameter, and i. = source wavelength).

Measurement of Nonreciprocal Phase Shift

In order to reach the ideal performance dis-the previous section, a number of problems

must be overcome. The measurement of nonreciprocalphase shift A@ with an uncertainty that is limited onlyby the photon shot noise will now be described.

A simple way of measuring A$ is illustratedin Fig. 5.53, where a T/2 bias is applied so as to oper-ate at the point of maximum slope. In thia way an in-crease in intensity correaponda to a negative A$ andvice veraa. Among the disadvantages of this method isthe stability of the bias and the need to compensate forlaser intensity fluctuations. A better method might beto employ a differential scheme in which two detectorsare placed astride a fringe as ahown in the lower dia-gram of Fig. 5.53. l%is scheme has twice the sensitiv-ity of the first, and better discrimination againatintensity variations. However, it still suffers fromthe instability of the operating points and requireshigh common mode rejection.

5-1

Fig. 5.53

JtLo ‘ $7 A#J—

iii-

I/

-7r 0 r 4#J—

Two DC methods for measurement of phasechange, LO, in a fiberoptic rotation-ratesensor.

A much better method is to use an a.c. modu-lation scheme employing nonreciprocal phase dither (seeRef. 11, Subsection 5.4.20) as shown in Fig. 5.54. Therequirements for optimum operation are that the ampli-tude of the phase modulation should be + r/2 and therate of the modulation should be high enou~h so that thedetector noise is dominated by photon shot noise. Fig.5.55 is a sketch of a typical noise spectrum of a lasershowing the large “l/f” noise component at low frequen-cies. The start of the ahot-noise-limited region de-pends on the particular light source and can be anywhere from a few kHz to a few hundred kHz. Using such

.MODULATION METHODS

I I ‘D

\,& .+-w ; o : we~NONRECIPROCAL

PHASE MODULATION

REQUIREMENTS:

● AMPLITuDE*r/2

cRATE – HIGH ENOUGH TO GIVE SHOT-NOISE LIMIT

Fig. 5.54 AC measurement of phase change, A$, in afiberoptic rotation-rate sensor.

ItINTENSITY

NOISE

PHOTON 1 ——-—-——SHOT —NOISE o f—

Fig. 5.55 Atypical intensity-noise spectrum of alaser showing inverae frequency (l/f) andphase noise.

9

a modulation scheme, the output of the photodetector isdemodulated in a phase-sensitive demodulator followedby a low-pass filter. In this way a zero output is ob-tained at A$ . 0, a positive voltage for A+< O and anegative voltage for A$ > 0. The main advantages of themodulation method are that the peak of the interferencepattern is used as the reference point (i.e., no needfor external offset) and that the null point is inde-pendent of intensity fluctuations as long as the modula-tion rate 1S high enough as mentioned above.

5.4.13 Methods of Nonreciprocal Phase Modulation

The various possibilities for achieving non-reciprocal phase modulation at high rates will now bedescribed. The phase shift $ that light experiences inpropagating along a single-mode fiber of length L andrefractive index n (Fig. 5.56) given by:

~ = 2~fnL/c (5.54)

where f 1S the frequency of the light in Hz and c isthe velocity of light in a vacuum. It should be notedthat the magnitude of $ does not depend on the direc-tion of propagation so that $Cw = $Ccw = $. This impliesthat if L, n, or f is varied, a nonreciprocal phaseshift cannot be generated.

Therefore, in order to generate a nonrecipro-cal phase shift, either Lcw ~ Lccw or ncw $ nccw or fcw+f Ccw”

c

“ @~w - 4CCW = ~ fn (Lcw – Lccw)

2T fL (ncw – ‘Ccw)● 4CW - @ccw ‘ ~

“ 4CW - 4CCW = gn Ufcw - fccw)

Fig. 5.56 Various possibilitiesphase modulation.

for nonreciprocal

One possibility of making Lcw ~ Lccw whetherIn a medium or in a vacuum is to mechanically dither theinterferometer at a high angular rate so that the Sagnacef feet itself resulting from this motion can provide thenecessary nonreciprocal phase ahift. This method has infact been used in early fiber gyros (see Ref. 13, Sub-section 5.4. 20) but is clearly not very desirable ingeneral.

In order to generate a nonreciprocal refrac-tive index, i.e. , ncw # n ccw there me a number of meth-ods that could be used. A simple scheme would be tomake the polarization of, say, the cw beam orthogonalto the polarization of ccw beam and then use an electro-optic (E/0) phase modulator to generate a polarization-dependent refractive index. Such a scheme has been dis-cussed and demonstrated ( see Ref. 11, Subsection 5.4. 20)

5-2

but suffers from the fact that orthogonally polarizedbeams propagating in the fiber do not experience theaame index thus generating a temperature dependent bias.

Another method of making ncw # nccw makes useof the Faraday effect either in the main fiber coil orIn a separate length of fiber. By applying a longitud-inal magnetic field to the fiber it is possible to causethe index for right circularly polarized light to bedifferent from that for left circularly polarized light.Even though the Verdet constant, i.e., the constant ofproportionality between magnetic field strength and in-dex difference, is small, it can be enhanced consider-ably by using a longer length of fiber. Again, thisscheme has been demonstrated recently (see Ref. 14, Sub-section 5.4.20).

Yet another nonreciprocal index scheme thathas enjoyed much popularity is the time delay modula-tion method (see Ref. 15, 16, 17, and 18, Subsection5.4.20), illustrated in Fig. 5.57. In this case advan-tage is taken of the comparatively long time the pho-tons spend in the fiber. A typical scheme would be to

A /

* ‘/’OUTPUT ‘D

14’Cw – $Ccw ~ 2$0 SIN (2T fm ~)I

AMPLITUDE OFPHASE MODULATION

‘f FOR fm = &

Fig. 5.57 The time-delay modulation method for a non-reciprocal fiberoptic rotation-rate sensor.

pla~e a phase modulator near the beamsplitter as shownin Fig. 5.57. The phase modulator can be constructedin many ways, such as an electrooptic crystal, or a fi-ber wound around a PZT. Now if the phase modulator isdriven at a frequency fm it is then possible to gener-ate a nonreciprocal phase shift given by ( see Ref. 18,Subjection 5.4.20):

r$cw - $Ccw . 2@05in(2nfmTD/2) (5.55)

where $0 is the magnitude of the reciprocal phase shiftgenerated by the phaae modulation and T ~ is the delaytime in the fiber which is given by nL/c. To maximizethe nonreciprocal phase shift it is necessary to makethe argument of the sin function = n/2 i.e. , by choos-ing fm = 112 ~. If fm is less than l/2TD, $0 has to beincreased to achieve the appropriate amplitude of thenonreciprocal phase shift. For a 1 km fiber the opti-mum f m is about 100 kHz.

0

The generation of nonreciprocal phase modula-tion by the frequency method will now be described (seeRefs. 11 and 18, Subsection 5.4.20). In this schemefcw is made different from fccw so that:

@ Cw -0Ccw = (2nnL/c)(fcw - fccw) (5.56)

A simple way of implementing this method is by employ-ing two acoustooptic (A/0) frequency shifters placedsymmetrically on either side of the beamsplitter withinthe interferometer. By driving the A/O with independentoscillators it is possible to generate both nonrecipro-cal phaae modulation as well as fixed nonreciprocalphase shifts. For example, In a 1 km fiber a frequencydifference fcw - f ccw of 50 kHz generates a nonrecipro-cal phase shift of T/2.

Related frequency methods have also been in-vestigated (see Refs. 19 and 20, Subsection 5.4.20).

5.4.14 Open Loop and Closed Loop Operation

The open loop sensor system is shown in Fig.5.58 where a nonreciprocal phase modulator (NRPM) isplaced near one fiber end and driven at fm. The out-put of the photodetector is then demodulated at fm ina phase senaitive demodulator. After low pass filter-ing the demodulator output is a sinusoidal function ofAt as illustrated in Fig. 5.58. For any given A$, ad.c. voltage output is obtained which is proportionalto A$. The disadvantages of the open loop system in-clude (a) the calibration of the demodulator outputsince this depends on the gains of the various ampli-fiers that precede it as well as on the intensity ofthe light source and (b) the nonlinear behavior of thedemodu~ator output with A$.

LIGHT

SOURCE

DETECTOR

1,

OUTPUT IwAIP

Fig. 5.58 Open-loop nonreciprocal phase modulation ina fiberoptic rotation-rate sensor.

In the closed loop system (see Refs. 11 and18, Subsection 5.4.20), shown in Fig. 5.59, the outputof the demodulator is passed through a servo amplifierwhich then drives a nonreciprocal phase transducer(NRPT) placed within the fiber interferometer. In thisway, the sensor is always operated at null, i.e., atA+ = O by generating a suitable nonreciprocal phaseshift in the NRPT that is equal to but opposite in signto that generated by a rotation 0. The output of thesystem ia then the output of the NRFT. Therefore, theNRFT becomes a critical element.

5-2

II

T NRPT

LIGHT NRPM I1. — A II

I l--clw fm

~ETEcToRL A — I-u

Smo*

DEMODOUTPUT

A+/

NULL

Fig. 5.59 Closed-loop nonreciprocal phase modulationin a fiberoptic rotation-rate sensor.

‘She advantages of the closed loop system overthe open loop system include (a) the output is indepen-dent of light source intensity variations since the sys-tem ia always operated at null (the modulation frequencymust be high enough to reach the photon shot noise);(b) the output is independent of the gains of individualcomponents in the measurement system as long as a veryhigh open-loop gain is maintained; and (c) the outputlinearity and stability depends only on the NRPT.

The NRPT could, for example, be a Faraday ef-fect device or an acoustooptic frequency shifter. If aFaraday device is used, then the stability depends onthe stability of the length of the fiber and the atabil-ity of the magnetic-field/phase-shift transfer func-tion. However, if the NRPT is an acoustooptic crystal,then a frequency difference Af = fcw - fccw is generatedto offset a A$ = (21TLD/loC)n caused by a rotation.Therefore:

A+ = 2rAfnL/c = (21TLD/aoC)il (5.57)

which implies that:

Af = (D/nAo)!2 (5.58)

Eq. (5.58) indicates that the scale factor stabilitydepends on the coil diameter D, n, and ~. If the nu-merator and denominator of Eq. (5.58) is multiplied bynD/4, then:

Af = [(nD2/4)/(nlomD/4)]~ = (4A/XoP)fl (5.59)

where P is the optical perimeter = nTD of the fibercoil. It should be noted that Eq. (5.59) is identicalwith Eq. (5.44) for either the ring laser or the passivereaonator approach.

5.4.15 Problems in Fiberoptic Rotation Sensors

So far the basic principles of fiber rotation-rate sensors with emphasis on the measurement of smallnonreciprocal phase shift in a multiturn fiber inter-ferometer have been described. A number of error aourcesthat can influence the performance of the fiber gyrowill now be described briefly.

1

-22

Fig. 5.60 lists several sources of error thatmust be dealt with in order to achieve the predictedperformance. Perhapa the major source of noise is back-scattering within the fiber (see Ref. 21, Subsection5.4.20) and at interfaces, particularly in a setup thatemploys discrete components. To overcome this problem,researchers have used broadband lasers (see Ref. 17 and22, Subjection 5.4.20), frequency jittered lasers (seeRef. 18, Subsection 5.4.20), phase modulators, (see Ref.23, Subsection 5.4.20), and even light-emitting diodes(LED) (see Ref. 24, Subsection 5.4.20). By destroyingthe temporal coherence of the light source the detectionsystem becomes sensitive only to the interference be-

RAYLEIGH SCAITERING IN FIBERSCAITERING FROM INTERFACESPOLARIZATION EFFECTSPRESENCE OF HIGHER ORDER MODESTEMPERATURE GRADIENTSNONIDEAL MODULATORSNONIDEAL POLARIZERSINTENSITY DEPENDENT NONRECIPROCITYLIGHT SOURCE PROBLEMSMEASUREMENT SYSTEM PROBLEMSSTRESS INDUCED EFFECTSMAGNETIC FIELD EFFECT

Fig. 5.60 Sources of noise and errors that must beconsidered in the design of a fiberopticrotation-rate sensor.

tween waves that followed identical counter-propagatingpaths. Thus, interference due to backacattering will,in principle, average to zero.

The problem that has received much attentionboth theoretically (see Refs. 25 and 26, Subsection5.4.20) and experimentally (see Ref. 17, Subsection5.4.20) is the error due to the polarization behaviorof the optical fiber. By uaing polarizers to establishthe axis of polarization (see Ref. 26, Subsection5.4.20) in the long-fiber interferometer, it has beenpossible to reduce polarization-dependent errors. Theuse of the now available single-mode polarization-pre-serving fibers (see Ref. 27, Subsection 5.4.20) mayturn out to be a convenient solution.

All the fiber gyros under study so far haveused single mode fibers. Care has to be taken to insurethat higher order transverse modes are highly attenuat-ed.

A number of error sources are related to tem-perature gradients, (see Ref. 28, Subsection 5.4.20)non-ideal polarizers, (see Ref. 29, Subsection 5.4.20)non-ideal modulators, stress induced effects, externalmagnetic field effects (see Ref. 30, Subsection 5.4.20)and electronics problems in the measurement system.

A very basic source of nonreciprocal phaseshift has been uncovered, namely that due to unequalintensities propagating along opposite directions inthe fiber (see Ref. 31, Subsection 5.4.20). This is anonlinear optical effect based on four-wave mixing thattakes place in a fiber having a third order nonlinearsusceptibility. Such an intensity-induced nonrecipro-city may be reduced by maintaining equal intensitiesin the counterpropagating beam.

5

5.4.16 Integrated Fiber “Gyros”

Although the early investigation of fiberop-tic “gyros” employed (see Refs. 19, 30, 32 and 33, Sub-section 5.4.20) discrete optical components for conven-ience, it is clear that if fiber gyros are to make alarge impact an integrated (see Ref. 34, Subsection5.4.20) optical system (Fig. 5.61) with a semiconductorlaser/LED as a light source must be uaed. Beamsplitterscan be replaced by either waveguide or fiber 3-dB coup-lers (see Ref. 17, Subsection 5.4.20). Nonreciprocal

4I NR MODULATOR

IQ=POuTpuT

f~

Fig. 5.61 An open-loop integrated fiberoptic rota-tion-rate sensor employing a phase trans-ducer.

phase modulators may employ a short length of fiberwound around a PZT, the Faraday ef feet, an integratedBragg cell, or other features.

Integrated polarizers (see Ref. 17, Subsec-tion 5.4. 20) and polarization controllers (see Ref. 17,Subsection 5.4. 20) are also feasible. In the closedloop approach shown in Fig. 5.62 the nonreciprocalphaae transducer could be a Bragg cell, a Faraday ef-fect device, or other device. In other words variouspossibilities exist for constructing a solid-state fi-ber gyro. An all-optical-fiber open-loop system hasalready been demonstrated with a very promising perfor-mance (see Ref. 17, Subsection 5.4.20).

ISERVO

DETECTORf~

Fig. 5.62 A closed-loop integratedtion-rate sensor employingducer.

fiberoptic rota-a phase trans-

5.4.17 ~

Once the various noise mechanisms in fibergyros were uncovered and understood, published perform-ance data began to improve rapidly. Fiber gyros employ-ing several hundred meters of fiber wound around a coilof 15 to 20 cm in diameter have demonstrated short termdrifts in the range of 0.1 - O.01”/hr for averagingtimes of about 10 seconds (see Refs. 17 and 18, Subsec-tion 5.4.20). Long term drift of O.lO/hr for more thanone hour has also been demonstrated (see Refs. 17 and18, Subsection 5.4.20).

5.4.18 Summary of Rotation-Rate Sensors

In summary, fiberoptic rotation sensors havedemonstrated promising preliminary performance. Howevermost of the causes of short term noise are understood,the causes of long term drift need further study. Clear-ly, the emphasis must now be placed on integrated de-vice development.

5.4.19 General Conclusions Regarding FiberopticSensors

It may be concluded for this entire chapterthat fiberoptic sensors demonstrate tremendous poten-tial for application in any area that requires the sens-ing of physical parameters, including electric fields,magnetic fields, forces, temperature, pressure, linearand rotation displacements, velocities, and accelera-tions. Application areas include navigation, medicalengineering, surveying, transportation, telemetry (com-munication), in fact, any area in which measurementsare to be made.

5.4.20 References

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

D.H. Eckhardt, Proc. Soc. Photo-Opt. Instru. Eng.~, 172 (1978).

M.O. Scully, in Proc. of the Fifth InternationalConf. on Laser Spectroscopy, H. Walther and K.Rothe, eds. (Springer-Verlag, Berlin, 1979); M.P.Haugan, M.O. Scully, and K. Just, Phys. Lett. ~,88 (1980).

J.H. Simpson, Astron. & Aeron. ~, #10, 42 (1964).

G. Sagnac, Compt. Rend=, 708 (1913).

E.J. Post, Rev. Mod. Phys. 39, 475 (1967).—

A.H. Rosenthal, J. Opt. Soc. Am. ~, 1143 (1962).

V. Vali and R.W. Shorthill, Appl. Opt. ~, 1099(1976).

S. Ezekiel and S.R. Balsamo, Apply Phys. Lett. 30,478 (1977).

—

G.A. Sanders, M.G. Prentiss and S. Ezekiel, Opt.Lett. ~, 569 (1981).

T.A. Dorschner, H.A. Haus, M. HoIz, I.W. Smith,and H. Stata, IEEE. J. Quant. Electron, QE-16,1376 (1980).

J.L. Davis and S. Ezekiel, Proc. Soc. Photo-Opt.Instrum. Eng. 157, 172 (1978).—

A. Yariv, “Introduction to Optical Electronics”,Holt, Rinehart, & Winston, (1976).

5-2

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

26.

27.

28.

29.

30.

31.

32.

33.

34.

G. Pircher, M. Lacombat and H. Lefevre, Proc. Soc.Photo-Opt. Instrum. Eng. 157, 212 (1978).—

W.C. Davis, W.L. Pondrom and D.E. Thompson, Proc.of International Conf. on Fiberoptic Rotation Sen-sors, M.I.T., (Nov. 1981), Springer-Verlag (to bepublished).

H. Arditty, M. Papuchon, K. Thyagarapan, and C.Puech in Digest or Topical Meeting on Integratedand Giroled-Wave Optics, O.S.A. Meeting, Washing-ton, D.C. (1980).

R. Ulrich, Opt. Lett. ~, 173 (1980).

R.A. Bergh, H.C. Lefevre and H.J. Shaw, Opt. Lett.~, 502 (1981).

J.L. Davis and S. Ezekiel, opt. Lett. g, 505(1981).

D.E. Thompaon, D.B. Anderson, S.K. Yao and B.R.youmans, Appl. Phys. Lett. 33, 940 (1978).—

R.F. Cahill and E. Udd, Opt. Lett. ~, 93 (1979).

C.C. Cutler, S.A. Newton, and H.J. Shaw, Opt. Lett.~, 488 (1980).

R. Ulrich, Opt. Lett. ~, 173 (1980).

K. Bohm, P. Ruaser, E. Weidel and R. Ulrich, Opt.Lett. ~, 64 (1981).

K. Bohm, P. Marten, K. Petermann, E. Weidel andR. Ulrich, Electon. Lett. ~, 352 (1981).

R. Ulrich, Proc. of International Conf. on Fiber-optic Rotation Sensors, M.I.T. (November, 1981),Springer-Verlag (to be published).

G. Schiffner, W.R. Leeb, H. Krammer and J. Wittmsn,Appl. Opt. 18, 2096 (1979).—

I.p. Kaminow, J. Quant. Elect. Q.E.-17, 15 (1981).

D.M. Shupe, Appl. Opt. 19, 654 (1980).—

E.C. Kintner, Opt. Lett. ~, 154 (1981).

K. Bohm, K. Petermann and E. Weidel, Opt. Lett. ~,180 (1982).

S. Ezekiel, J.L. Davis and R. Hellwarth, Proc. ofInternational Conf. on Fiberoptic Rotation Sen-sors, M.I.T. (Nov. 1981), Springer-Verlag (to bepublished).

R. Goldstein and W.C. Rnss, Proc. Soc. Photo-Opt.Instrum. Eng. 157, 122 (1978).

M.N. McLandrich and H.F. Rast, Proc. Soc. Photo-Opt. Instrum. Eng. ~, 127 (1978).

M. Papuchon and C. Puech, Proc. Soc. Photo-Opt.Instrum. Eng. 157, 218 (1978).—

3

CHAPTER 6FIBEROPTIC SENSOR ARRAYSAND TELEMETRY SYSTEMS

Ease of multiplexing and modulation and thefundamental properties of lightwaves and optical fibersmake them suitable for use in multisensory uniform andrandom arrays for many different applications. Thischapter will cover the important characteristics of sen-sor arrays, their connection into telemetry systems fortransmission of baseband data within the array, and thecharacteristics of fiberoptic transmission lines fortelecommunication systems.

6.1 FIBEROPTIC SENSOR ARRAYS

6.1.1 Fiberoptic Sensor Array DesignConsiderations

6.1.1.1 General Design Considerations

The sensor system selected for a particularapplication will depend on many considerations. Forexample, the individual sensors that are selected de-pend on the parameter to be sensed, the sensitivity re-

quired, the dynamic range of the parameter to be sen-sed, the baseband frequencies, and the noise and Powerlevels. The geographic distribution of the sensors inan array will be governed by the distribution of loca-tiona at which parameters are to be aenaed. Othervariables to be selected are the modulation scheme andwhether an analog or a digital form will be used for aparticular application. These and other considerationsmay be summarized as follows:

FIBEROPTIC SENSOR ARRAY DESIGN CONSIDERATIONS

SENSOR TYPEIntensity ModulationPhase ModulationFrequency ModulationPolarization ModulationWavelength Modulation

DISTANCE BETWEEN SENSOR ELEMENTSANALOG VS DIGITAL TRANSMISSIONSIMPLEX, DUPLEX, MULTIPLEX, OR COMBINATIONSIGNAL PROCESSING REQUIREMENTSSENSOR/LINR CALIBRATION REQUIREMENTSPOWER LEVELSSYSTEM NOISENUMEER OF SENSOR CHANNELSMAXIMUM FREQUENCY OF SIGNAL INFORMATIONOPERATIONAL NOISE ENVIRONMENTSIGNAL DYNAMIC RANGESENSOR LEAD LENGTHSDESIRED TRANSMISSION SCHEMEDESIRED MULTIPLEXING

6.1.1.2 Specific Design Considerations

Detailed design considerations for a fiber-optic sensor array and associated telemetry depend onthe method of energizing the array, the type of sensor

6

used, and the telemetry methods that are used. Designaspects differ from one basic configuration to another,therefore detailed design aspects will be discussed inthe next subsection, Fiberoptic Sensor Array Basic Con-figurations.

6.1.2~

The method of energizing an array and thetype of fiberoptic sensors used in the array are ofteninterrelated. For example, suppose an array of base-band-modulated darkfield microbend sensors are eachsequentially mounted on a single fiber and each is pre-ceded by a mode-stripper in such a manner that eachmicrobend sensor of the baseband signal causes an amountof light proportional to the baseband signal amplitudeto enter the cladding. Following each microbender isa tap designed to remove this baseband signal from thecladding and send it via the tap (coupler) to a commonreturn bus.photodetected

PULSEDLIGHTSOURCE(LASER) 1

The return bus output signals may beas shown in Fig. 6.1. If the array is

MODE STRIPPER MODE STRIPPER

TAP TAP TAP

DETECTOR

BUS COUPLERS

Fig. 6.1 A fiberoptic darkfield microbend sensor ar-ray telemetry system with single return bus.

a linear array of equally spaced sensors and the opti-cal feed bus is pulsed, the pulses on the return buswill be automatically time-division multiplexed forthe return telemetry. If the sensors are not equallyspaced and the amount of fiber required to createequal spacing is excessive, the arrangement shown inFig. 6.2 can be used. The source output is continuousin this case. Each microbend cladding mode stripperoutput is fed to a separate photodetector via an inde-pendent optical fiber as shown in Fig. 6.2. Returntelemetry for both of these arrangements is discussedbelow in greater detail. Both of these arrangementsmake use of darkfield sensing.

-1

CONTINUOUSLIGHT MICROBEND SENSOR ARRAY

MODE STRIPPER

MODE STRIPPERSTRIPPER

,. .: :. .

Fig. 6.2 A fiberoptic darkfield microbend sensor ar-ray telemetry system with multiple cablereturn.

Brightfield sensing can also be accomplishedin a fiberoptic sensor array as shown in Fig. 6.3. A

STAR COUPLERI .

.

..CONTINUOUS \ .)

): MICROBEND BRIGHTFIELD

SENSOR ARRAY

DETECTOR

ARRAY

Fig. 6.3 A fiberoptic microbend brightfield star-coupler-fed sensor array telemetry system.

star coupler is fed by a continuous light source, e.g.,a laser or an LED. Each output of the star-coupler isfed to a baseband-modulated microbend fiberoptic bright-field sensor. The output signal of each fiberopticsensor in the array is separately fed to an array ofphotodetectors for further processing and transmission.~so, an electrical power bus to a light source (LED)at each sensor can be used to energize the baseband-modulated microbend fiberoptic brightfield sensor asshown in Fig. 6.4. The electrical bus is continuously

LIGHT SOURCE

ELECTRICAL POWER BUS

)

I

‘“F. . . .(LED) (LED) (LED)

. ● MICROBEND SENSOR

. . ARRAY

. .

.

Fig.

. /

DETECTOR ARRAY

6.4 A fiberoptic microbend brightfield electri-cal-bus-fed sensor array telemetry system.

6-2

energized and either the return optical cables are eachreturned to a photodetector in an array, or the returnbus may be a single optical cable with time-divisionmultiplexed signals from equally-spaced sensors fed toa single photodetector as discussed earlier.

The sensor array can also consist of an arrayof optical grating sensors that modulate the output ofindividually-coupled light sources (LEDs) powered bylight pulses on a common electrical bus as shown inFig. 6.5. The grating outputs are individually coupl-

ELECTRICAL POWER BUS>

I

:fl “ ‘))

PHOTODETECTORARRAY

Fig. 6.5 A fiberoptic optical grating electrical-bua-fed senaor array telemetry system.

ed to photodetectors in an array via fiberoptic cables.Some of the performance features of these and otherfiberoptic sensor array configurations will now bediscussed in some detail.

An array of sensors may be used to beam-formor to signal average. In the former case it is neces-aary to distinguish, i.e. maintain separation of, theoutput signals from the individual sensors. In thelatter case the signals from a number of sensors aresummed (OR-gated). For example, beam forming is usedin echo ranging, while averaging can be used to dis-criminate between signals that arrive normal (perpen-dicular, transverse) to a linear array and those thatarrive parallel (longitudinal) to the array. Thus,very often the spatial distribution of an array offiberoptic sensors can be used to accomplish the multi-plexing, mixing, or summing, of signals from the array.Although the principle of operation of only a lineararray of sensors will be discussed, the same principlescan be applied to multidimensional arrays.

A linear array of fiberoptic sensors may beenergized by means of a common bus. The bus may be anelectrical conductor, fed by a direct-current powersource or an alternating-current power source, or thebus may be an optical fiber fed by a relatively high-powered optical continuous-output source, such as alaser. Alternatively, in each of these situations, thepower source output can be pulsed rather than be con-tinuous, giving rise to four posaible arrangements,namely continuous electrical, continuous optical,pulsed electrical, and pulsed optical power. In anycaae, the fiberoptic sensors (transducer, modulators)in the linear array may be either directly connectedto the optical bus by means of a fiberoptic coupler,or a light source at each sensor may be connected tothe electrical bus. The selection of the appropriate

-3

method of sensor energization will depend on the powerbudget, risetime budget, distances to and within thearray, and other matters related to the specific appli-cation.

The physical parameter variation (baseband)to be sensed, such as a sound wave, a magnetic fieldvariation, a pressure wave, or a force variation, willmodulate the optical input to the fiberoptic sensor,thus producing an optical baseband-modulated signal out-put. This sensor output signal can be telemetered to adistant location (for detection and processing) in anyof a number of different ways depending on spatial,timing, compositional, and other factors.

For the pulsed-bus method of energization ofan equally-spaced linear array of sensors, spatial dis-tribution of the sensors will cause the baaeband-modu-lated output signal pulse from each sensor of the arrayto occur at a different time according to the time ittakes for a pulse to propagate from one sensor to an-

other. If these signals are all fed into a singlecommon return bus, they will be automatically time-division multiplexed on that bus. This arrangement isshown in Fig. 6.6. Assume a pulse of light is dis-

PHOTO– PULSEDOETECTOR SOURCE

I r PULSED SOURCE OPTICAL FEEO BUSwlTH M. l

LENGTHL~

)J LINEAR ARRAY

SPACEDINTENSITY-. . .

MODULATION

{r)J

EQUALLY-SPACEO PULSES IN AN OPTICAL RETURN SUS

Fig. 6.6 A fiberoptic darkfield optical-bus-fed sen-sor array telemetry system with single op-tical return bus.

patched along the feed bus. A coupler at each sensorlocation taps a fraction of the light from the bus.The pulse of light enters each sensor in turn where itis modulated by the baseband signal imposed by the sen-sor. The modulated pulse travels via the return busbsck to the photodetector for further processing. Theminimum time that can be allowed for the spacing be-tween the leading edges of pulses in the return bus isthe propagation time between a given sensor locationand the next sensor in the array and return to the givensensor location. The distance between sensors isL/(m - 1), where L is the length of the linear arrayand m is the number of sensors. The wave has to travelthe distance between aensors in the feed bus and in thereturn bus, therefore the travel distance is 2L/(m - 1).The speed of propagation of a lightwave in the bus isc/n, where c is the speed of light in a vacuum and nis the refractive index of the core. It iS assumed therefractive index is the same for both busses. The timeof propagation is the distance divided by the speed,thus, the time between leading edges of output pulsesis:

to=2[L/(m-1)] /(c/n)=2nL/c(m-1) (6.1)

The pulse repetition rate (PRR) of the pulses emanatingfrom the linear senaor array is given by:

‘Warray = l/t = c(m - 1)/2nL (6.2)

6

For 50 sensors in a linear array, an opticalfiber bus core refractive index of 1.5, a linear array500 meters long, Eq. (6.1) indicates that the time be-tween the leading edges of array output pulses is:

to=(2)( l.5)(500)/3(108) (49)=102 ns (6.3)

The corresponding pulse repetition rate, PRR, is:

PRR = l/t. = 1/102(10-9) = 9.8 kfPPS. (6.4)

Thus, the input feed bus pulses cannot bewider than to. This is the rate at which the baseband-signal modulated pulses will emerge from the input-out-put end of the array. Also, some time should be allowedbetween pulses for random variations of sensor spacing,delays through sensor leads from and to the busses, andpulse risetimes. Therefore, the pulse length shouldnot exceed 0.9to or about 90 ns for the above example.If they are wider, they are liable to overlap in thereturn bus. They can be narrower. The pulses will ar-

rive as a train of pulses at the photodetector. Thepulses in the train will come from and be in the samesequence as the sensors are positioned in the lineararray. These events occur each time the feed bus ispulsed and as many pulses will be in each array outputpulse train as there are sensors in the array. Thephotodetector must be capable of responding to about10 Mpps for the above example. If any analog-to-digi-tal (A-D) conversion is to take place in a single A-Dconverter fed by the return bus, the length of thepulses must be long enough to allow for analog to digi-tal conversion. The repetition rate of the pulses inthe train can be reduced by placing additional fiberbetween the sensors or by using a fiber with a higherrefractive index, as indicated by Eq. (6.2).

Various methods can be used to telemeter thesensor-modulated signals from the sensor array to aphotodetector. For example, the detector could be anoptical repeater if long distance optical transmissionis required, or the output of the photodetector couldbe transmitted electrically, via a wire line, coaxialcable, or radio-link. The radio frequency carriercould be modulated by the detected analog pulses or byan analog-to-digital converter output. The above dis-cussion applies each time a single light pulse is sentalong the fiber bus. The maximum safe pulse durationwas shown to be, from Eq. (6.1) and allowing a 10%safety margin:

‘msx = 1.8nL/c(m - 1) (6.5)

The maximum rate at which the pulses can bedispatched down the optical fiber feed bus is limitedby the overall length of the array. Each pulse musttravel twice the full length of the array and clear thefirst sensor before the next pulse can be applied tothe array. This maximum pulse rate is the maximum rateat which the baseband signal inputs to the fiberopticaensors can be sampled. The minimum time between lead-ing edges of feed bus pulses is twice the time lengthof the array, plus the pulse length (maximum possiblepulse width is assumed) plus a safety margin for rise-time and settling time. Therefore, these considera-tions will yield a minimum sampling period ts of:

t+ = 2nL/c + 1.8nL/c(m - 1) + tr(6.6)

ts = [2 + 1.8/(m - l)]nL/c + tr

where m is the number of aenaors in the linear array, nis the refractive index of the fiber busses, L is thelength of the array, c is the velocity of light in a

vacuum, and t= is the overall risetime to be calculat-ed later in this chapter. This value of ta can be re-duced to the extent that the pulse width can be reduc-ed. If there are only a few sensors in the array thesecond term in bracketa in Eq. (6.6) is significant.As the number of sensors is increased, the second termin Eq. (6.6) becomes less significant. Eq. (6.6) doesnot apply to one senaor because then L = O, the secondterm in brackets becomes indeterminate, and in factthere is no array. In this case, only the risetimerequirement will place a limit on the sampling period.The maximum permissible sampling rate PR~s is:

Pluqs.= l/ts (6.7)

where ts is defined in Eq. (6.6). The sampling ratecan be arbitrarily reduced, but should not be less thantwice the highest significant frequency component inthe baseband signal in order to obtain reproduction ofthe baseband signal without significant distortion(Nyquist criterion).

Another method for energizing an array of sen-sors is to connect the array to a pulsed electrical busas shown in Fig. 6.7, rather than the pulsed optical

7’I ‘1 w ,LENGTH L-~

WLSSDELECTRICALF

L-RARRAYOFMEWYSPACEDSENZORS

WITNLSOAND

INTSN.91v-M~L4T10N

EWAUY-SPACEDPJSES NANOFTCAL REluRssus SENSORS

Fig. 6.7 A fiberoptic lightfield pulsedbus-fed sensor array telemetrysingle optical return bus.

electrical-system with

bus just described. A light source, such as an LED, isoptically connected to each sensor. Thia is the bright-field form of senaor energization. The return bus canbe the same, as was shown in Fig. 6.6, and the analysisabove still applies except that the propagation timein the electrical bus will be different. In this case,the electrical sampling pulae period will be:

telec=l/2 [ts+[2+l.8/(m-l)]L/v+trc] (6.8)

where the variables are as in Equation (6.6), v is thevelocity of propagation in the electrical bus, and trcis the combined electrical and optical risetimes thatwill be discussed later in this chapter.

Another configuration for energizing a ran-domly-distributed (non-linear) array of fiberoptic aen-sors is shown in Fig. 6.8. A continuous source oflight (laser) energizes a star coupler that may beplaced at the center of the array to reduce fiber re-quirements. The output of the coupler is fed to eachfiberoptic sensor where it is modulated by the basebandsignal. The senaor outputs are individually fed to anarrayof photodetector (PDs). In the arrangementshown in Fig. 6.8, the inputs to the photodetector (PD)array (one PD for each sensor) are time-division multi-plexed, sampled, digitized, and telemetered as a digi-tal data bit stream via a fiberoptic cable to anotherlocation for exploitation. In this case, there ia no

6-4

requirement for any specific spatial relationship amongthe sensors. The minimum sampling period for each sen-sor tssen in the array will be:

‘asen = mtad (6.9)

where m is the number of sensors in the array and tadis the analog-to-digital conversion time. This pre-sumes a photodetector for each sensor output, a multi-plexer (for polling each photodetector output), and aaingle A-D converter with its sample-and-hold and otherassociated circuitry aa shown in Fig. 6.8.

>#

Il--+-l

EEk5?ltlzlFig. 6.8 A fiberoptic star-coupler-fed sensor random

array telemetry system with multiple andsingle cable returns.

The random array of fiberoptic sensors may beenergized instead by a direct-current electrical busas shown in Fig. 6.9. In this case, there is a contin-

CONTFWOUS (DC) ELECTRICAL FEED BUS

J

Fig. 6.9 A fiberoptic electrical direct-current bus-fed sensor array telemetry aystemmultiple and single cable return.

with

Theis

uous-output light source (LED) for each sensor.baseband-modulated optical output of each sensorseparately cabled to a photodetector array and proces-sed there in a manner similar to the preceding arrange-ment that had the continuous optical feed as was shownin Fig. 6.8.

The preceding discussion applied primarily tointensity-modulated lightfield and darkfield sensors.The outputs of arrays of other tYPes of sensors canalso be telemetered to locations distant from the sen-sors. An interferometer sensor array configuration isshown in Fig. 6.10. The optical outputs of all fiber-

. . .

(REPEAT OF

R,G”T S,DE,OPTICAL BuSm

L——...-.!

\ I COUPLERS

ELECTROOPTIC PHOTODETECTORS

INTEGRATED CHIP DETECTIONIFEEDBACKDIGITIZATION(MULTIPLEXERLEDCLOCK

L

Fig. 6.10 A fiberoptic interferometric star-coupler-fed sensor array telemetry system with op-tical multiple cable and single cable re-turn and integrated optical circuit chip.

optic sensors are brought to a common point, an elec-trooptic chip. The integrated optical chips are notyet commercially available, however, they are underdevelopment. A single optical fiber is used to conductthe output of the electrooptic chip to a distant loca-tion. Ml signal processing is done at the array loca-tion on the chip. The output of each senaor is sentto the single integrated fiberoptic chip for processingvia a separate fiber. If It should prove desirable touse less fiber, use can be made of the spatial separa-tion between sensors and the outputs can be automatic-ally time-division multiplexed provided the signal pro-cessing can be accomplished at each interferometricsensor as ahown in Fig. 6.11. In this arrangement, asingle optical return bus is used to telemeter the out-puts to a distant location.

T!+AE Owwm

0~-–

LASER 1I

REFEREW3EARM ‘

IIII

> ELECTROOPTCCH!PPOWER

1Tlt.lEDIvISlON

MULTIPLEXERM U L T I P L E X E R

ELECTRCAL BUS :

L--—-.—— ...__._J

Fig. 6.11 A fiberoptic interferornetric star-coupler-fed equally spaced sensor array telemetrysystem with electrical outputs to a singleelectrical return bus.

6-5

There are many other variations and combina-tions of the basic fiberoptic sensor-array telemetryschemes shown here. The basic options include theselection of the type of telemetry link (to and fromthe sensor array, electrical, optical, or electroopti-cal); the type of fiber optic sensor (interferometric,intensity, phase, darkfield, brightfield); the type ofcoupling (star, tapped bus); the type of light sources(laser-powered or LED-powered bus, LED at each sensor);signal types (analog, discrete); multiplexing schemes;and many others. Each of these options will incur adifferent set of technical problems that require solu-tion, a different set of costs, and a different set ofperformance characteristics. For example, frequency-division multiplexing of fiberoptic sensor outputs canalso be applied by energizing the common feed bus ofthe equally-spaced-sensor arrays discussed earlier witha constantly-changing-frequency pulse (frequency ramp).Thus, each fiberoptic sensor in the linear equally-spaced array will be fed a different frequency to bemodulated by the baseband signal. The outputs can bedemultiplexed with appropriate narrowband filters.

6.1.3 Fiberoptic Sensor Array Budgets

Fiberoptic aensor array budgets may be pre-pared in much the same manner as for the telemetry bud-geta to be described in Subsection 6.2.3. Risetime,power, cost, and other budgets for fiberoptic sensorarrays depend on the same set of factors as for theentire sensor-telemetry system. tin optical power bud-get for the sensor array shown in Fig. 6.20 is as

follows:

SENSOR ARRAY POWER BUDGET

OUTPUT POWERLaser output power 7 mW = 38.5 dB VWCoupling loas in fiberpigtail (78% Coupling)

AVERAGE POWER OUTPUT

SYSTEM LOSSStar coupler insertion lossStar coupler splitting loss (1:60)Coupler insertion loss (2, ldB each)3 dB coupler aplitting lossFiber loss (300 m, 5 dB/km)Splicing loss (6, 0.5 dB each)

TOTAL

TOTAL

POWER.

6.2

optic

SYSTEM LOSS

AVAILABLE MARGIN 37.3 - 29.3 =

MARGIN AT EACH DETECTORAntilog of 0.80 =

FIBEROPTIC TELEMETRY SYSTEMS

- 1.2 dB37.3 dB UW

2.0 dB17.82.03.01.53.0

29.3 dB

8.0 dB VW

6.3 UW

The properties of optical fibers and fiber-sensors have been discussed in detail in prior

chapters where particular attention was given to con-struction (materials and geometry), principles of opera-tion (light transmission properties of fibers), andrelative advantages of fiberoptic sensors over othertypes of sensors. Various ways were discussed in whichfiberoptic sensors can be designed to measure absolutemagnitudes or relative changes of a physical parameter,develop an output signal that is a function of theseabsolute or relative values, and emit this signal in aform suitable for subsequent processing and transmis-sion. In essence, the fiberoptic aensor is a trans-ducer; it provides the transform that enables an on-

6

site measurement of a physical parameter to be repre-sented in a form (baseband signal) that can be directlyand immediately processed and transmitted to anotherlocation, where it can be further processed and ex-ploited for any desired use or application. Most, ifnot all, applications will require that the signal froma sensor be telemetered to a location other than thepoint of its generation. There are virtually no limitson the range of telemetering distances that may be re-quired. llus, many fiberoptic sensors permit directoptical data transmission without conversion to elec-trical signals until photodetection. This section willbe devoted to the configuration and use of fiberopticsensor arrays, the telemetering of their outputs toother locations, and the reconversion of these signalsto useful forms. Topics include system considerations,sensor systems, data transmission, data link analysis,repeater design, cable and connector design, and thebudgeting of time, power and cost in telemetry systems.These topics may be summarized as:

FIBEROPTIC: TELEMETRY SYSTEMSSYSTEN GENERAL CONSIDEIbiTIONSLINR ANALYSIS: RISETINE, POWER,

AND COST BUDGETSSENSOR SYSTEMSREPEATER DESIGNCABLE AND CONNECTOR DESIGNEND-TERMINAL RECEIVER CONSIDERATIONS

The basic components of a telemetry system, from thesensors of the variations of a physical parameter tothe instruments for displaying, recording, or simplyusing a representation of the variation at some desti-nation user location are shown in Fig. 6.12.

?P PHYSICAL

PARAMETER

0TRANSDUCER

I s-f(p)

ElENCODERMOOULATORMULTIPLEXERCONVERTER

TRANSMITTER

SOURCE

YEND INSTRUMENT

DISPLAY

SOUND

RECORD

COMPUTE

E@TRANSMISSION I SINK

Fig. 6.12 Basic components of a fiberoptic arraytelemetry system.

6.2.1 Fiberoptic Telemetry System Design OptiOnS

Mny options are open to the designer of afiberoptic telemetry system. These include the deter-mination of the overall system configuration; the de-sign and selection of fiberoptic senaors, cables, andconnectors; the design and selection of transmittersand receivers; and the specification of system para-meters, such as signal-to-noise ratios, distortionlimits, permissible bit error-rates, multiplexingschemes, modulation methods, and the coding, sensing,and detection arrangements.

6-

6.2.2 Fiberoptic Telemetry System BasicConfigurations

Perhaps the most general telemetry systemconfiguration is the multisource (sensor array), multi-user (user-array) general communication network-con-nected system shown in Fig. 6.13. The simplest system

FIBEROPTIC, RADIO,OR WIRE

ARRAYFIBEROPTIC

SOURCE CABLES1

m------

L

TRANS-MISSIONSYSTEM

-----El.---b

Fig. 6.13 Generalized fiberoptic telemetry system.

is a single sensor connected to a single output devicevia a single channel. Many variations are poasible,for example the multisource, multiplexed, single user,fiberoptic data link configuration shown in Fig. 6.14.

El-1

FIBEROPTICCABLES

USER END INSTRUMENTS

0

RECORDERDISPLAY DEVICELOUDSPEAKER

COMPUTERTRANSMITTER

SIGNAL

I 1’

CONDl-4 TIONER

FOCABLE photodetectorAND DEMUX

. . .5

‘B-J...n

Fig. 6.14 A multisource multiplexed single-uaer fi-beroptic sensor array telemetry system.

Various arrangements for the transmission ofsignals from a fiberoptic sensor array to many usersvia different types of fiberoptic data links are ahownin Fig. 6.15. The simplex, half-duplex, full-duplex,and multiplex schemes illustrated in Fig. 6.15 describevarious system configurations with different capabili-ties. These configurations may be connected to operateas one-way-at-a-time, two-way alternate, or two-waysimultaneous systems. For example, two simplex chan-nels could be associated for operating a two-way simul-taneous data link.

SIMPLEX

DUPLEX

%T21cl-lT,

mRI

—

w —R2

mT2

‘“’’’’”x Km7dlFig. 6.15 Generalized transmission schemes.

6.2.3 Telemetry System Budgets

Each telemetry system component interactswith other components within many time and space con-straints. This gives rise to many different ways ofaPPIYing the constraints. Each component may provideuseful power, consume available power, occupy limitedspace, contribute to overall weight, poasesa a usefullife, require maintenance, has an acquisition and con-nection cost, or has other features that affect thewhole system. Thus, each component makes a contribu-tion to, or imposes a liability on, the whole systemin each of these areas. If there are limits to re-sources or characteristics that are imposed on thewhole system, there will be a requirement to budgetthem. h obvious example is to place a limit on systemcost, space, and weight and then aelect a aet of com-ponents whose total cost, space, and weight do notexceed theae limits. Budgeting of time, power, and costwill be discussed for fiberoptic telemetry systems.

6.2.3.1 Rise Time Budget Analysis

Distortion, length of lines, attenuation,signaling (pulse-repetition) rates, and dispersion willplace a limit on the length of time that can be allowedfor a step or pulse input to a fiberoptic transmitterto reach the 90% of maximum signal level at the outputterminal of the receiver. This risetime is distributedover the electrical and optical serially-connected(tandem connected) components of the link on the basisof an approximated Gaussian “distribution in which thecombined risetime of the components in tandem is thesquare root of the sum of the squares (RMS) of all therisetimes of the serially-connected components. Nor-mally the total link risetime is the root-meansquare ofthe transmitter, cable, and receiver risetimes. How-ever, these components themselves may have serialelements each with individual risetimes. For example,the transmitter may have an electronic risetime and afiberoptic pigtail and coupler risetime. The cablemay have splices or repeaters. All the risetimes ofthese are combined on the same RMS basis. A schematicdiagram of a simple fiberoptic link ia shown in Fig.6.16. The elements that comprise the risetime of thefiberoptic link are as follows:

6

FIBEROPTIC TRANSMITTER FIBEROPTIC RECEIVER

I FIBEROPTIC SPLICE I3+! -’,G m4’ E

‘\ \’FIBEROPTIC CONNECTOR FIBEROPTIC CABiE

Fig. 6.16 A fiberoptic data link.

TRANSMITTER RISETIME, tr(xmtr., primarily due to the—————the light source and driver e ectronics.

FIBER RISETI~-, tr(cable), due to the modal disper-———sion (variation in group delay between fiber modes)and material dispersion (nonlinear variation of the.—refractive index, or as a function of wavelength).

Modal dispersion in an optical fiber is acombination of intramodal dia~ersion and intermodal—-— —dispersion. Intramodal ~ is pulse broadeningin an optical fiber. It is primarily a function ofthe spectral bandwidth of the source and the materialdispersion, to be discussed later. The intramodaldispersion, Sintram, of an optical fiber is given by:

sintram = (SAL/c)d2n/d21 (6.10)

where S = Spectral bandwidth of sourcek = Wavelength of source, midbandL = Length of fiber

= Speed of light in a vacuumd2n/di~ = Material dispersion, in which n is the core

refractive index and 1 is the source wave-length

The only deaign option for reducing intramodal disper-sion at a given source wavelength and length of fiberis to reduce the source spectral bandwidth. The spec-tral bandwidth of a typical LED is of the order of0.05 Vm whereaa that of a typical laser is 0.002 pm.

Intermodal dispersion is pulse broadening dueto differences in propagation velocity, and hence pro-pagation time, among the various modes. Proper shap-ing of the refractive index profile of an optical fibercan reduce intermodal dispersion to a minimum. Inter-modal dispersion, Sinterm, is given by:

Sintem = (LnA/2c)pi (6.11)

where L = Length of fibern = Refractive index at center of fiberA = (nl-n2)/nl, where nl and n2 are the maximum

and minimum refractive indices , respectively.It is called the index difference parameter

c = Speed of light in a vacuumpi = Refractive index profile parameter, ideally

equal to 2.25, based on zero intermodal dis-persion

The individual contributions to dispersion within modesand among modes in a given optical fiber follow a Gaus-sian distribution. Therefore, if Eq. (6.10) and (6.11)are squared, added, and the length, L, factored, andthe square root of the sum of the squares is taken, the

-7

following is obtained:

[ 1L-BWP= [(SX/c)d2n/dA2]2+[(nA/*c)pi]2 1’2 (6.12)

where L-BWP is the optical fiber length-bandwidth pro-duct. Many of theae parameters are fixed by the opti-cal fiber manufacturer. In addition, the modal disper-sion caused by a fiber can be expressed in terms of therisetime for a step input optical signal. This can beempirically determined for typical high performancecommercially available optical fiber. The parametersgiven in Eqa. (6.10) and (6.11), and therefore (6.12),contribute to the fiber riaetime modal dispersion co-efficient used in Eq. (6.13) below.

The portion of the fiber risetime due tomodal dispersion (intramodal and intermodal) ia givenempirically for a typical high-performance commerciallyavailable optical fiber, as:

FIBER RISETIME DUE TO MODAL DISPERSION

trmo(cable) = 530/L-BWpo ‘s (6.13)

where L-BWPO =

L-BWP =Leff =

where L=

530 =

The

(L-Bwp)/Leff = Optical 3-dB bandwidth ofthe fiber.

Length-bandwidth product, MRz-km.L x = Effective length of fiber.

Actual length of fiber.0.5 < x < 1Short lengtha, < 1 km, x = 1Long lengths, x = 0.7 or 0.8.Fiber risetime modal dispersion coeffi-cient for typical high-performance com-mercially available optical fiber.

portion of the fiber risetime due to

where

material dispersion is given aa:

FIBER RISETIME DUE TO MATERIAL DISPERSION

‘rma(cable) = 1.1 MSL (6.14)

M = Material dispersion coefficient, givenin nslnm-km and as shown in Fig. 6.17.

S = Spectral bandwidth of source, nmL = Link length, km

A typical curve for the value of M, the ma-terial dispersion coefficient, as a function of wave-length for two specific glasses is shown in Fig. 6.17.

0.25

015

010

0.05

0

Fig. 6.17 T h e

/00 900 1100 1:

WAVELENGTH(nm))

material dispersion coefficient versuswavelength for two types of glasses.

6-

RECEIVER RISETIME, tr(rcvr), due to the photode-tector and its aaaociated electrical circuits. Thereceiver risetime la normally given by the manu-facturer or can be constructed or eatimated fromthe manufacturer’s data.

Normally a Gauasian distribution of the rise-times is assumed, and thus forcomponents the overall risetimegiven as:

‘r(sya) = [t2*(xmtr) +

2‘r ma(cable) + ‘r(rcvr)

a set of sequentialfor the system is

2r mo(cable) +

1/2(6.15)

However, the total risetime for the link,

‘r(sys)~ cannot exceed the maximum allowable risetimefor the link. In digital systems, the allowable rise-time is limited by the requirement to prevent the biterror rate (BER) due to interaymbol (interpulse) inter-ference from exceeding a prescribed value. In analogsystems the frequency response at high frequencies mustbe sufficient to prevent distortion of the base bandaignals. For example, in the nonreturn-to-zero (NRZ)method of signal representation (code), ‘he ‘r(sys)must be less than 0.7 times the bit interval, express-ed as the reciprocal of the bit rate. If the bit rateia 7.0 Mb/see, the maximum value tr(sys) can have iais 100 nsec for NRZ coding. For return-to-zero (RZ)coding the factor is 0.5, in which case, for the samebit rate of 7.0 Mb/see, the maximum allowable tr(sya)is 71.4 ns.

The following is given as an example of ariaetime budget for a typical fiberoptic link:

LINR

FIBEROPTIC LINK RISETIME BUDGET

DESCRIPTION

Data rate, Rw 7.0 Mb/seeLink length, L 1.5 kmLength-bandwidth-product, L-BWF 50 MHz-kmLight source LEDOperating wavelength,a 0.830 PmLight source spectral width, S 0.020 pm

COMPONENT RISETIMES

Transmitter [tr(xmtr)] (Manufacturer) *O ns

Fiber modal dispersion risetime [trmo(cable)]

(L-BWo) = (L-BWP)/Lx = 50/1.5°”8 = 36.1 MRz-km

‘rmo(cable) = 530/(L-BWPo) = 530/36.1 = 14.7 ns

Fiber material dispersion risetime [t_(cable)]

M = 75 ns/m-km (Manufacturer)

‘rma(cable)=l- lMsL=( 101)(75)(0”02)(1-5)=2”5ns

Receiver risetime [tr(rcvr)] (Manufacturer)

‘r(rcvr) = 375/Belec = 375/50 = 7.5 ns 56.3

LINR RISETIME

Substituting the above risetimes in Eq. (6.15) theoverall system (link) risetime is calculated to be26 ns.

8

MAXIMUM ALLOWABLE RISETIME = 0.7/RN~ = 100 nS

RISETIME BUD(ZT MARGIN = 7fI ns

The 74 ns margin between the maximum allow-able risetime based on the required signaling rate andthe system risetime for all the components can be usedin many ways. For example, the cable could be madelonger, the signaling rate could be increased, or acheaper cable with a greater material or modal disper-sion per unit length could be used. However, otherbudgets, such as the power budget, may place limits ontheae changes. Perhaps the one single fact to rememberin regard to risetime is that it represents reciprocaldollars, i.e., the longer the risetime, the cheaperthe component. Therefore, except for a power safetymargin, all allowable risetime should be used up forthe performance requirement in a given application.

6.2.3.2 Optical Power Budget Analysis

The optical power requirement of a givenfiberoptic telemetry system is also a matter of dis-tribution of power over a serial or a parallel set offiberoptic channels. For example, if there are starcouplers, there must be sufficient input power to sat-isfy the input power requirement for each parallel out-put channel. Serially connected components, such ascables, splices, and couplers, will each have an inser-

tion loss. Repeaters will insert a gain. The lossesand gains are added to obtain the source-to-receiveroverall loss. The optical power dissipation that canbe allowed is the difference between the sum of thetransmitter and repeater optical power outputs and therequired receiver (photodetector) optical power inputin order to keep the bit error rate (BER) below, orsignal-to-noise ratio (S/N) above, a specified value.A typical allowable optical power loss between trans-mitter and receiver for various data rates at an allow-able BER of 10-9 is shown in Fig. 6.18. Normally one

tLASER-LAUNCHED

o POWER RANGE

-lo LED-LAUNCHED--..POWER RANGE _______ -14=

II

g

n

-20

-30

-40

-50

-60

-70

-80

BER =10-9

I

-901 1 1 11 10 100 1000

DATA RATE (Mb/s)

Fig. 6.18 optical power loss versus data rates forthe fiberoptic data link used in the opti-cal power budget analysis in Section 6.1.3.

would not use up all the available power, but maintaina safety margin of a few dB to insure satisfactory per-formance. The allowable loss is then distributed overthe fiberoptic link components as shown in Fig. 6.16and given in the following example:

6-

FIBEROPTIC LINR OPTICAL POWER BUDGET

LINK

(Fig. 6.16)

DESCRIPTIONData Rate, RLink length, LOperating wavelength

TRANSMITTER POWER, pTLight source typeAverage source optical powerFiber coupling lossAverage launched optical power,

REQUIRED RECEIVER POWRR, pREQDetector typeRequired bit error rate, BERReceiver bandwidthReceiver sensitivityLink margin‘REQ

7.0 Mblsec1.5km0.830 nm

LED 0.1 mW-10 dBm-4 dB-14 dBm

PIN-FET1(3-950 MHz-55 dBm+ 7 dB-48 dllm

ALLOWABLE LINK LOSS OVER MARGIN, PALpm = PT - PmQ = -14 -(-48) = 34 dB

LINR LOSS COMPUTATION

Contributor Unit Quantity Total

Recr coupling 3.0 dB 1 3.0 dBConnectors 2.0 2 4.0Splices 0.5 4 2.0Cable 5.0 dB/km 1.5 km 7.5SplittersMargin 2.0 dB 2.0Total link loss 18.5 dB

REMAINING POWER MARGIN(Allowable - Total link loss) = 34- 18.5

= 15.5 dB

Since a link margin of 7 dB and a link losscomputation margin of 2 dB have already been allowed,the entire 34 dB may be used up. The loss in the linkof the given design is 18.5 dB. Therefore, there is anexcess total available optical power margin of 15.5 dB.It may be cheaper to use up this excess margin byselecting cheaper cable components with greater lossesor it may be cheaper to choose a lower-power source.Link power is like dollars, it is best to get by withthe least power, low power sources being cheaper. How-ever, link loss is more like reciprocal dollars, thegreater the power loss, the cheaper the components.Therefore, there is a trade-off to be made in order tominimize the overall cost of a fiberoptic link.

6.2.3.3 Cost Budget Analysis

The cost of a fiberoptic telemetry systemwill be based on judicious maximal use of availablerisetime and minimal use of power as well as many otherfactors. Fiberoptic cable designs, repeater spacing,multiplexing schemes, allowable BERs, cable routings,the use of overhead versus subterranean cables, avail-ability of components, simplicity of design and fabri-cation, and ease of maintenance, are just a few of themany factors that will enter into the overall cost ofthe system.

6.2.4 Fiberoptic Telemetry System SpecificConfigurations

An example of a set of the final design para-

9

meters for the field tested fiberoptic long-haul tele-metry system shown in Fig. 6.19 is as follows:

LONG HAUL FIBEROPTIC LINR PERFORMANCE DATA

SYSTEM LENGTHREPEATER SPACINGNUMBER OF REPEATERS

DiameterLengthWeight

OPEIUiTING DEPTHCABLE DIAMETERCABLE STRENGTHDATA FORMATFULL DUPLEXWAVELENGTHSHIGH BIT RATE CHANNEL

Bit Error Rate (BER)Low Bit RateBit Error Rate (BER)

70 km6.8 to 8 km82.9 cm

30.5 cm< 400 g1000 m

2.4mm60 kg (0.8% Strain)Digital PCM1 Fiber0.83 and 1.06 pm22 Mb/s

< 10-943 kb/s

< 10-7

The above system is the Naval Ocean SystemsCenter and the International Telephone and Telegraph(NOSC/ITT) Undersea Single Fiber Multirepeater FullDuplex Electrooptical Data Link, a schematic diagram ofwhich was shown in Fig. 6.19.

HBR RCVR_HBR(22 MBISEC) EOREP1

LBRXMTRLBR (43KBISEC)C

)

SPACING: 8km BTWN REPEATERSLBR

I IliBR

Al= .83pm LASER

A2=106#mLED EOREP2

-I

11

SENSOR,

STRING HBR(A1) ~ EOREP8

liBRXMTRLBRRCVR _LBR(A2)

Fig. 6.19 The Naval Oceans Systems Center and the In-ternational Telephone and Telegraph (NOSC/ITT) undersea single fiber multirePeaterfull duplex electrooptical data link.

There probably is no limit to the number ofdifferent fiberoptic sensor array system configurationsthat can be designed, considering the number of energi-zation methods, types of sensors, and return telemetrymethods that can be uaed. Four specific fiberoptictelemetry system and sensor array configurations areshown in Figs. 6.20 through 6.23. Specific designaspects of basic configurations will be discussed infollowing subsections.

6-10

PROCESSING STATION T R A N S M I S S I O N PARALLEL SENSOR ARRAY

LINK

,—

2+DEMODU-

LATOR

SIGNALPROCESSOR

LASER hOR LED \

: F I B E R O P T I CCONNECTOR

it-1

RECEIVER

P H O T O D E T E C T O R [

DDISPLAY

Fig. 6.20 An example of a fiberoptic sensor arraymultimode intensity modulated telemetrysystem.

PROCESSING STATION TRANSMISSION LINEARSENSOR ARRAYLINK

t

[.DEMODU

LATORq J J 1

: FIBER

8

SIGNAL; C O U P L E R S

PROCESSOR

DISPLAY

Fig. 6.21 AII example of a fiberoptic sensor arraymultimode intensity modulated telemetrysystem.

PROCESSINGSTATION

D

TIMING

c=FIBEROPTC

RECEIVER

clDEMOCY.JLATOR

aSIGNAL

PROCESSOR

DSPLAY

I

TRANSMISSIONLINK

ELECTRICAL FOWER

-FIBEROPTIC CASLE

I

ARRAY

Fig. 6.22 An example of a fiberoptic interferornetricsensor array telemetry system.

PROCESSING STATION T R A N S M I S S I O N wAVELENGTHM ULTIPLEXEDLINK ARRAY

;DIFFRACTION: GRATING

[

BROADs:::~::M

LdFIBEROPTIC

CONNECTOR

BDEMODU-

LATOR

SfGNALPROCESSOR

; ~A’&

iRECEIVER

IQ

n

c1OISPLAY

Fig. 6.23 An example of a fiberoptic diffractiongrating senaor array telemetry system.

6.3 FIBEROPTIC SENSOR ARRAY TELEMETRY TRANSMIS-SION LINE PARAMETERS

6.3.1 Transmission Line General Parameters

Fiberoptic array data transmission line de-signs include a large but manageable number of optionsand variables. A few of these are as follows:

GENERAL FIBEROPTIC TRANSMISSION LINE DESIGN PARAMETERS

SIGNAL MODEAnalog, digital, hybrid, discrete

MODULATION SCHEMEPhase, frequency, intensity, polarization, wave-

lengthCHANNEL CAPABILITY

Simplex, duplex, half-duplex, diplex, multiPlexOPERATIONAL MODE

One way, one way at a time, two way simultaneousCABLE DESIGN

Fibers, strength members, conductors, jacket,filling, insulation, buffering, spacing type,spacing

FAIL-SAFERedundancy, power margin, tolerance to breaks

ATTENUATIONAbsorption, scattering, insertion loss, bit errorrate (BER)

DISPERSIONBit error rate (BER), distortion, signal-noiseratio

RELIABILITYFailure rates, failure modes

OVERALL CHANNEL SIGNALING RATEIn digital systems the number of transmissionlines or channels will be determined by the totaldata signaling rate requirements and the multi-plexing schemes that are used. For example, assumemany channels with different signaling rates anddifferent digital pulsing schemes connect two sta-tions. Then, the total data aignaling rate (capa-city between the stations, or as an output capacityfrom one to many stations) for a group of m paral-lel channels in which Ti is the minimum intervalin seconds between signal transitions for the i-thchannel and ni is the number of significant condi-tions of modulation, is given by:

mRT = ~ (1/Ti) log2 ni (6.16)

1=1

6-1

For m parallel channels with equal pulse intervals,this reduces to:

RE = (m/T) log2 n. (6.17)

For two condition modulation, this reduces to m/T.For a single channel, RT reduces to (l/T) log2n,and with 2 conditions, I/T, i.e., the baud ratefor one channel. Each of the multiplexed fiberop-tic channels can be used as an analog (voice,sound, continuous signal) or as a digital (pulsecoded) channel.

6.3.2 Transmission Line Specific Parameters

The construction features of a fiberoptic orelectrooptic transmission line (cable) depend on manyenvironmental factors. Some of these are as follows:

FIBEROPTIC CABLE DESIGN PAMMETERS ANDENVIRONMENTAL FACTORS

PHYSICAL STRENGTH PARAMETERSTensile StrengthRadial Compression StrengthFlex ResistanceBend ResistanceAbrasion ResistanceVibration ResistanceStrength Member LocationStrength Member Materials

ENVIRONMENTAL FACTORSOperating TemperatureOperating PressureMoisture/Chemical/Other Resistance

OPTICAL FIBER PARAMETERSMultimode or Single ModeGlass or PlasticRefractive Index ProfileCore ConcentricityCladding Outer DiameterNumerical ApertureFiber Jacket MaterialFiber Jacket ThicknessDispersion (Modal and Material Multimode

vs Singlemode)Attenuation Per Unit LengthLose and Bandwidth StabilityCostings on FibersNumber of FibersEase of JoiningSize of Fibers

CABLE PARAMETERSSize of CableBend RadiiSheathingLocation of FibersArmor Requirements

ELECTRICAL FEATURESElectrical HeatingWire SizeNumber of ConductorsShielding

h example of an electrooptic cable cross-section is shown in Fig. 6.24. The need for built-in-

1

55/125 pm, F.4uI-TIMODE,Gl, OPTICAL FIBER \

EL BUFFER TOD. OF 1.02 mm

15 CU-CLAD-STEEWIRES – EACH 0.0. D. – AS HELIX

;KET TO 2.54 mm

Fig . 6.24 A cross section of one of a large number ofdifferent electrooptic cable designs.

cable fiberoptic repeaters is determined by the rise-time and power budgets, which in turn, depend on atten-uation and cable length-between-repeaters. An exampleof a fiberoptic electrooptic repeater is shown in Fig.6.25. This repeater handles a high bit-rate in one di-

+=+

HBR(A,)

— OPTCALTOPROCESSING—

STATION — DuPLEXER

LSR(A2) H=?HSR

OPTICALDU~ER —

LSR

OTHER REKATERS

Fig. 6.25 h example of a fiberoptic full duplex re-peater.

rection for user data and a low bit-rate in the otherdirection for control and supervisory data in a singlefiberoptic cable. An arrangement for the optical du-plexers that was shown in Fig. 6.25 is sho~ in Fig.6.26.

TOHSRRCVR

_HSR

6 Q (). . . ---A,

p ‘_LSR

A2 Q AZFROM--- LSRXMTR

- - - -

~..

‘- ‘- ““-~%1:

DICHROICFILTER

Fig. 6.26 An arrangement for a fiberoptic duplexer.

tin indication of the power-loss-per-hertzversus frequency for an optical fiber, compared to wirepairs and coaxial cables, iS sbo~ in Fig. 6.27. Notethat in the graded-index fiber the loss-per-hertz isalmost independent of frequency for frequencies up toalmost one gigahertz.

6-1

‘r4

24

~01 1000

FREQUENCY (MHz)

Fig. 6.27 The optical power loss per hertz for onekilometer lengtha of several types of cablesat various frequencies.

6.3.3 Multiplexing with Optical Fibers

Multiplexing may be accomplished with opticalfibers in the following ways:

FREQUENCY-DIVISION MULTIPLEXING (FDM)Modulate a single optical wavelength with a dif-ferent carrier frequency for each channel.

WAVELENGTH-DIVISION MULTIPLEXING (WDM)Use two or more optical sources each with a differe-nt wavelength for each channel.

TIME-DIVISION MULTIPLEXING (TDM)Different time-slot for each channel.

sPAcE-DIvxsIoN MULTIPLEXING (fiDM)Different fiber for each channel.

POLARIZATIONDifferent form of polarization for each channel.

The multiplexing scheme that is used for agiven application depends on the number of channels re-quired and the cost factors for each scheme. A typicalmultiplexing arrangement is shown in Fig. 6.28. In

m2

$

SENSORARRAY

1

TRANSMl~ER

IJULILS,GNAL / \ ( /

-’45-J ‘RECE’VERAQQ.. nlln

Fig. 6.28 An example of a fiberoptic sensor linear-array telemetry system with single opticalrepeatered cable return.

this figure, the signals from the sensor array aremultiplexed on a time-division multiplexing (TDM) basisso that only one series of repeaters is required for asingle fiber. This basic fiberoptic link consists ofa fiberoptic transmitter (modulated light source), a

2

fiberoptic cable (optical cable), and a fiberopticreceiver (photodetector). Electrical-to-optical andoptical-to-electrical conversion (transduction) is pre-sumed at each end, though such presumption is not al-ways true for all fiberoptic links. For example, thereceiving end may consist of a fiberscope (display de-vice) or simply a flashing light indicator of on-offconditions.

6.3.4 Connector Parameters

There are many performance requirements anddesign considerations that enter into the choice ofsuitable connectors for fiberoptic cables. In additionto the optical insertion loss introduced by the connec-tor, other optical features such as axial misalignment,axial offset, and spacing between fibers must be con-sidered, as was indicated in Chapter 3. Some of theconnector physical features and design considerationsare as follows:

CONNECTOR DESIGN CONSIDERATIONS

NUMEER OF ELECTRICAL LEADS AND SIZENUMBER OF OPTICAL FIBERS AND SIZEOPERATING TEMFERiTURR AND PHESSUREMOISTURE AND DIRT RESISTANCEFIELD MATABILITYSTRAIN RELIEF DESIGN

An example of a ruggedized connector is shownin Fig. 6.29.

ACHlEVED2.8dS LOSS WHEN COUPLING

50#m CORE0.2 NAGRAOEDINOEX FIBER

Fig. 6.29 A ruggedized fiberoptic cable connector.Courtesy Standard Telecommunications Labor-atories Limited, Harlow, Essex, England;and ITT Cannon, Basingstoke, Hampshire,England.

6.4 END-TEHMINa (RECEIVER) C0N51DEWT10N

After a physical parameter, such as a soundwave or a varying magnetic field, has been sensed andtransformed by a fiberoptic sensor into modulated lightthat is then transmitted to a point of use via a fiber-optic telemetry system, the modulated light has to bedemodulated in order to recover the information-bearingsignal. One or more photodetectors may be required toobtain an electrical signal that may be used as is orfurther processed by electrical circuits. Demultiplex-ing may be required to obtain the separate signals thatwere originally generated or transmitted. For digitaldata, decoding will be necessary to convert the pulsecodes to analog form or to recover alphanumeric data.In some cases, the incoming signals need not be con-verted to electrical signals, but ULSY be directly dis-

6-1

played as light signals, such as for signaling on-offconditions or for telemetering images received via amultifiber coherent optical cable connected directlyto the faceplate of a fiberscope. Thus, the type ofprocessing that must be performed on incoming lightwavesignals at an end terminal depends on the specificapplication.

6.5 SUMMARY

The topics that were covered in this chapterincluded fiberoptic telemetry system configuration;system risetime, power and cost budgeting; sensor arraydesign and construction; and fiberoptic transmissionconsiderations, including multiplexing and fiberopticcable, repeater, and connector design considerations.

3

APPENDIX

FIBEROPTIC SENSORS GLOSSARY

e

This Glossary on fiberoptic aensors is intended toprovide definitions of the terms used in this Handbookand to provide supplementary information directly re-lated to the topics discussed. Many topics that wereintroduced in the various chapters are developed infurther detail in thia Glossary. l%is approach was usedto avoid burdening the reader with details and explana-tions of terms aa topics were covered. For example,Maxwell’s equations, solid state electronics, electro-optic effects, electromagnetic theory, multiplexingand modulation methods, and various coefficient fortransmission, reflection and attenuation are coveredin this Gloasary.

The definitions in this Glossary are consistentwith international, national, Federal, military, andtechnical society atandards. Many were taken from themore comprehensive Fiberoptic and Lightwave Communi-cations Standard Dictionary, Illustrated, 284 pages;and from the Communications Standard Dictionary,Illustrated. 1045 Dazes. by Martin H. Weik, Van.-. .Nostrand Reinhold Company, 135 W. 50th Street, NewYork, New York, 10020.

A

absorption. The transference of some or all of theenergy contained in an electromagnetic wave to thesubstance or medium in which it ia propagating orupon which is is incident. Abaorbed energy fromincident or transmitted lightwaves is converted intoenergy of other forms, usually heat, within thetransmission medium, with the resultant attenuationof the intensity. See intrinsic absorption.

acceptance angle. The maximum angle, measured from thelongitudinal axis or centerline of an optical fiberto an incident ray, within which the incident raywill be accepted for transmission along the fiber,that is, total internal reflection of the incidentray occurs. If the acceptance angle for the fiberis exceeded, total internal reflection will not oc-cur and the incident ray will be lost by leakage,scattering, diffuaion, or absorption in the clad-ding. The acceptance angle is dependent upon therefractive indicea of the two media that determinethe critical angle. For a cladded fiber in air,the sine of the acceptance angle is given by thesquare root of the difference of the squares of theindices of refraction of the fiber core and ~he cla -ding. In mathematical notation, sine= (n -n 7

where 0 ia the acceptance angle, n, is tiie r~~l~c~tive index of the core, and n2 is the refractiveindex of the cladding. Synonymous with acceptanceone-half angle.

A-

acceptance cone. A solid angle whose included apexangle is equal to twice the acceptance angle. Raysof light within the acceptance cone can be coupledinto the end of an optical fiber and still maintaintotal internal reflection for all the rays in thecone. Typically, an acceptance cone is 40°.

acceptance one-half angle. Synonym for acceptanceangle.

acceptor. In an intrinaic semiconducting material (suchas galium arsenide), a dopant (such as germaniumthat has nearly the same electronic bonding struc-ture as the intrinsic material, but with one lesselectron among its valence electrons than that re-quired to complete the intrinsic bonding structuralpattern. This pattern leaves a “space” or “hole”for one electron for each dopant atom in the struc-ture. The dopant atoms are relatively few and arefar apart and hence to not interfere with the elec-trical conductivity of the intrinsic material. Anelectron from a neighboring intrinsic material atomcan fill the hole at the dopant site, leaving a holefrom whence it came; thus, the hole can appear tomove or wander about, although with less mobilitythan the electrons that are free and exceas to donoratoms. Also see donor; electron; hole.

acoustooptic effect. The changes in diffraction grat-ings or phase patterns produced in a transm.lssionmedium conducting a lightwave when the medium issubjected to a sound (acoustic) wave, due to thephotoelaatic changes that occur. The acoustic wavesmight be created by a force developed by an imping-ing sound wave, the piezoelectric effect, or magne-tostriction. The effect can be used to modulate alight beam in a material since many properties,such as lightconducting velocities, reflection andtransmission coefficients at interfaces, acceptanceangles, critical angles, and transmission modes,are dependent upon the diffractive changes thatoccur. The effect includea the phase transductionmechanism used in fiberoptic sensors, i.e., t hchange in phase that occurs due to the change inlength and refractive index caused by the acousticpresaure. Also see electrooptic effect.

acoustooptics. The study and application of the inter-relation of acoustics and optics. Synonymous withoptoacoustics.

amplification by stimulated emission of radiation(laser). See light amplification by stimulated emis-sion of radiation (laser).

amplitude modulation (AM). The modulation of the ampli-tude of a wave serving as a carrier, by another waveserving as the modulating signal. The amplitude ex-cursions of the carrier are made proportional to aparameter of the modulating signal that bears theinformation to be transmitted.

1

.

angstrom. A unit of length equal to 10-10 meter, 10-1nanometer, and 10-4 micron.

aperture. See numerical aperture (N. A. ).

array. See sensor array.

attenuation. The decrease in power of a signal, lightbeam, or lightwave, either absolutely or as a frac-tion of a reference value. The decrease usuallyoccurs as a result of absorption, reflection, dif-fusion, scattering, deflection, or dispersion froman original level and usually not as a result ofgeometric spreading, i.e., the inverse sqwre ofthe distance. In an optical fiber, attenuation Isundesirable for transmission purposes but desirablefor prevention of leakage or clandestine detection.Optical fibers have been classified as high-loss(over 100 dB/km), medium loss (20 to 100 db/km),and 10W1OSS (less than 20 dB/km).

Bband. See conduction band; energy band; valence band.

bandwidth. 1. A range of frequencies, usually speci-fying the number of hertz of the band or the upperand lower limiting frequencies. 2. The range offrequencies that a device is capable of generating,handling, passing, or allowing, usually the rangeof frequencies in which the response is not reducedgreater than 3 dB from the maximum response.

baseband. The band of frequencies associated with orcomprising an original signal from a modulatedsource. In the process of modulation, the basebandis occupied by the aggregate of the transmitted sig-nals used to modulate a carrier. In demodulation,it is the recovered aggregate of the transmittedsignals. The termis commonly applied to cases wherethe ratio of the upper to the lower limit of thefrequency band is large compared to unity.

beam splitter. h optical device for dividing a lightbeam into two separated beams. One simple beamsplitter consists of a plane parallel plate, withone surface coated with a dielectric or metalliccoating that reflects a portion and transmits a por-tion of the incident beam; i.e., part of the lightis deviated through an angle of 90°, and part iSunchanged in direction. A beam splitter may alsobe made by coating the hypotenuse face of a 45°-90”prism and cementing it to the hypotenuse face ofanother. The thickness of the metallic beam split-ting interface will determine the proportions of thelight reflected and transmitted. In metallic beamsplitters, an appreciable amount of light is lost byabsorption in the metal. It may also be necessaryto match the reflected and transmitted beam forbrightness and for color. In these cases, it isnecessary to use a material at the interface thatgives the same color of light by transmission andreflection. Nhere color matching at the surface orinterface cannot be accomplished, a correcting colorfilter may be placed in one of the beams. In afiber-to-fiber beam splitter, evanescent couplingcan be used to transfer optical energy from onefiber to another.

bend. See ordinary bend.

bend loss. See microbend loss.

A-2

birefringence. The splitting of a light beam into twodivergent components upon passage through a doubly-refracting transmission medium, with the two com-ponents propagating at different velocities in themedium. In an optical fiber, birefringence is re-lated to the strain in the fiber which causes thefiber to be a single polarization transmissionmedium.

Bragg cell. An acoustooptlc device that accepts fixedfrequency monochromatic light and that has a base-band vibrating element capable of modulating the in-put lightwaves producing an output lightwave with afrequency equal to the frequency of the input light-wave plus the frequency of the baseband input signal.The Bragg cell has application as part of an inter-ferometer in which heterodyne detection is used.

Brewster angle. The angle, measured with respect tothe normal, at which an electromagnetic wave inci-dent upon an interface surface between two dielec-tric media of different refractive indices is totallytransmitted into the second medium. The magneticcomponent of the incident wave must be parallel tothe interface surfa~~l The Brewster angle is givenby: tan B = (~2/E1) , where B is the Brewster an-gle, c1 is the electric permittivity of the incidentmedium, and e2 is the electric permittivity of thetransmitted medium. The Brewster angle is a conven-ient angle to transmit all the energy in an opticalfiber to an outside detector. There is no Brewsterangle, for which there is total transmission andtherefore zero reflection, when the electric fieldcomponent is parallel to the interface, except whenthe permittivities are equal, in which case thereis no interface. Mso, for entry into a more densemedium, such as from air into an optical fiber: tanB = (n2/nl), and from a more dense medium into aless dense medium, such as fiber to air: tan B =(nl/n2), where nl and n2 are the refractive indicesof the air and fiber, respectively.

brightfield sensor. In fiberoptic, a sensor in whichthe optical power modulated by the sensor is all ora large fraction of the total optical power fed toor available to the sensor. Synonymous with light-field sensor. Contrast with darkfield sensor.

budget. See optical power budget; power budget; rise-time budget.

bulk coupler. In fiberoptic, a coupler that has oneinput and many outputs.

bundle jacket. The outer protective covering appliedover a bundle of optical fibers.

bus. 1. One or more conductors that serve as a commonconnection for a related group of devices. 2. Oneor more conductors used for transmitting optical orelectrical power or signals.

ccable. 1. A jacketed bundle or jacketed fiber in a

form that can be terminated. 2. A group of con-ductors that are bound together, usually with a pro-tective sheath, a strength member, and insulationbetween individual conductors and for the entiregroup. See fiberoptic cable.

cable jacket. The outer protective covering appliedover the internal cable elements.

carrier. 1. In communications, a wave, pulse train,or other signal suitable for modulation by an infor-mation-bearing signal to be transmitted over a com-munication system. 2. h unmodulated emission. Acarrier is usually a sinusoidal wave, a recurringseries of pulses, or a direct-current (DC) signal.See charge carrier.

cavity. See resonant cavity.

charge carrier. tin atomic or molecular particle thatpossesses an electric charge and is capable of mov-ing under the influence of an electric or magneticfield. For example, an electron, a hole, or an ion.

cladding. An optical transparent material, with a re-fractive index lower than that of the core, placedover or outside the core material of an opticalwaveguide that serves to reflect or refract light-waves in order to confine them to the core. Thecladding also serves to protect the core.

cladding mode stripper. 1. A material applied to op-tical fiber cladding to allow light energy beingtransmitted in the cladding to leave the cladding ofthe fiber. 2. A piece of optical material or anoptical component that can support only certain elec-tromagnetic wave propagation modes. In particular,it does not support the propagation modes in thecladding of a cladded optical fiber, slab dielectricwaveguide, or integrated optical circuit. The strip-per effectively removes the cladding modes withoutdisturbing the core-supported propagation modes.

close-confinement junction. A synonym for single heter-ojunction.

CMos. See combined metal oxide semiconductor.

coating. See optical fiber coating.

coherence length. The coherence time of a light beammultiplied by the velocity of the light, namely(1/cAv)c = l/Av. AI.SO see coherence time.

coherence time. In beam of light propagating in a vac-uum, the time obtained from the expression l/cAv,where c is the velocity of light in a vacuum, v isthe reciprocal of the wavelength, and Avis the vari-ation or spread of v over time for the beam. Inmaterial media, the c is replaced by c/n, where n isthe refractive index. Also see coherence length.

coherent bundle. A bundle of optical fibers in whichthe spatial coordinates of each fiber are the sameor bear the same spatial relationship to each otherat the two ends of the bundle. Synonymous withaligned bundle.

A-3

coherent light. Light of which all parameters are pre-dictable and correlated at any point in time orspace, particularly over an area in a plane perpen-dicular to the direction of propagation or over timeat a particular point in space. Contrast withincoherent light.

collection angle. Synonym for acceptance angle.

combined metal oxide semiconductor. A metal oxide semi-conductor that consists of both positively-doped andnegatively-doped material.

common-mode. 1. Pertaining to any uncompensated com-bination of generator or receiver ground potentialdifference (voltage), generator common return offsetvoltage, and longitudinally-coupled peak randomnoise voltage measured between the receiver circuitground and receiver cable with the generator endsof the cable short-circuited to ground. 2. Thealgebraic mean of the two voltages appearing at thereceiver input terminals with respect to the receiv-er circuit ground. 3. Pertaining to the relativeoptical intensity fluctuations between two coherentelectromagnetic (light) waves.

common-mode rejection ratio (CMRR). The ratio of thecommon-mode interference voltage or optical inten-sity at the input of a circuit to the interferencevoltage or optical intensity at the output of thecircuit.

conduction band. In a semiconductor, the range of elec-tron energy, higher than that of the valence band,possessed by electrons sufficient to make them freeto move from atom to atom. When they leave thevalence band, they are free to move under the influ-ence of an applied electric field and thus theyconstitute an electric current.

conductor. 1. In fiberoptic, a transparent mediumthat is capable of transmitting or conveying light-waves a useful distance. 2. In electric circuits,a material that readily permits a flow of electronsthrough itself upon application of an electric field.Electrical conductors include copper, aluminum,lead, gold, silver, and platinum. The conductivityis specified by: J = aE, where J is the currentdensity in amperes/square meter for S1 units, E isthe applied electric field in volts/meter, and o isthe conductivity in reciprocal ohms/meter. Also seedielectric. Contrast with insulator.

connector. In fiberoptic, a device that permits thecoupling of signals from one optical fiber or cableto another.

connector insertion loss. The power loss sustained bya transmission medium, such as a wire, coaxial cable,optical fiber cable, or integrated optical circuitcomponent, due to the Insertion of a connector be-tween two elements, which would not occur if themedia were continuous without the connector i.e.,if there were no reflected, absorbed, dispersed,or scattered power.

controllable coupler. See electronically controllablecoupler.

core. The central primary light-conducting region of amaterial medium, such as an optical fiber, the re-fractive index of which must be higher than that ofits cladding in order for the lightwaves to betotally reflected or refracted. Most of the opticalpower is in the core.

coupler. In optical transmission aystems, a componentused to interconnect two or more optical fibera.Also see connector; bulk coupler; electronic&lly-controllable coupler; reflective star-coupler; 3-dBcoupler.

coupling. The connection, attachment, or binding ofoptical elements, electric circuit elementa, elec-tric and magnetic fields, propagation modes, or elec-tromagnetic wave component, such as surface wavesand evanescent waves, to internal waves in wave-guides, dielectric slabs, or other interdependentassociations and interactions of events and materialsin a system. For example, two optical fibers or cer-tain elements in an integrated optical circuit maybe coupled together in some manner to preserve signalcontinuity. See evanescent field coupling.

coupling coefficient. Synonym for coupling ratio.

coupling efficiency. In fiberoptic transmission, theratio of the optical power on one side of an inter-face to the optical power on the other side. Forexample, the ratio of the power developed by a lightaource to the power accepted by a bundle of fibers,or the power received at the end of a bundle offibers to the power that impinges on a photodetector.For light sources with emitting areas larger thanfiber core diameters, the product of fiber numericalaperture (N.A.) and core diameter is a good indica-tor of maximum coupling efficiency. For othersources, such as small laser diodes with emittingareas small than the fiber core diameter, the N.A.alone is a relevant indicator of coupling efficiency,usually expresaed as a percentage.

coupling loss. In a fiberoptic coupling, the opticalpower loss caused by the coupling itself, a lossthat would not occur if the optical fiber were con-tinuous without the coupling.

coupling ratio. The ratio of power on the output sideof a coupling to the power on the input side. Thecoupling ratio is always less than unity. Synonymouswith coupling coefficient. Also see 3-dB coupler.

critical angle. The angle, with the normal, at whichan electromagnetic wave incident upon an interfacesurface between two dielectric media, at which totalreflection of the incident ray first occurs as theincident angle with the normal to the incident aur-face is increased from zero, and beyond which totalinternal reflection continues to occur although withincreased attenuation at a rate determined not onlyby the electromagnetic parameters of the transmis-sion medium, but also by the frequency and the inci-dence angle. The wave is guided along the reflect-ing surface with no average transport of energy intothe second medium, and the intensity of the reflect-ed wave is exactly equal to the intensity of theincident wave. The wave in an optical fiber willbe confined to the fiber for all incidence anglesgreater than the critical angle. The critical angleis given by sin ec = (~2/~1) 1/2 where 9C is thecritical angle and Cz and c1 are the permittivitiesof the transmitted (outside) and incident medium(inside), respectively, and where El is always great-

A

er than =2; e.g. , the case for an optical fiber (con-ducting a wave), and air. In terms of refractiveindices, the critical angle is the incidence anglefrom a denser medium, at an interface between thedenser and less dense medium, at which all of thelight is refracted along the interface, i.e., theangle of refraction is 90°. When the criticalangle is exceeded, the light is totally reflectedback into the denaer medium. The critical anglevaries with the refractive indices of the two mediawith the relationship, sin Oc = n2/nl, where n2 isthe index of refraction of the less dense medium, nlis the refractive index of the denser medium, and 9Cis the critical angle, as above. In terms of totalinternal reflection in an optical fiber, the criti-cal angle is the smallest angle made by a meridionalray in an optical fiber that can be totally reflect-ed from the innermost interface and thus determinesthe maximum acceptance angle at which a meridionalray can be accepted for transmission along a fiber.Also see total internal reflection.

critical radius. The largest radius of curvature of anoptical fiber, containing an axially propagatedelectromagnetic wave, at which the field outside thefiber still detaches itself from the fiber and rad-iates into space because the phase-front velocitymust increase to maintain a proper relationship withthe guided wave inside the fiber. Thia velocity can-not exceed the velocity of light, aa the wavefrontsweeps around the outside of the curved fiber. Thiscauses attenuation due to a radiation loss. Thefield outside the fiber decays exponentially in adirection transverse to the direction of propaga-tion. It is the radius of curvature of an opticalfiber at which there is an appreciable propagationmode conversion loss, due to the abruptness of thetransition from straight to curved. For a radiusof curvature greater than the critical value, thefields behave essentially as in a straight guide.For radii smaller than the critical value, consider-able mode conversion takea place.

D

dark current. ~’e current that flows in a photodetec-tor when there is no radiant energy or luminous fluxincident upon its aensitive surface, i.e., when thereis total darkness. Dark current generally increaaeawith increaaed temperature for most photodetectors.For example, in a photoemissive photodetector, thedark current is given by:

Id = AT2eq’$lkT

where A is the surface area constant, T is the ab-solute temperature, q is the electron charge, $ iathe work function of the photoemisaive surface mater-ial, and k is Boltzmann’s constant.

darkfield sensor. In fiberoptic, a sensor in whichthe optical power tapped and modulated by the sensoris a small fraction of the total optical power fedto or available to the sensor. Contrast with bright-field sensor.

data. Representation of facts, concepts, or instruc-tions in a manner suitable for communication, inter-pretation, or processing by human, manual, semiauto-matic, or fully-automatic means. The charactersused as data may assume any form or pattern to whichmeaning may be assigned in order to represent infor-

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mat ion. Data may be transferred or transported fromplace to place, auch as from city to city; from posi-tion to position, such as from coordinate poaitionto coordinate position in the display space on thediaplay surface of a display device as display ele-ments, display groups, or display images; or fromlocation to location, such as in computer or bufferstorage as characters or words. Data may be holesin tapes or cards; magnetized spots on discs, drums,tapes, cards, or chips; electrical current or volt-age pulses in a wire; or modulated electromagneticwaves in free space or in optical fibers. Data maybe presented on a CRT screen, a LED or gas panel, afiberscope faceplate at the end of a coherent bundleof optical fibers, or other surface suitable for datadisplay.

data link. 1. A communication link suitable for trans-mission of data. The data link does not include thedata source and the data sink. 2. TWO data sta-tions and their connecting network, operating insuch a manner that information cantween the stations. See fiberoptic

dB. See decibel.—

dBV. Decibel referred to one volt.

be exchanged be-data link.

dBm. Decibel referred to one milliwatt.

decibel (dB). A gain or attenuation factor measured as10 times the logarithm to the base 10 of a power oracoustic energy ratio, or aa 20 timea the logarithmto the base 10 of the voltage or current ratio withreference to l-ohm impedance or pressure ratio. Theratio consists of a reference value as the ratiodenominator and the value to be defined or measuredas the numerator. If the logarithm is positive again is represented by decibels that are positiveand if loss or attenuation is defined or measured,the decibels are negative. For example, if the ratioof optical power at the end of an optical to thepower, at the beginning in 0.500, the 10SS iS ex-pressed as 10 log 0.500 = -3.0103 dB., i.e., 3 dBdown. Since the individual component gain or lossratios introduced by serially connected cables, am-plifiers, optical fibers, and other circuit or opti-cal elements are multiplicative, the decibel gainsand losses need only be added or subtracted accord-ing to sign. Thus, the mathematical relationshipsare:

dB = 10 loglO(P1/P2)

= 10 loglo(E12/Rl)/E22/R2)

= 10 loglo(112R1)/122R2)

If R1=R2, then:

dB = 10 loglo(E12/E22) = 10 loglo(112/122)

= 20 log10(E1/E2) = 20 loglo(I1/12)

where P is the electrical or optical power, E is theelectrical voltage, I is the electrical current, andR is the resistance or like impedance and the sub-scripts identify the two pointa of comparison ofpower, voltage, or current. The dB is one tenth thesize of a bel, which is too large for convenient use.

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decollimation. In a lightwave guide, the spreading ordivergence of light due to internal and end effects.Such effects include curvature, irregularities ofsurfaces, erratic variations in refractive indices,occlusions, and other blemishes that may cause dis-persion, absorption, scattering, deflection, dif-fraction, reflection, and refraction.

defect. See interstitial defect; vacancy defect.

deflection. 1. A change in the direction of a travel-ing particle, usually without loss of particle kine-tic energy, repreaenting a velocity change withouta speed change. 2. A change in the direction of awave, beam, or other entity, such as might be accom-plished by an electric or magnetic field rather thanby a prism (refraction), a mirror (reflection), oroptical grating (diffraction).

delay distortion. See waveguide delay distortion.

demodulation. 1. To undo or reverse the effects ofmodulation; i.e., to remove the intelligence-bearingsignal from a modulated carrier or to reconstitutethe aignal that performed the modulation. 2. Theprocess in which a modulated wave is processed toderive a wave having substantially the characteris-tics of the original modulating wave.

density. See optical power density.

depletion region. A region near a semiconductor junc-tion in which there is a reduced concentration ofcharge carriers.

detection. See heterodyne detection; homodyne detec-tion; phase detection.

detector. A device responsive to the presence of astimulus. See photodetector.

dielectric. Pertaining to material composed of atomswhose electrons are so tightly bound to the atomicnuclei that electric currents are negligible evenunder applied high electric fields. That is, scarce-ly any electrons of the material are in the conduc-tion band; most remain in the valence band, evenwhen high electric fields are applied, thua qualify-ing the material to be called an insulator. Conduc-tion currents in dielectrics are nearly zero. Chargesthat might accumulate in one place tend to remainfor relatively long periods of time. Most opticalelements and optical fibers are dielectric. A tran-sient polarization current occura only when an elec-tric field is applied or removed, due to dipolerotation and alignment and polarization. Polariza-tion and polarization currents are specified inMaxwell’s equationa by the electric permittivity,E, of dielectric materials. Also see conductor.

dielectric optical waveguide. See slab dielectric op-tical waveguide.

dielectric waveguide. See alab dielectric waveguide.

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diffraction. 1. The procesa by which the propagationof radiant waves or lightwaves are modified as thewaves interact with objects or obstacles. Some ofthe rays are deviated from their path by diffractionat the objects, whereaa other rays remain undeviatedby diffraction at the objects. As the objects be-come small in comparison with the wavelength, theconcepts of reflection and refraction become useless,and diffraction plays the dominant role in determin-ing the redistribution of the rays following inci-dence upon the objects. Diffraction results fromthe deviation of light from the paths and foci pre-scribed by the rectilinear propagation laws of geo-metrical optics. Thus, even with a very small, dis-tant source, some light, in the form of bright anddark bands, is found within a geometrical shadowbecause of the diffraction of the light at the edgeof the object forming the shadow. Diffraction grat-ings, with spacings of the order of the wavelengthof the incident light also cause diffraction thatresults in the formation of light and dark areascalled “diffraction patterns.” Such gratings canbe ruled grids, spaced spots, or crYstal latticestructures. 2. The bending of radio, sound, orlightwaves around an object, barrier, or apertureedges.

diode. See light-emitting diode (LED).

dispersion. 1. The process by which rays of light ofdifferent wavelength are deviated angularly by dif-ferent amounts; e.g. , as with prisms and diffractiongratings. 2. Phenomena that cause the refractiveindex and other optical properties of a transmissionmedium to vary with wavelength, also refers to thefrequency dependence of any of several parameters,for example, in the process by which an electromag-netic signal is distorted because the various fre-quency components of that signal have different pro-pagation characteristics and paths. Thus, the com-ponents of a complex radiation are dispersed orseparated on the basis of some characteristic. Aprism disperses the components of white light bydeviating each wavelength a different amount. Forexample, 2.5 nsec/km might be a maximum allowabledispersion for an 18.7 Mbit/see pulse repetitionrate with 10 km repeater spacing. 3. The alloca-tion of circuits between two points over more thanone geographic or physical route. See intermodaldispersion; intramodal dispersion; material disper-sion; modal dispersion; waveguide dispersion.

distortion. See waveguide delay distortion.

diversity. See polarization diversity.

donor. In an intrinsic semiconducting material, a do-pant that has nearly the same electronic bondingstructure as the intrinsic material, but with onemore electron among its valence electrons than thatrequired to complete the intrinsic bonding pattern,thus leaving one “extra” or “excess” electron foreach impurity (dopant) atom in the structure. Thedopant (i.e., the donor) atoms are relatively fewand far apart and hence to not interfere with theelectrical conductivity of the intrinsic material.Tin or tellurium can serve as a dopant for galiumarsenide. The extra electron moves or wanders fromatom to atom more freely than the bound electronsthat ar required to complete the bonding structure,although interchanges actually occur with the boundelectrons. The extra electrons move about morefreely than the holes created by acceptors. Hence,the electrons are more mobile than the holes. Under

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the influence of electric fields, the electrons andholes move in the direction of the field accordingto their sign, thus constituting an electric cur-rent. Also see acceptor; electron; hole.

E

electromagnetic interference. Interference caused orgenerated in a circuit by electromagnetic radiationenergy coupling. The radiation may be lightwaves,radio waves, gamma rays, high-energy neutrons, x-rays, or microwaves. Sources include artificaltransmissions and emissions as well as naturalsources, such as cosmic and solar sources. Thephenomenon of interference is considered to occurwhen electromagnetic energy causes an unacceptableor undesirable response, malfunction, degradation,or interruption of the intended operation or per-formance of electronic equipment.

electromagnetic pulse (EMP). A broadband, high-inten-sity, short-duration burst of electromagnetic en-ergy, such as might occur from a nuclear detonation.In the case of a nuclear detonation, the electromag-netic pulse (signal) consists of a continuous spec-trum with most of its energy distributed throughoutthe lower frequencies between 3 Hz and 30 kHz.

electromagnetic wave (EMW). The effect obtained when atime-varying electric field and a time-varying mag-netic field interact, causing electrical and msgne-tic energy to be propagated in a direction that isdependent upon the spatial relationship of the twointeracting fields that are interchanging their ener-gies. The most common EMU consists of time-varyingelectric and magnetic fields that are directed atright angles to each other, thus defining a plane inwhich they both lie, i.e., polarization plane. Thedirection of energy propagation is perpendicular tothis plane, and the wave is called plane polarized.A plane-polarized wave may be linearly, circularly,or elliptically polarized depending on the phaserelationship between the varying electric and msgne-tic fields. When launched initially, the interact-ing and interrelated time-varying electric and mag-netic fields are produced by an electric current,consisting of moving electric charges that oscillatein time and space, such as might oscillate In a wire,called an antenna. If an electric field is made tovary in time in a conductive medium in order to pro-duce an oscillating current, an electromagnetic wavewill be launched that can propagate energy throughmaterial media and a vacuum. If the time and spatialdistributions of currents are given, the electromag-netic field intensities, power flow rates, and energydensities can be determined everywhere in space, pro-vided also that the parameters of the material inthe space are known. Lightwaves are electromagneticwaves that can travel in optical fibers where theycan be trapped and guided, and can be made to ener-gize photodetectors.

electron. A basic negatively charged particle with achar e of 1.6021 x 10-19 C and a mass of 9.1091 x

f10-3 kg. It is outside the nucleus of the chemicalelements, exists with different discrete energylevels in a given chemical element, differentiatesthe elements by its population outside the nucleus,and is the moving matter that contributes the mostto the formation of electric currents and voltages.Also see acceptor; donor; hole.

6

electron-hole recombination. The combining of an elec-tron and a hole resulting in a decrease in electronenergy and the production of a photon.

electronically-controllable coupler. An optical ele-ment that enables other optical elements to be coup-led to, or uncoupled from, each other, in accordancewith an applied electrical signal. For example, twoparallel slab dielectric waveguides with an opticalmaterial between them whose refractive index can bealtered by application of an electronic signal, thusturning the coupling of the waveguides on or off ac-cording to the signal.

electrooptic coefficient. A measure of the extent towhich the refractive index changes with applied highelectric field, auch as several parts per 10 thou-sand for applied fields of the order of 20 V/cm.Since the phase shift of a lightwave is a functionof the refractive index of the transmission mediumin which it is propagating, the change in index canbe used to phase-modulate the lightwave by shiftingits phase at a particular point along the guide, bychanging propagation time to the point.

electrooptic device. 1. An electronic device that useselectromagnetic radiation in the visible, infrared,or ultraviolet regions of the frequency spectrum;emits or modifies noncoherent or coherent electro-magnetic radiation in these same regions; or uaessuch electromagnetic radiation for its internal oper-ation. The wavelengths handled by theae devicesrange from approximately 0.3 to 30 microns. 2. Elec-tronic devices associated with light, aerving aasources, conductors, or detectors. Synonymous withoptoelectronic device.

electrooptic effect. The change in the refractive indexof a material when subjected to an electric field.It can be used to modulate a light beam in a mater–ial since many light propagation properties are de-pendent upon the refractive indices of the transmis-sion medium in which the light travels.

electrostrictive effects. The change in physical dimen-sions that occurs to certain materials when they areplaced in an electric field.

EMI. See electromagnetic interference.

EMP. See electromagnetic pulse.

emission. See spontaneous emission.

emission of radiation. See light amplification by stim-ulated emiasion of radiation (laser).

energy band. A specified range of energy levels that aconstituent particle or component of a substance mayhave. The particles are uaually electrons, protons,ions, neutrons, atoms, or molecules. Some energybands are allowable and some are unallowable forspecific particles. For example, electrons of agiven element at a specific temperature occupy onlycertain energy bands. Examples of energy bands arethe higher and lower level ranges of the conductionand valence bands.

energy gap. The difference in energy level between thelower limit of the conduction band and the upperlimit of the valence band.

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energy level. The discrete precise amount of kineticand potential energy possessed by a body, such as anorbiting electron. A quantum of energy is absorbedor radiated depending on whether an electron movesfrom a lower to a higher energy level or vice versa.

evanescent-field coupling. Coupling between two wave-guides, auch as an optical fiber or an integratedoptical-circuit (IOC), in which the waveguides areheld parallel to each other in the coupling region,with the evanescent waves on the outside of one ofthe waveguides entering the coupled waveguide, bring-ing some of the light energy with it into the coupl-ed waveguide. In optical fibers and planar dielec-tric waveguides, close-to-core proximity or fusionis required. The evanescent field of the core modescan be made available by etching away the fibercladding or locally modifying the refractive index.

evanescent wave. In a waveguide conducting a transverseelectromagnetic wave, the wave on the outside of theguide. It will radiate away at sharp bends in theguide if the radiua of the bend is less than thecritical radius. It uaually has a frequency smallerthan the cutoff frequency above which true propaga-tion occurs and below which the waves decay exponen-tially with distance from the guide. Evanescentwavefronts of constant phase may be perpendicularor at an angle less than 90” to the surface of theguide.

extrinsic fiber loss. Optical power loss in an opticalfiber aplice, connector, or coupling caused by endseparation, axial displacement, axial misalignment,reflection, or other external condition involved inimplementation or use and subject to the control ofthe uaer.

F

Fabry-Perot interferometer. A high-resolution multi-ple-beam interferometer consisting of two opticallyflat and parallel glasa or quartz plates held a shortfixed diatance apart, the adjacent aurfaces of theplatea or interferometer flata being made almoattotally reflecting by a thin silver film or multi-layer dielectric coating. If one plate is moved withrespect to the other, interference patterns are pro-duced. If the ends of an optical fiber are made re-flective, moving one end with reapect to the otherwill also result in an output signal when monochro-matic light is inserted into the fiber.

Faraday effect. Synonym for magnetooptic effect.

FDM. See frequency-division multiplexing.

fiber. See graded-index fiber; low-loss fiber; multi-mode fiber; optical fiber; SELFOCc fiber; self-focus-ing optical fiber; single-mode fiber; step-indexfiber; optical-fiber coating.

fiber length-bandwidth product. The product of thelength of an optical fiber and the spectral width oflightwavea propagating within it, usually expressedin micron-kilometers.

fiber loss. See extrinsic fiber loss; intrinsic fiberloss; optical fiber loss.

7

fiberoptic. Pertaining to optical fibers and the sys-tems in which they are used, such as sensor, tele-metry, and telecommunication systems.

fiberoptic cable. Optical fibers incorporated into anassembly of materials that provides tensile strength,external protection, and handling properties compar-able to those of coaxial cables. Fiberoptic cables(light guides) are a direct replacement for conven-tional coaxial cables and wire pairs. The glass-based transmission facilities occupy far less physi-cal volume for an equivalent transmission capacity,which is a major advantage in crowded undergroundducts. Manufacturing, installation, and maintenancecosts are less. These advantages, with the reduceduse of critical metals, such as copper, is a strongimpetus for the use of fiberoptic cables.

fiberoptic data link. A data link, consisting of a mod-ulated light source, a fiberoptic cable, and aphotodetector, that can handle signals in the formof a modulated lightwave. Synonymous with opticaldata link.

fiberoptic ribbon. Synonym for optical fiber ribbon.

fiberoptic (FO). 1. As first defined by Kapany in1956, the art of the active and passive guidance oflight (rays and waveguide modes) in the ultraviolet,visible, and infrared regions of the spectrum alongtransparent fibers through predetermined paths. 2.The technology of guidance of optical power, includ-ing rays and waveguide modes of electromagneticwaves along conductors of electromagnetic waves inthe visible and near-visible region of the frequencyspectrum, specifically when the optical energy isguided to another location through thin transparentstrands. Techniques include conveying light orimages through a particular configuration of glassor plastic fibers. Incoherent optical fibers willtransmit light, as a pipe will transmit water, butnot an image. Coherent optical fibers can transmitan image through small (2-12 microna diameter), clad,optical fibers that are in a fixed spatial relativeposition at both ends. Specialty fiberoptic com-bine coherent and incoherent aspects.

fiberoptic sensor. A sensor in which a parameter (pro-perty, characteristic) of an optical waveguide (op-tical fiber), or of a lightwave propagating in anoptical fiber, is varied in accordance with an inputbaseband signal thus modulating the lightwave in thewaveguide. Synonymous with optical fiber sensor;optical sensor. Also see sensor.

fiberoptic sheath. An outer protective covering placedover an optical fiber, bundle, or cable.

fiberoptic splice. A nonseparable junction joining oneoptical conductor to another.

fiber ribbon. See optical fiber ribbon.

fiberscope. A receiving device consisting of an entrypoint, at which a bundle of optical fibers can enter,and a faceplate surface on which the entering fiberscan uniformly terminate, in order to display the op-tical image received through the fibers. The bundleof fibers transmit a full color image that remainsundisturbed when the bundle is bent. By mountingan objective lens on one end of the bundle and aneyepiece at the other, the assembly becomes a flex-ible fiberscope that can be used to view objects thatare otherwise Inaccessible for direct viewing. The

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transmitter is a similar device, except that an imageis focused on it for transmission. The device isused to transmit images. Also see coherent bundle.

fiber sensor. See fiberoptic sensor.

field coupling. See evanescent field coupling.

focusing optical fiber. See self-focusing opticalfiber.

frequency-division multiplexing (FDM). Multiplexing inwhich the available transmission frequency range isdivided into narrower bands, each used as a separatechannel. When an optical fiber transmits more thanone frequency at the same time, each frequency canbe modulated with a different information-bearingsignal.

frequency modulation. The modulation of the frequencyof an electromagnetic, elastic, sound, or other waveserving as a carrier, with another wave serving asthe modulating signal, such that the frequency ex-cursions of the carrier are proportional to a para-meter of the modulating signal bearing the informa-tion to be transmitted. It is a form of angle modu-lation in which the instantaneous frequency of aaine wave carrier is caused to depart from the car-rier frequency by an amount that is proportional tothe instantaneous value of the modulating signal.Combinations of phase and frequency modulation arealso considered as frequency modulation.

Fresnel equations. See reflection coefficient, trans-mission coefficient.

G

E!-Fl” See energy gap.

geometric spreading. In a wave propagating in a trans-mission medium in which there are no sources, thedecrease in power density as a function of distancein the direction of propagation. As a curved wave-front, such as for divergent electromagnetic waves,moves in the direction of propagation, the availablepower at one point must be spread over a larger areaat the next point in space; e.g., a point source oflight has its light energy spread over larger andlarger spherical surfaces as the distance from thesource increases.

graded-index fiber. An optical fiber witb a variablerefractive index that is a function of the radialdistance from the fiber axis, the refractive indexgetting progressively lower away from the axis. Thischaracteristic causes the light rays to be continu-ally refocused by refraction in~o the core. As aresult, there is a designed continuous change inrefractive index between the core and cladding alonga fiber diameter. Synonymous with gradient-indexfiber.

gradient-index fiber. A synonym for graded-index fiber.

8

group velocity. The velocity of propagation of the en-velope produced when an electromagnetic wave is modu-lated by, i.e., mixed with, another wave of a differ-ent frequency. The group velocity is the velocityof information propagation and, loosely, of energypropagation. It is the velocity of transmissionof energy associated with a progressing wave consist-ing of a group of sinusoidal components; i.e., thevelocity of a certain feature of the wave envelope,e.g., the crest. The group velocity differs fromthe phase velocity. Only the latter varies withfrequency. In general, the group velocity, repre-sentated as:

is less than the phase velocity, represented as;

IJJ/i3‘P “

where B is the angular velocity, ( u= 2n’f) and u isthe propagation constant.

guide. See waveguide.

H

heterodyne detection. In fiberoptic, detection basedon the use or mixing of two or more frequencies.For example, if a lightwave is fed to a Bragg cell,it produces an output lightwave frequency that isthe sum of the input lightwave frequency and thebaseband frequency; an interferometer can be used torecover the baseband frequency.

heterodyning. The mixing of an electromagnetic wave ofone frequency with a wave of another frequency toproduce one or more additional frequencies. Usuallythe sum and difference frequencies will be producedwhen waves of two different frequencies are combinedin a nonlinear device, such as a nonlinear ampli-fier.

heterojunction. In a laser diode, a boundary surfaceat which a sudden transition occurs in material com-position across the boundary. For example, in asemiconductor, a change in the refractive index aswell as a change from a positively-doped (p) regionto a negatively-doped (n) region; or a positively-doped region with a rapid change in doping level,i.e., a high concentration gradient of dopant versusdistance. In most heterojunctions, change in geo-

metric cross-section occurs across which a voltageor voltage barrier exists. Heterojunctions provide acontrolled level and direction of radiation confine-ment. There usually is a step in the refractiveindex level at each heterojunction. Contrast withhomojunction. See single heterojunction.

hole. In physical electronics and solid-state devices,a semiconducting material containing a dopant thathas one less electron for each atom than that re-quired to complete the intrinsic bonding structure,a site at which an electron is missing to completethe bonding structure. Initially, the hole is creat-ed by the impurity atoms, but if an electron from aneighboring atom moves in to “fill” the hole, theneighboring atom will have a hole; thus, the holecan be considered to have migrated. Also see accep-tor; donor; electron.

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homodyne detection. In fiberoptic, detection based onthe use of only one frequency. For example, a detec-tor that makes use of a varying-length fiber to ac-hieve modulation of the phase of the lightwave atthe output end of the fiber; the input baseband sig-nal modulates the length of the fiber and thus thereis no change in frequency of the lightwave.

homogeneous medium. In optical systems, a transmissionmedium whose light-transmission parameters, such asthe parameters of the constitutive relations, arespatially constant and not a function of space coor-dinates, although they may vary as a function oftime, temperature, pressure, humidity, or other para-meter uniformly throughout the medium.

homojunction. In a laser diode, a single junction; i.e.,a single region of shift in doping from positive tonegative majority carrier regions, or vice versa,and a change in refractive index, all at one bound-ary. Hence one energy-level shift, one barrier, andone refractive-index shift constitute a aingle homo-junction. Constrast with heterojunction.

Iincident ray. A ray of light that falls upon, or

strikes, the surface of any object. The ray is saidto be incident at the surface.

incoherent light. Light of which not all parametersare predictable and correlated at any point in timeor space, such as scattered or diffused light.Contrast with coherent light.

index. See refractive index.

index profile. See radial refractive index profile.

index-profile mismatch loss. See refractive-index-pro-file mismatch loss.

index profile parameter. See refractive index profileparameter.

index-matching material. Alight-conducting materialused in intimate contact with optical componentssuch as optical fibers and lenses, to reduce opticalpower losses by using materials with refractive in-dices at interfaces that will reduce reflection,increase transmission, avoid scattering, and reducedispersion.

insertion loss. 1. In a communication system, the de-crease in signal level that results from the inser-tion of a series component in a transmission circuit.It is expressed as a percent, in decibels, or as aper unit coefficient or fraction. The loss may bepositive or negative, that is, greater or less thanunity when expressed as a ratio (per unit fractionor coefficient). If the insertion loss is negativeit is considered as a gain. When it is expressedas a fraction, ratio, or per unit, it is the decreasein signal level caused by the insertion divided bythe signal level before insertion. 2. In an opti-cal fiber, the optical power loss due to all causes,usually expressed as decibels/kilometer. Causes ofloss may be absorption, scattering, diffusion, leakymodes, dispersion, microbending, or other causes or

9

methods of coupling power outside the fiber. Forexample, in an optical component such as a 3-dBcoupler, the insertion loss is considered as thatin excess of the 3-dB associated with splitting thelight between two fibers. 3. In lightwave trans-mission systems, the power lost at the entrance toa wavegufde due to any and all causes, such asFresnel reflection, packing fraction, limited numer-ical aperture, axial misalignment, lateral displace-ment, initial scattering, or diffusion.

insulator. A substance with a molecular structure inwhich all electrons remain in the valence band,rather than in the conduction band, even under theinfluence of high electric field gradients, andtherefore a material that is used to prevent theflow of electric current when electric fields exist.tiso see dielectric. Contrast with conductor.

integrated optical circuit (IOC). A circuit, or groupof interconnected circuits, consisting of miniaturesolid state optical components. Examples of suchcomponents include light-emitting diodes, opticalfilters, photodetectors (active and passive), andthin-film optical waveguides on semiconductor or di-electric substrates. Components onan IOC chip mightinclude semiconductor injection lasers, modulators,filters, lightguides, switches, couplers, logicgates, pulse shapers, differential amplifiers, andoptical memories. Synonymous with optical integrat-ed circuit.

integrated optics. The design, development, and opera-tion of circuits that apply the technology of inte-grated electronic circuits produced by planar mask-ing, etching, evaporation, and crystal film growthtechniques to microoptical circuits on a singleplanar dielectric substrate. Thus, a combinationof electronic circuitry and optical waveguides areproduced for performing various communication,switching, and logic functions, including amplifica-tion, gating, modulating, light generation, photo-detecting, filtering, multiplexing, signal process-ing, coupling, and storing.

intensity. See luminous intensity.

intensity sensor. In fiberoptic, a fiberoptic sensorin which the optical intensity of a light ray (beam)is varied in accordance with a baseband signal byvarying the light propagation properties of an opti-cal fiber. For example, a microbend sensor.

interference. See electromagnetic interference.

interferometer. An instrument in which the interfer-ence effects of lightwaves are used for purposes ofmeasurement, such as the measurement of the accuracyof optical surfaces by means of Newton’s rings, themeasurement of optical paths, linear and angulardisplacements, phase changes due to pressure, rota-tion, and temperature effects on the sensing arm ascompared to the reference arm. See Fabry-Perotinterferometer; Mach-Zehnder interferometer; Michel-son interferometer; Sagnac interferometer; _n-Green interferometer.

interferometric sensor. In fiberoptic, a fiberopticsensor that employs the principles of interferornetryto performa sensing function. For example, aFabry-Perot interferometer used as a fiberoptic sensor.Also see interferometer.

A-1

interferometry. The scientific discipline devoted tothe study and useful application of interferenceamong electromagnetic waves.

intermodal disperson. Dispersion (pulse broadening)that results from propagation time differences amongthe various modes in an electromagnetic pulse. Inter-modal dispersion can be reduced by appropriate re-fractive index profile shaping.

internal reflection. In an optical element in which anelectromagnetic wave is propagating, a reflection atan outside surface from the inside such that a wavethat is incident upon the surface is reflected whollyor partially back into the element itself. Opticalfibers depend on internal reflection for the success-ful transmission of lightwaves in order that thewaves do not leave the fiber; namely, the wave energyis confinded to or bound to the fiber. Also seetotal internal reflection.

internal reflection sensor. See near total internal re-flection sensor.

interstitial defect. In the somewhat ordered array ofatoms and molecules in optical fiber material, asite at which an extra atom or molecule is insertedin the space between the normal array. The defectcan serve as a scattering center, causing diffusion,heating, absorption, and resultant attenuation. Alsosee vacancy defect.

intrinsic absorption. In lightwave transmission media,the absorption of light energy from a traveling orstanding wave by the medium itself, causing attenua-tion as a function of distance, material properties,mode, frequency, and other factors. Intrinsic ab-sorption is primarily due to charge transfer bandsin the ultraviolet region and vibration or multi-phonon bands in the near infrared, particularly ifthey extend into the region of wavelengths used inoptical fiber, namely, 0.7 to 1.2 microns.

intramodal dispersion. The dispersion (pulse broaden-ing) that occurs within one of the modea in an elec-tromagnetic pulse. Intramodal dispersion in an op-tical fiber is a function of the spectral bandwidthof the light source and the material dispersioncaused by the fiber. It is usually the only type ofdispersion preaent in a monomode fiber.

intrinsic fiber loss. Optical power loss in an opticalfiber or optical fiber splice, connector, or coupl-ing, caused in the manufacturing process, such asrefractive index profile mismatch, diameter differ-ences, scattering, absorption, and other causes notsubject to the control of the user.

intrinsic region. In a semiconductor junction, a regionthat lies between a positively-doped region and anegatively-doped region and that does not containany dopant. Synonymous with i-region.

inversion. See population inversion.

Ioc. See integrated optical circuit.

i-region. Synonym for intrinsic region.

0

isotropic material. A substance that exhibits the sameproperty when tested along an axis in any direction.For example, a dielectric material with the samepermittivity to electric fields, a glass with thesame refractive index for a lightwave, or the sameconductivity to electric currents, in all directions.

Jjacket. See bundle jacket; cable jacket.

junction. See heterojunction; homojunction; p-n junc-tion.

K

Kerr cell. A substance, usually a liquid, whose refrac-tive index change is proportional to the square ofan applied electric field. If the substance is con-figured to be part of an optical path, the cell canprovide a means of modulating the light in the opti-cal path.

Llasing. A phenomenon occurring when resonant frequency

controlled energy is coupled to a specially preparedmaterial, such as a uniformly-doped semiconductorcrystal that has free-moving or highly mobile loose-ly-coupled electrons. AS a result of resonance andthe imparting of energy by collision or close ap-proach, electrons are raised to highly excited energystates, which, when they move to lower states, causequanta of high-energy electromagnetic radiation tobe released as coherent lightwaves. This actiontakes place in a laser.

LED. See light emitting diode.

length. See coherence length.

length-bandwidth product. See fiber length-bandwidthproduct.

light. See coherent light; incoherent light; polarizedlight.

light amplification by stimulated emission of radiation(lasers). A coherent-light generator in which mole-cules of certain substances absorb incident electro-magnetic energy at specific frequencies, store theenergy for short periods in higher energy-band levelsand then release the energy, upon their return tothe lower energy levels, in the form of light at par-ticular frequencies in extremely narrow frequencybands. The release of energy can be controlled intime and direction so as to generate an intensehighly directional narrow beam of electromagneticenergy that is coherent, i.e., the electromagneticfields at every point in the beam are uniquely andspecifically definable. Diode lasers and helium-neon lasers make use of a resonant cavity that ispumped to high energy levels to cause Populationinversion and lasing action.

light-emitting diode (LED). A diode that operates sim-

ilar to a laser diode, with the same total outputpower level, the same output limiting modulation

A -

rate, and the same operational current densities,but without lasing action. The high current densi-ties of thousands of amperes per square centimeteroften cause catastrophic and graceful degradation.Compared to the laser diode, the LED possessesgreater simplicity, tolerance, and ruggedness, andabout 10 times the spectral width. Typical peakspectral power output for a gallium arsenide LEDoccurs at 0.910 pm (microns), with a spectrum about0.005 pm wide. An aluminum arsenide LED operates at0.820 pm at a 10-MHz-wide spectrum. Both operate atroughly l-mW spectral power output and a 50-mAdriving current.

lightfield sensor. Synonymous with brightfield sensor.

light pipe. 1. An optical element that conducts lightfrom one place to another, such as an optical fiberor slab-dielectric waveguide. 2. A hollow tube witha reflecting inner wall that guides lightwaves inits hollow center. 3. An optical fiber.

light ray. A line perpendicular to the wave-front of alightwave indicating its direction of propagationand representing the lightwave itself.

light source. A device that produces or emits light-waves, such as a light-emitting diode, a laser, or alamp.

linear medium. An electromagnetic wave transmissionmedium with constitutive parameters, such as electricpermittivity, magnetic permeability, and electricconductivity (and hence refractive index), that re-main constant under the influence of applied electricand magnetic fields. For example, in the relationsB=uH, D=cE, andJ=uE, thep, e, and u are con-stant at a given point even though the fields arechanging.

link. See data link; fiberoptic data link.

lock 100P. See phase-lock loop.

w“ See phase-lock loop.

loss. See coupling loss; extrinsic fiber loss; inser-tion loss; intrinsic fiber 10SS; microbending 10SS;optical fiber loss; refractive-index-profile mis-match loss.

low-loss fiber. AII optical fiber having a low energyloss, due to all causes, per unit length of fiber,usually measured in decibels/kilometer at a speci-fied wavelength. Low-loss is usually considered tobe below 20 dB/km. In low-loss fiber, attenuationof a propagating wave is caused primarily by scat-tering due to metal ions, by absorption due to waterin the OH radical form, and by Rayleigh scattering.Low-loss fiber attenuation rates are approaching 0.01dB/km.

luminous intensity. The ratio of the luminous fluxemitted by a light source, or an element of thesource, in an infinitesimally small cone about thegiven direction, to the solid angle of that cone,i.e., luminous flux emitted per unit solid angle.

I I

M

Mach-Zehnder interferometer. An interferometer in whichan electromagnetic wave is split, each half travel-ing around half a loop in opposite directions, onevia a beam splitter and a fixed mirror, the othervia a movable mirror and a beam splitter, both halvesbeing recombined at a photodetector where their rela-tive phase can reinforce or cancel. The moveablemirror modulates the resultant intensity at thephotodetector.

magnetooptic. Pertaining to the control of lightwavesby means of magnetic fields, for example by rotatingthe magnetic polarization of a lightwave and thusachieving polarization modulation or by cementingor coating ferromagnetic material on the outside ofa fiber and using the magnetostrictive effect toalter the length of a fiber in the sensing arm ofan interferometer thus obtaining a method of con-verting magnetic field variations to light intensityvariations. Synonymous with optomagnetic

magnetooptic effect. The rotation of the polarizationplane of lightwaves in a transmission medium broughtabout when subjecting the medium to a magnetic field(Faraday rotation). The effect can be used to modu-late the light beam in a material, since many pro-perties, such as conducting velocities, reflectionand transmission coefficients at interfaces, accep-tance angles, critical anglea, and transmissionmodes, are dependent upon the direction of propaga-tion at interfaces in the media in which the lighttravels. The amount of rotation is given by:

A = aHL

where a is a constant, H is the magnetic fieldstrength, and L is the propagation distance. Themagnetic field is in the direction of propagation ofthe lightwave. Also, by coating or cementing ferro-electric material to a fiber, the magnetostrictiveeffect can be used to alter the length of a fiber inthe sensing arm of an interferometer, thua obtaininga method of converting magnetic field variations tolight intensity variationa. Synonymous with Faradayeffect.

magnetooptic modulator. A modulator that makes use ofthe magnetooptic effect to modulate a lightwave car-rier.

magnetostriction. The phenomenon exhibited by somematerials in which dimensional changes occur whenthe material is subjected to a magnetic field, usu-ally becoming longer in the direction of the appliedfield. The effect can be used to launch a shock orsound wave each time the field is applied or changed,possibly giving rise to phonons that could influenceenergy levels in the atoms of certain materials suchas semiconductors and lasers and thereby serve as amodulation method. Along with photon or electricfield excitation, the phonon energy could providethreshold energy to cause electron energy leveltransitions, causing photon absorption or emission.The effect can also be used to change the physicaldimensions of an optical fiber that is wrappedaround or cemented to or jacketed by, a magnetostric-tive (ferromagnetic) material and thus modulate alight beam in the fiber.

margin. See power margin.

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material dispersion. 1. The variation in the refrac-tive index of a transmission medium as a function ofwavelength, in optical transmission media used inoptical waveguides; e.g., optical fibers, slab di-electric waveguides, and integrated optical cir-cuits. Material dispersion contributes to group--delay distortion, along with waveguide-delay dis-tortion and multimode group-delay spread, i.e., thespreading of a pulse. 2. The part of the totaldispersion of an electromagnetic pulse in a wave-guide caused by the changes in properties of thematerial with which the waveguide, such as an opti-cal fiber is made, due to changes in frequency. Aswavelength increasea, and frequency decreases, mate-rial dispersion decreases. At high frequencies, therapid interactions of the electromagnetic field withthe waveguide material (optical fiber) renders therefractive index even more dependent upon frequency.

Maxwell’s equations. A group of basic equations, ineither integral or differential form, that (1) des-cribe the relationships between the properties ofelectric and magnetic fields, their sources, and thebehavior of these fielda at material media inter-faces; (2) express the relations among electric andmagnetic fields that vary in space and time in mater-ial media and free space; and (3) are fundamental tothe propagation of electromagnetic waves in materialmedia and free space. The equations are the basisfor deriving the wave equation that expresses theelectric and magnetic field vectors in a propagatingelectromagnetic wave in a transmission medium suchas a lightwave in an optical fiber. Maxwell’sequations in differential form are:

vx E = -aBlatv. H = J + aD/3tV. B=OV“ D=o

where E, H, B, and D are the electric field inten-sity, the magnetic field intensity, the magneticflux density, and the electric flux density (elec-tric displacement) vectors, respectively, J is theelectric current density, and pis the electriccharge density, the v is the “del- space derivativeoperator, expressing differentiation with respectto all distance coordinates, the VX being the curland the v - being the divergence. The partial deri-vatives are with respect to time. These equationsare Used in conjunction with the constitutive rela-tions to obtain useful practical results given ac-tual sources of charge and current in real media.These are only valid when the field and currentvectors are single-valued, bounded, continuous func-tions of poaition and time, and have continuousderivatives.

medium. See homogeneous medium; linear medium; source-free medium; transmission medium.

meridional ray. In an optical fiber, a light ray thatpasses through the central axis of the fiber, isinternally reflected, and is confined to a singleplane, called the meridian plane. Also see skew ray.

metal oxide semiconductor. A semiconductor composed ofdoped metal oxide, such as silicon oxide (Si02). Seecombined metal oxide semiconductor.

2

Michelson interferometer. b interferometer in whichan electromagnetic wave is split. One half is thenreflected from a fixed mirror and back through thesplitter to a photodetector, the other half is passeddirectly through the splitter to a movable mirror(transducer) that reflects it back to the splitterwhere it is reflected to the same photodetector.The two waves can phase enhance or cancel and thusmodulate the intensity at the photodetector in accor-dance with a baseband input signal to the movablemirror. If an optical fiber is used, the ends ofthe fiber form the reflecting surfaces. Moving oneend with respect to the other produces the same ef-fect as moving the mirror.

microbend. A small bend or induration in the outersurface of an optical fiber core that causes light-waves in the core to penetrate into the claddingand thus leak from the fiber. Contrast with ordi-nary bend.

microbend loss. In an optical fiber, the loss or atten-uation in signal power caused by small bends, kinks,or abrupt discontinuities in the direction of thefibers, usually caused by fiber cabling or by wrap-ping fibers on drums. Microbending losses usuallyresult from a coupling or guided modes among them-selves among the radiation modes when light raysenter the cladding at the microbends or get reflectedat larger than critical angles and hence also enterthe cladding. Use can be made of microbend loss bycreating microbends in number and amplitude in ac-cordance with a baseband signal and thus modulatingleakage. Contrast with ordinary bend.

microbend sensor. A transducer capable of convertingmechanical mvement, such as displacement actuatedby applied forces or pressures, into a modulatedlightwave in an optical fiber. The microbenderintroduces microbends in the fiber thus modulatingthe lightwave intensity by causing leakage in accor-dance with the information-bearing baseband signal.

micrometer. See micron.

micron (lhn or P). A unit of length in the metric sys-tem equal to one-millionth of a meter, i.e., 10-6

meter. Synonymous with micrometer.

mismatch 10ss. See refractive-index-profile-mismatchloss.

mixing box. See optical mixing box.

mixing rod. See optical mixing rod.

modal dispersion. 1. The difference in propagationtime for each of the modes propagating in an opticalfiber, resulting in a broadening of a light pulse.2. In the propagation of an electromagnetic wave orpulse in a waveguide, the changes introduced in therelative magnitudes of the frequency components ofthe wave or pulse. The guide is capable of support-ing or introducing only a fixed number of frequen-cies depending on its geometry and material para-meters, such aa permeability, permittivity, and con-ductivity.

mode. 1. A specific condition or arrangement of elec-tromagnetic waves in a transmission medium, particu-larly in a waveguide. The total number of dimension-al modes that a step-index optical fiber can support,couple to, or radiate into is given by:

1= ~2a2 (n12-n22)/A2

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where a is the fiber radius, nl and n2 are the re-fractive indexes of core and cladding, and 1 is thewavelength. There are additional degenerate modesthat can be supported, such as polarization andevanescent modes. 2. In communication systems, aform or medium for transmission of voice, image,digital data, or other signala.

mode stripper. See cladding mode stripper.

mode volume. For a large number of modes, N = fn2/2,where fn is the V-parameter (normalized frequency orV-value).

modulation. 1. The variation of a characteristic orparameter of a wave in accordance with a character-istic or parameter of another wave. For example, avariation of the amplitude, frequency, or phase of acarrier wave in accordance with the wave form thatrepresents information by means of superposition,mixing, or transduction. The carrier may be a con-tinuous direct-current (DC) signal or a continuousalternating signal such as a sinusoidal wave. Thecarrier is used as a means of propagation. Thesuperimposed or mixed aignal is used as the intelli-gence-bearing signal. The variation of the modulat-ed carrier is detected at the receiver. The infor-mation or intelligence frequencies are normally call-ed the baseband. 2. In fiberoptic, the variationof a characteristic or parameter of a lightwave inorder to superimpose an information-bearing signalon a carrier wave. For example, a variat~on of theamplitude, frequency, or phase of a lightwave by ananalog or digital baseband signal in a fiberopticsensor, transmitted in an optical fiber, and recover-ed by a photodetector. The carrier may be a contin-uous lightwave when it is not modulated by the sen-sor. Contrast with demodulation. See amplitudemodulation; phase modulation; polarization modula-tion; frequency modulation.

modulator. A device that accomplishes modulation, thatis, has the capability of varying one signal in ac-cordance with the variations of another aignal. Thus,it converts baseband signal into a modulated carrier.

moving grating sensor. A sensor consisting of a fixedand moveable grating of transparent and opaque areassuch that the intensity of light passing through ismodulated according to the amount that the trans-parent areas of both gratings coincide (overlap) aathe movable grating is moved according to the ap-plied baseband aignal.

multimode fiber. An optical fiber waveguide that willallow (support) more than one mode to propagate.Multimode optical fibers have a much larger core (25to 75 microns) than aingle-mode fibers (2 to 12microns diameter) and thus permit nonaxial rays ormodes to propagate through the core.

multiplexing. See frequency-division multiplexing; po-larization multiplexing; space-division multiplex-ing; time-division multiplexing (TDM); wavelength-division multiplexing (WDM).

N

nanometer. One thousandth of a micron, i.e. , 10-9

met er.

near total internal reflection sensor. In fiberoptic,a fiberoptic sensor that operates on the principleof varying the property of an optical fiber in sucha manner that the amount of light that leaks intothe cladding ie altered by varying the critical anglein accordance with a baseband signal, auch as byaltering the refractive index or the ordinary bendradius, thus altering the internal reflection.

noise. In a fiberoptic system, the sum of unwanted ordisturbing energy introduced into the system fromnatural or man-made sources, such as unwanted light-waves coupled into an optical fiber or unwanted modu-lation of lightwaves in an optical fiber due to en-vironmental conditions that alter the propagation ormodulation characteristics of an optical fiber orfiberoptic sensor.

noise power. The power that is developed by unwantedelectromagnetic waves from all sources in the outputof a device, such as a transmission channel or ampli-fier. Noise power is usually the total noise powerof waves with frequencies within the passband of thesystem or device. Croastalk, distortion, and lnter-modulation products are usually classed as noise.

normalized frequency. See V-parameter.

numerical aperture (N.A.). A measure of the light-ac-cepting property of an optical fiber. For example,glass; given by:

N.A. = (n12-n22)1/2

i.e., the square root of the difference of thesquares of the refractive indices of the core, nl,and the cladding, n2. If nl is 1.414 (glass) and n2is 1.0 (air), the numerical aperture is 1.0 and allincident rays will be trapped. The numerical aper-ture is a measure of the characteristic of an opti-cal waveguide in terms of its acceptance of imping-ing light. The degree of openness, light-gatheringability, angular acceptance, and acceptance cone areall terms describing the characteristic. It may benecesaary to specify that the refractive indices arefor step index fibera and for graded index fibers;nl is the maximum index in the core and n2 is theminimum Indexin the cladding. As a number, theN.A.expresses the Mghtgathering power of a fiber. Itis mathematically equal to the sine of the acceptanceangle. A method of meaauring the N.A. is to excitethe fiber in the visible region and display the lightemerging from the end perpendicularly on a screenabout 10 to 30 cm away. The measured diameter ofthe projected circle of light divided by twice thedistance from the fiber end to the screen is thenumerical aperture. The numerical aperture is alsoequal to the sine of the half-angle of the widestbundle of rays capable of entering a lens, multipliedby the refractive index of the medium containingthat bundle of rays, i.e., the incident medium.Typical numerical apertures for plastic-clad fusedsilica optical fibers range from 0.25 to 0.45.

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0optic. See fiberoptic.

optical cable. See fiberoptic cable.

optical circuit. See integrated optical circuit.

optical data link. See fiberoptic data link.

optical fiber. A single discrete optical transmissionelement or waveguide usually consisting of a fibercore and a fiber cladding that can guide a lightwaveand is usually cylindrical in shape. It consistseither of a cylinder of transparent dielectric mater-ial of a given refractive index whose walls are incontact with a second dielectric material of a lowerrefractive index; or of a cylinder whose core has arefractive index that gets progressively lower awayfrom the center. The length of a fiber is usuallymuch greater than its diameter. The fiber reliesupon internal reflection to transmit light along itsaxial length. Light enters one end of the fiber andemerges from the opposite end with losses dependentupon length, absorption, scattering, and other fac-tors. A lightwave in an optical fiber can be modu-lated by changing the light propagation parametersof the fiber. A bundle of fibers has the abilityto transmit a picture from one of its surfaces toanother, around curves, and into otherwise inaccess-ible places with an extremely low losa of definitionand light, by the proceas of total internal reflec-tion. One optical fiber classification scheme isto divide them into plastic, glaas, or plastic-cladfuaed silica fibers; then into step-index multimode,graded-index multimode, or step-index single modefibers. Plastic is less brittle than glass but hasincreased attenuation compared to glass. Synonymouswith light pipe. See self-focusing optical fiber.

optical fiber coating. A protective material bonded toan optical fiber over the cladding to preserve fiberatrength and inhibit cabling losses by providing pro-tection againat mechanical damage, protection again-st moisture and debilitating environments, compat-ibility with fiber and cable manufacture, and com-patibility with the jacketing proceas. Coatings in-clude fluorpolymers, Teflonc, Kynarc, polyurethane,and many others. Application methods include dip-coating (for those in solution), extrusion, spraycoating, and electrostatic coating.

optical fiber jacket. A material used to cover an op-tical fiber, whether or not it is cladded or coated.

optical fiber loss. The optical power loss in an opti-cal fiber, usually expressed in dB/km.

optical fiber preform. Specially-shaped material fromwhich an optical fiber is made, usually by drawingor rolling. For example, a solid glass rod made witha higher refractive index than the tube into whichit is alipped, to be heated and drawn or rolledinto a cladded optical fiber; ortive-index rods surrounding aindex rod heated and drawn into adrawing procesa results in fiberthan the preforma.

four lower-refrac-higher-refractive-cladded fiber. Themany times longer

4

optical fiber ribbon. A rowof optical fibers laminat-ed in a flat plastic strip. Synonymous with fiber-optic ribbon.

optical fiber sensor. Synonym for fiberoptic sensor.

optical integrated circuit. A synonym for integratedoptical circuit.

optical mixing box. A fiberoptic coupler consisting ofa piece of fiberoptic material that receives severaloptical frequencies and that mixes them to producedichromatic or polychrometic lightwaves for dispatchvia one or more outputs for transmission elsewhereand perhaps subsequent separation into the constitu-ent frequencies to produce the original informationintroduced by the modulation of each of the consti-tuent frequencies. The mixing box usually has re-flective inner surfaces, except at the ports. Thelightwaves entering the box are usually a group ofmonochromatic waves each of a different frequencyand each modulated separately.

optical mixing rod. An optical mixing box that has thegeneral shape of a right circular cylinder, usuallywith pigtails to serve as entrance and exit ports.

optical power budget. In an optical transmission sys-tem, the distribution of the available power that isrequired for transmission within specified distor-tion limits or error rates. The distribution isusually in terms of decibels for each component ofthe system from source to sink. Components includethe light source pigtail, connectors, cable, splices,and detector pigtail.

optical power density. The optical energy per unit timetransmitted by a light beam through a unit area nor-mal to the direction of propagation or the directionof maximum power gradient, expressed in watts persquare meter or joules per second-(square meter).A watt is a J/S.

optical power efficiency. The ratio of the emittedelectromagnetic power of an optical source to theelectrical input power to the aource.

optical repeater. An optical/optical, optical/electri-cal, or electricalloptical signal amplification andprocessing device. The repeater usually accepts anoptical signal, converts it into an electrical sig-nal (photodetection) amplifies it, and converts itback to an optical signal for further transmission.

optical sensor. See fiberoptic sensor.

optical waveguide. See slab dielectric optical wave-guide.

optics. See integrated optics.

optoacoustics. Synonym for acoustooptics.

optoelectronic. 1. Pertaining to the conversion ofoptical power or energy into electrical power orenergy, such as the conversion of an optical signalinto an electrical signal. Also see electrooptic.2. Synonym for electrooptic.

optoelectronic device. See electrooptic device,

optomagnetic. See magnetooptic.

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optostrain. Pertaining to the change in lightwave pro-pagation characteristics caused by changes in wave-guide parameters due to strain resulting from ap-plied stress (tensile, compression, shear, bending,torsional or combinational stress). Synonymous withoptostress.

optostress. A synonym for optostrain.

ordinary bend. A bend in the core of an optical fiberin which the central axis of the core may be said tohave a bend with finite nonzero radius. If theradius of the bend is smaller than the criticalradius, light will leak from the core as total in-ternal reflection no longer takes place. Bending afiber from more than to less than the criticalradius can be used to modulate the light intensityor the leakage. Contrast with microbend.

oxide semiconductor. See combined metal oxide semicon-ductor.

Pparameter. See refractive index profile parameter.

PD. See photodetector.—

phase detection. Obtaining an output electrical signalproportional to an input lightwave phase angle thatvaries with respect to a fixed reference in accor-dance with a baseband input signal. Often phase de-tection can be accomplished by conversion to ampli-tude detection.

?hase-lock loop. An electronic circuit that controlsan oscillator so that it maintains a constant phaseangle relative to a reference signal source. Thesystem can be used in situations in which signalsthat are shifted in phase with respect to one an-other maintain a fixed or specified phase relation-ship. In spread-spectrum systems a phase-lock loopis used to cause an oscillator internal to the feed-back loop to oscillate at an incoming carrier fre-quency. The feedback, or servoloop, circuit utili-zes the output of a phase-sensitive detector, via alow pass filter, to control the frequency of its ownreference signal. The feedback loop is damped topermit tracking of the carrier phase changes at theinput, but not tracking of the modulation changes.The arrangement also provides a low noise threshold.In fiberoptic systems, a similar arrangement canbe used to control the phase of a continuous or modu-lated lightwave carrier.

phase modulation (PM). Angle modulation in which theinstantaneous phase angle of an unmodulated sinewave carrier is varied proportionally in accordancewith the instantaneous value of the amplitude of amodulating signal.

phase velocity. The velocity with which a specificpoint on a sine wave (e.g., the peak value of theelectric vector of an electromagnetic wave) is pro-pagated in a material medium or in free space. Thisconcept can only strictly be applied to a singlefrequency wave, such as an unmodulated carrier wave.The phase velocity is the propagation velocity of auniform plane sinusoidal wave, given as the wave-length times the frequency of the wave. The phase

5

velocity is also the velocity at which an observerwould have to move to make the wave characteristicsappear to remain constant in phase in a given med-ium. The phase velocity in a given medium is equalto the velocity of propagation of the wave dividedby the refractive index of the medium when the waveis an electromagnetic wave. It is not the velocityof electromagnetic energy propagation, although itmay be higher than the velocity of light in freespace. For a given frequency, the wavelength is lessin material media than in free space when electromag-netic waves are involved. In nondispersive media,the phase velocity and the group velocity are equal.Also see group velocity.

photodetector (PD). A device that is capable of ex-tracting information from a lightwave by producingan electrical output signal from an optical inputsignal.

yhoton. A quantum of electromagnetic energy. Theenergy of a photon is hf, where h is Planck’s con-stant, and f is the frequency of the radiation.

ylane of polarization. See polarization plane.

p-n junction. In a semiconductor (solid-state) device,the interface between semiconducting ~terial thathas been doped positively, i.e., with an impuritymaterial that produces holes (acceptor sites) on oneside of the interface, and material that producesrelatively free electrons (donor sites) on the otherside. The junction is usually assumed to be abrupt,or linearly graded in its transition region acrossthe interface.

Pockel cell. A material, usually a crystal, whose re-fractive index change is linearly proportional to achange in an applied electric field, the materialbeing configured so as to be part of another system,such as an optical path. The cell thus provides ameans of modulating the light in the optical path.

polarimetric sensor. In fiberoptic, a sensor in whicha baseband input signal alters the polarization of alightwave in an optical fiber or the output inten-sity is varied by a process of polarization selec-tion.

polarization. The direction of the electric field vec-tor of an electromagnetic wave, such as a lightwave.It is the property of a radiated electromagneticwave that describes the time-varying direction andamplitude of the electric field vector, that, to-gether with the magnetic field vector, makes up thewave. It is specifically illustrated by the figurethat is traced in space as a function of time bythe extremity (tip) of the vector that representsthe electric field with its base at a fixed point inspace, as observed along the direction of propaga-tion. In general, for a plane polarized wave, thefigure is elliptical and it is traced in a clockwiseor counterclockwise sense. Circular polarizationand linear polarization are obtained when the ellipsebecomes a circle or a straight line, respectively.Clockwise sense rotation of the electric field vec-tor is designated right-hand polarization, and count-erclockwise sense rotation is designated left-handpolarization. Sense of rotation is obtained by view-ing the rotating electric field vector while facingin the direction of propagation. The direction ofpropagation is the forward direction of a right-handscrew obtained when the electric vector is rotatedthrough the smaller angle into the magnetic vector,

A-1

the direction of propagation being perpendicularto both fields, namely, the direction of the Poynt-ing vector.

polarization diversity. 1. Pertaining to the abilityto change the direction of polarization of an elec-tromagnetic wave, usually at the source of radia-tion, by changing the direction of the polarizationplane, the horizontal or vertical polarization, i.e.,the polarization angle with respect to a fixed refer-ence or the linear, circular, elliptical, or helicalpolarization. 2. Pertaining to two or more typesof polarization. 3. Any method of diversity trans-mission and reception in which the same informationsignal is transmitted and received simultaneouslyon orthogonally polarized waves with fade-indepen-dent propagation characteristics. Also see diver-sity reception.

polarization modulation. The modulation of an electro-magnetic wave in such a manner that the polarizationof the carier wave, such as the direction of polari-zation of the electric and magnetic fields, or theirrelative phasing, to produce changes in polarizationangle in linear, circular, or elliptical polariza-tion, is varied according to a characteristic of aninformation-bearing input signal, such as a pulse-or-no-pulse digital signal. In optical fibers orother waveguides, polarization shifts that are madein accordance with an input signal variation are apractical means of modulation.

polarization multiplexing. Multiplexing accomplished byusing two mor more lightwave polarization modes inthe same transmission medium at the same time withthe same frequency. Each polarization mode wouldconstitute a separate channel.

polarization plane. In a transverse, or ordinary, elec-tromagnetic (TEM) wave, the plane defined by theelectric and magnetic field vectors of the wave;i.e., both field vectors at a point lie in, andtherefore define, the polarization plane. The di-rection of propagation, or power flow, of the waveis perpendicular to both the electric and magneticfield vectors at the point, i.e., perpendicular tothe polarization plane at that point. The wavefrontlies in the polarization plane. The Poynting vec-tor, ExH, is perpendicular to the polarization plane.

polarized light. A light beam whose electric vectorvibrates in a direction that doea not change, unlessthe propagation direction changes; i.e., it is in aplane perpendicular to the direction of propagation.If the time-varying electric vector can be brokeninto two perpendicular components that have equalamplitude and that differ in phase by 1/4 wave-length, the light is said to be circularly polar-ized. Circular polarization is obtained wheneverthe phaae difference between the two perpendicularcomponents is any odd, integral number of quarterwavelengths. If the electric vector is resolvableinto two perpendicular components of unlike ampli-tudes and differing in phase by values other thanO, 1/4, 1/2, 3/4, 1, etc., wavelengths, the lightbeam is said to be elliptically polarized.

population inversion. A redistribution of energy levelsin a population of elements such that, instead ofhaving more atoms with lower-energy-level electrona,there are fewer atoms with higher-energy-level elec-trona. That ia, an increaae in the total number ofelectrons in the higher excited states occurs atthe expense of the energy in the electrons in the

6

ground or lower state and at the expense of theresonant energy source (i.e. , the pump). This isnot an equilibrium condition. It is forced and mustbe maintained, i.e, stimulated. The generation ofpopulation inversion is caused by pumping. Whenelectrons revert to their lower levels, photons areemitted obtaining laser action. In a stimulatedmaterial, such as a semiconductor, the upper energylevel of two possible electronic energy levels in agiven atom, distribution of atoms, molecule, or dis-tribution of molecules, has a higher probability(usually only slightly higher) of being occupied byan electron. When population inversion occurs, theprobability of downward energy transition givingrise to radiation, is greater than the probabilityof upward energy transitions, giving rise to photonabsorption, resulting in a net radiation level, thusobtaining stimulated emission, i.e., laser action.

=“ See transmitted power.

power budget. The allocation of available power in asystem to the various functions that need to be per-formed. For example, in a fiberoptic data link, thedistribution of available optical power among allthe elements of the link, such as couplers, splices,fibers, and pigtails; or in a satellite communica-tion system, the distribution of the available powerin a satellite for maintaining orientation, maintain-ing orbit control, and for the reception and retrans-mission of signals. See optical power budget.

power density. See optical power density.

power margin. An extra amount of power that may bespecified by a designer because of uncertainties inthe empirical design method, loss, characteristics,material variability, and variation in equipment per-formance parameters and characteristics. For ex-ample, in an optical power budget, the optical power,PM, that remains after subtracting the sum of allthe optical losses, PL, and the power input requiredby a photodetector, PR, from the available opticalpower output by a source, P5, i.e.,

pM = ps - [pL+pR].

profile. See radial refractive index profile.

profile mlsmstch loss. See refractive-index-profilemismatch loss.

profile parameter. See refractive index profileparameter.

*“ See electromagnetic pulse (EMP).

punch-through voltage. In a semiconductor junction, avoltage equal to that required to just overcome thepotential barrier of the junction to permit the flowof electrons that are in the conduction band.

R

radial refractive-index profile. In an opticalwith a circular cross section, the refractive

fiberindex

described as a function of the radial distance fromthe center. For example, the function:

n=n~ f(r)

A-17

where n is the refractive index at a radial distancer from the center, nl is the refractive index at thecenter, and f(r) is the function of r that expressesthe index at the distance r from the center , usuallyindependent of radial direction. Also see refractiveindex profile parameter.

radiation. See light amplification by stimulated emis-sion of radiation (laser).

~. See light ray; meridional ray; reflected ray;skew ray.

Rayleigh scattering. The scattering of lightwaves pro-pagating in material media due to the atomic or mole-cular structure of the material and variations inthe structure as a function of distance. The scat-tering losses vary as the reciprocal of the fourthpower of the wavelength. The distances betweenscattering centers must be small compared to thewavelength. Rayleigh scattering sets a theoreticallower limit to the attenuation of a propagatinglightwave as a function of wavelength, ranging from10 dB/km at 0.50 micron to 1 dB/km at 0.95 micron.Material scattering is caused primarily by Rayleighscattering. Rayleigh scattering is also due to thevariation in molecular density of intrinsic mater-ial; for example, the familiar light green color ofpop bottles is due to Rayleigh scattering from dis-tributed iron atoms. This represents the limitingabsorption. Also since it decreases with A, thishas resulted in using higher wavelengths to achievelow-loss fiber. Minimum attenuation is due to de-creases in absorption due to Rayleigh scatteringand increases due to OH- vibration. Also see scat-tering.

ray trapping. Preventing a lightwave from leaking froma waveguide. For example, total internal reflectioncauses ray trapping.

recombination. See electron-hole recombination.

reflected ray. A ray of electromagnetic radiation,usually light leaving a reflecting surface. The rayIndicates the path after reflection.

reflection. When electromagnetic waves, such as lightrays, strike a smooth, polished surface, their re-turn or bending back into the medium from whencethey came. Specular or regular reflection from apolished surface, such as a mirror, will return amajor portion of the light in a definite directionlying in the plane of the incident ray and the nor-mal. After specular reflection, light can be madeto form a sharp image of the original source. Dif-fuse reflection occurs when the surface is rough andthe reflected light is scattered from each point inthe surface. These diffuse rays cannot be made toform an image of the original source, but only ofthe diffusely reflecting surface itself. Also seeSnell’s law; internal reflection; total internalreflection.

reflection coefficient. 1. The ratio of the reflectedfield strength to the incident field strength whenan electromagnetic wave is incident upon an inter-face surface between dielectric media of differentrefractive indices. If, at oblique incidence, themagnetic field component of the incident wave isparallel to the interface, the reflection coeffic-ient is given by:

R = (nlcosA - n2cosB)/(nlcosA + n2cosB)

where nl and n2 are the reciprocals of the refrac-tive indices of the incident and transmitted med-iums, respectively, and A and B are the angles ofincidence and refraction (with respect to normal),respectively. If, at oblique incidence, the elec-tric field component of the incident wave is paral-lel to the interface, the reflection coefficient isgiven by:

R = (n2cosA - nlcosB)/(n2cosA + n~cosB)

These equations are known as the Fresnel equationsfor such cases. For large smooth surfaces, the re-flection coefficient may be near unity, such as forhighly polished mirrors. At near grazing incidenceangles, that is nearly 90° from the normal to thesurface, even rough surfaces may reflect relativelywell, i.e., total reflection occurs. 2. At anyspecified point in a transmission line between apower source and a power sink (absorber), the vectorratio of the electric field associated with the re-flected wave to that associated with the incidentwave. The reflection coefficient, RC, is given by

RC = (Z2-Zl)/(Z2+Zl) = (SWR-1)/(SWR+l),

where Z1 iS the impedance looking toward the source,Z2 is the impedance looking toward the load, and SWRia the standing wave ratio. Also see transmissioncoefficient.

reflection sensor. See near total internal reflectionsensor.

reflective star-coupler. An optical-fiber coupling de-vice that enables signals in one or more fibers tobe transmitted to one or more other fibers by enter-ing the signals into one side of an optical cylin-der, fiber, or other piece of material, with a re-flecting back-surface in order to reflect the dif-fused signals back to the output ports on the sameaide of the material, for conduction away in one ormore fibers.

refraction. The bending of oblique (non-normal) inci-dent electromagnetic waves or raya as they cross theinterface between a transmission medium of one re-fractive index into a medium of a different refrac-tive index. The velocityof propagationof theelec-tromagnetic waves change when passing from a mediumto one with a different refractive index. Also seeSnell’s law

refraction angle. When an electromagnetic wave strikesan interface surface between media with differentrefractive indices and is wholly or partially trans-mitted into the new medium, the acute angle betweenthe normal to the surface at the point of incidenceand the refracted ray.

refractive index. 1. The ratio of the velocity oflight in a vacuum to the velocity of a given fre-quency of light in the transmission medium whose re-fractive index is desired; e.g., n = 2.6 for certainkinds of glass. 2. The ratio of the sines of theincidence angle and the refraction angle when lightpasses from one medium to another. The index be-tween two media ia the relative index, while theindex when the first medium is a vacuum is the ab-solute index of the second medium. The refractiveindex expressed in tables is the abaolute index,i.e., vacuum-to-substance at a certain temperature,

A-1

with light of a certain frequency. Examples: vacuum,1.000; air, 1.000292; water, 1.33; ordinary crownglass, 1.516. Since the index of air is very cloaeto that of vacuum, the two are often used inter-changeably. The refractive index of a substanceis given as:

where p is the magnetic permeability of the sub-stance, E ia the electric permittivity, P. is themagnetic permeability of a vacuum, and E. is theelectric permittivity of a vacuum, although nearlythe same relative to air.

refractive index profile. See radial refractive indexprofile.

refractive-index-profile mismatch loss. A 10SS Of Sig-

nal power that occurs when two optical fibers arebutt-coupled and their refractive index profiles arenot the same.

refractive index profile parameters. The exponent i inthe relation that expresaes the refractive index asa function of the radial diatance from the centralaxis of an circular optical fiber, i.e., in theexpression:

nfnl = [1-(r/a)i]l/2

where n is the refractive index at the radial dis-tance r and a is the radiua of the fiber core. Fora step-index fiber i= co for r<a and i=O for r>a; fora parabolic graded-index fiber, i=2. A value of i=2.25 will minimize or eliminate intermodal disper-sion and maximum the length-bandwidth product.

rejection ratio. See common-mode rejection ratio(CMRR).~. A bounded region in a material med-

ium, such as a free rectangular space in a lasercrystal, a length of metal hollow tubing closed onboth ends, a short length of optical fiber with mir-rors on both ends, or the reflection could be due toa 3-dB coupler or a splice associated with the inser-tion loss, or a region of such geometrical dimen-sion, such as two parallel walls that are a multipleor submultiple of wavelengths apart, that a standingwave (electromagnetic, acoustic, or elastic) canbe austained and raised to high intensity by applica-tion of stimulation (applied energy of appropriatefrequency) from outside or inside the cavity. Reson-ant cavities are used in some lasers in which theyform part of the laser head.

ribbon. See optical fiber ribbon.

risetime. In pulse circuits, the time required for apulse to reach a specific magnitude from a givenlevel. For example, the time required for a voltageor a light pulse to change from 0.1 to 0.9 of itsmaximum value.

risetime budget. In fiberoptic transmission systems,an accounting of all the riaetimea (time requiredfor a lightpulse to reach a apecified level) in aaequence of optical and electrical components. Be-cause the distribution of photon energies in light-waves are Gausaian, the risetimes of a aequence ofcomponents are combined as the aquare root of thesum of the squarea of the individual ristimes.

8

sSagnac interferometer. An interferometer in which a

lightwave is split and passed in opposite directionsaround the same rigid rotating loop by means of mir-rors to a single photodetector. The phase cancella-tion and enhancement, and hence light intensity atthe photodetector, will vary as the angular velocityis varied, thus obtaining a measure of angular ac-celeration.

scatter. The process in which the direction, frequen-cy, phase, or polarization of sound or electromag-netic waves is changed when the waves encounter oneor more discontinuities in the transmission mediumthat have lengths of the order of a wavelength.Scattering usually implies a random or disorderedchange or distribution in the incident energy.

scattering. The deflection of electromagnetic wavescaused by movement of free and bound charges (e.g.,electrons, protons, and ions) in a transmissionmedium, the scattered fields being created as a re-sult of the movement. The scattered field and theincident field define the total field. See Rayleighscattering.

sm. See space-division multiplexing.—

self-focusing optical fiber. ATI optical fiber that iscapable of focusing lightwaves by precision-controlof geometry, refractive indices, light wavelength,and other parameters. The fiber is frequency-selec-tive.

SELFOC fiber. Self-focusing optical fiber produced byNippon Electric Company and Nihon Sheet Glass Com-pany.

semiconductor. A material, such as diamond, silicon,galium-arsenide, germanium, gray tin, tellurium, andselenium, that has a filled valence-electron energyband separated by a finite band-gap energy from ahigher-energy conduction band. Thus, semiconductorsare neither insulators, with large band gaps andsmall electronic nobilities, nor metallic conductorswith extremely high conductivities. Semiconductorspossess covalent bonding wherein electron pairs areheld tightly in the region between adjacent atoms orions. The band-gap energy is the energy required tobreak an electron out of one of theae bonds. Semi-conductors are often grown in single crystals andsliced or cut, to form diodes, transistors, lasers,and LEDS, thus preserving an ordered crystal latticestructure suitable for accepting positive or nega-tive dopants. See combined metal oxide semiconduc-tor; metal oxide semiconductor.

sensor. A device or means to extend the natural sen-ses. For example, equipment that detects or indi-cates terrain configuration or that detects the pre-sence of objects or their motion by means of energythat is emitted or reflected by the objects; equip-ment that detects physical variables, such as tem-perature, pressure, humidity, weight, vibration, oracceleration; equipment that detects the presence orintensity of illumination, radio waves, ionizationdensity, electric fields, or magnetic fields; orequipment that detects the presence of chemicals,such as pollutants and irritants; or the presence ofradioactivity. Most detectors are in fact trans-ducers, since they convert energy to another form

A

and amplify it. They are usually designed to meas–ure variations in the quantities that they are sens-ing. A fiberoptic sensor makes use of changes inits light propagation properties to detect and meas-ure the environmental changes it is subjected to.See brightfield sensor; fiberoptic sensor; darkfieldsensor; interferometric sensor; intensity sensor;microbend sensor; near total internal reflectionsensor; polarimetric sensor.

sensor array. A spatial distribution of sensors. Thespatial distribution may be used to obtain basebanddirectional information and to achieve various formsof multiplexing.

sheath. See fiberoptic sheath.

signal. 1. A time-dependent value attached to a tran-sient physical phenomenon used to convey data, e.g.,the variation of light intensity at a point in anoptical waveguide to represent a binary digit, thelight-level change propagating as a pulse along theguide. 2. An impulse, either electrical, as in awire; acoustic, as used in aonar; or a short burstof light energy, as generated by a laser and coupledto an optical fiber for guidance and transmissionand for conversion back to an electrical pulse atthe far end of the fiber.

signal processing. The transformation of an input sig-nal, i.e., a specific wave shape, into some otherdesirable form or other wave shape, usually by meansof particular electronic circuits, lens systems,waveguides, antennae, or other circuit elements,such as detectors, rectifiers, pulse compressors,pulse expanders, pulse generators, nonlinear cir-cuits, or gates. It includes the detection, shap-ing, converting, coding, or time positioning of anelectrical, electromagnetic, or acoustic signal.

single heterojunction. In a laser diode, a single junc-tion involving two energy level shifts and two re-fractive index shifts, used to provide increased con-finement of radiation direction, improved control ofradiative recombination, and reduced nonradiative(thermal) recombination. Synonymous with close-con-finement junction.

single-mode fiber. An optical fiber that supports thepropagation of only one mode. Usually a low-lossoptical waveguide with a very small core (2 to 12microns diameter). It requires a laser source forthe input signals because of the very small entranceaperture (acceptance cone) and the narrow spectralwidth. The small core radius approaches the wave-length of the source, consequently only a singlemode is generated and propagated.

skew ray. In an optical fiber, a light ray that is notconfined to a plane, does not pass through the opti-cal axis, is not parallel to the optical axis, andyet is totally internally reflected, thus taking acurling (corkscrew) path. In certain graded indexfibers, the skew ray travels in a helical path alongthe fiber never intersecting the optical axis, par-ticularly as long as the fiber is straight. It isnot confined to the meridian plane or any otherplane, nor is it a meridional ray. Also see mer-idional ray.

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slab dielectric optical waveguide. An optical wave-guide consisting of rectangular layers or ribbonsof materials of differing refractive indices thatsupport one or more lightwave transmission modes,with the energy of the transmitted waves confinedprimarily to the layer of highest refractive index,the lower indexed medium serving aa cladding, jack-eting, or surrounding medium. Slab dielectric opti-cal waveguides are used in integrated optical cir-cuits for geometrical convenience, in contrast tothe optical fibers in cables for long-distancetransmission.

slab dielectric waveguide. An electromagnetic wave-guide consisting of a dielectric transmission mediumof rectangular cross section. The width and thick-ness of the guide may be controlled to supportspecific propagation modes; it may be cladded, pro-tected, distributed, and electronically controll-able; and it may be mounted on integrated electro-optical circuit substrate.

Snell’s law. When electromagnetic wavea, such as light,pass from a given transmission medium to a mediumof higher refractive index (denser) medium, its pathis deviated toward the normal. When paasing intoa less dense medium, its path is deviated away fromthe normal. Often called the lawSnell’s law defines this phenomenonthe relation between the incidencerefraction angle as follows:

sin@l/sine2 = n2/nl

where 81 is the incidence angle, ’32

of refraction,by describingangle and the

is the refrac-tion angle, n2 is the refractive index of the mediumcontaining the refracted ray, and nl is the refrac-tive index of the medium containing the incidentray. Stated in another way, both laws, that of re-flection and of refraction, are attributed to Snell,namely, when the incident ray, the normal to thesurface at the point of incidence of the ray on thesurface, the reflected ray, and the refracted rayall lie in a single plane, the angle between the in-cident ray and the normal is equal in magnitude tothe angle between the reflected ray and the normal.The ratio of the sine of the angle between the nor-mal and the incident ray, to the sine of the anglebetween the normal and the refracted ray, is a con-stant for a given wavelength of incident light.Also see refraction.

source. In fiberoptic sensors, as in communications,that part of a syatem from which signals or messagesare considered to originate. A fiberoptic sensor isthe source of baseband signals in a fiberoptic sys-tem. The source may be an optical source (unmodu-lated) or a signal source used to modulate the opti-cal source. See light source.

source-free medium. In fiberoptic, a transmissionmedium that does not contain a source of electromag-netic radiation, such as electric charges or magne-tic poles, other than a propagating or standingelectromagnetic wave.

solid state. Pertaining to the conduction of electriccurrents or magnetic flux, or the propagation ofelectromagnetic waves, within materials other thangases or other than a vacuum.

A-2

space-division multiplexing. The use of spatial sepa-ration between light beams, conductors, opticalfibers or other transmission media in order to ob-tain channel isolation. For example, the combiningof several independent and isolated fibers or wiresin a single bundle or cable in order to use eachfiber (or bundle) as a separate communication path,channel, or set of channels. A typical arrangementfor multiplexing might be to use time-division multi-plexing on each space-division multiplexed fiber pairin an optical cable.

splitter. See beam splitter.

~. In a laser, emission that doesnot bear an amplitude, phase, or time relationshipwith an applied signal and is therefore a randomnoiselike form of light radiation. Alao see stimu-lated emission.

spreading. See geometric spreading.

star-coupler. See reflective star-coupler.

step-index fiber. A fiber in which there is an abruptchange in refractive index between the core andcladding along a fiber diameter, with the core re-fractive index being higher than the cladding re-fractive index. There may be more then one layer,each layer with a different refractive index thatis uniform throughout the layer, but usually withdecreasing indices in the outside layers.

stimulated emission. In a laser, the emission of lightcaused by a signal applied to the laser such thatthe response is directly proportional to, and inphase coherence with, the electromagnetic field ofthe stimulating signal. This coherency between ap-plied signal and response contributes to the useful-ness of the laaer. Also see spontaneous emission.

stimulated emission of radiation. See light amplifica-tion by stimulated emission of radiation (laser).

strength member. In fiberoptic cables, a component ofthe cable that provides tensile strength and bendingresistance, therefore limiting stress (and strain)on the optical fibers in the cable.

stripper. See cladding mode stripper.

substrate. A material used to support or serve as afoundation, vehicle, or carrier for other materialthat has the required characteristics for specificapplication but does not have the proper phyaicalstrength to support itself, e.g., a block of mater-ial upon which active materials may be deposited byevaporative techniques or on which active materialsmay be bonded by cementing or etching techniques.The substrate is usually inert or passive relativeto the active material mounted upon it.

switch. See waveguide switch.

0

T

TDM. See time-division multiplexing.—

telecommunication. Communication over relatively largedistances by any transmission, emission, or recep-

tion of signals, signa, writing, images, and sounds,or intelligence of any nature by wire, radio, vis-ual, or other electrical, electromagnetic, optical,acoustic, or mechanical means. The process enablesone or more users to pass to one or more other usersinformation of any nature delivered in desirableforms, such as written or printed matter, fixed ormoving pictures, words, music, visible or audiblesignals, or signals that can control the functioningof equipment or mechanisms. Also see telemetry.

telemetry. The branch of science and technology devotedto the process of measuring the values of variables,such as pressure, temperature, humidity, blood flow,radiation levels, or sound levels; transmitting theresults of the measurements by some means to a dis-tant station; and interpreting, indicating, display-ing, recording, or using the information that isobtained. Also see telecommunication.

time. See coherence time.

time-division multiplexing (TDM). Multiplexing in whichseparate channels are established by connecting onecircuit automatically to many signal sources sequen-tially in time. The signals from the severalsources, such as an array of fiberoptic sensors,share the time of the circuit by using the circuitin successive time slots. Each discrete time inter-val is assigned to a particular signal source. Syn-chronizing pulses are used to asaist in demultiplex-ing at the distant end of the circuit. Thus, thetime of an optical fiber can be divided among manysignal sources, by allowing two or more signalsources to use the channel at different times. Thechannel may be shared by automatically switching tothe several sources and connecting each one to thechannel during the specific time period allocated

to that source. For example, if each aource is as-signed to a given channel for 1 Vsec out of eachmillisecond, 1,000 sources can be accommodated(multiplexed) by the channel. During a given timeinterval the entire available frequency spectrumcan be used by the channel to which it is assigned.In general, time-division multiplexed systema usepulae transmission or analog sampling. The multi-plexed pulse string may be considered to be theinterleaved pulse strings of the individual channels.The individual channel pulses may be modulated ineither an analog or digital manner.

total internal reflection. Reflection that occurs with-in a substance when the incidence angle of a lightray striking a boundary surface is greater than thecritical angle and therefore the entire energy ofthe ray is reflected back into the substance andnone is transmitted across the surface.

total internal reflection senaor. See near total inter-nal reflection sensor.

transducer. A device capable of transforming energyfrom one form to another, usually with such fidelitythat if the original energy time and spatial distri-bution represents information, the transformed ener-gy can represent the same information or a function

A-

of that information. For example, a fiberoptic sen-sor that converts a pulse pressure wave into a modu-lated lightwave, a microphone that converts a soundwave to a corresponding electrical current, a modu-lated laser that converta electrical currents tomodulated lightwaves, a photodetector that convertsmodulated lightwaves to electrical current, or apiezoelectric crystal that produces a voltage pro-portional to the time derivative of the pressurewave that impinges upon it. See optoacoustic trans-ducer.

transmission coefficient. The ratio of the transmittedfield strength to the incident field strength whenan electromagnetic wave is incident upon an inter-face surface between dielectric media of differentrefractive indices. If, at oblique incidence, theelectric field component of the incident wave isparallel to the interface, the transmission coeffi-cient is given by:

T = 2n2cosA/(n2cosA + nlcosB)

where nl and n2 are the reciprocals of the refrac-tive indices of the incident and transmitted media,respectively, and A and B are the incidence angleand refraction angle (with respect to the normal tothe interface surface), respectively. If, at obli-que incidence, the magnetic field component of theincident wave is parallel to the interface surface,the transmission coefficient is given by:

T = 2n2cosA/(nlcosA + n2cosB)

These equations are known as the Fresnel equationsfor these cases.

transmission medium. Any subatance that can be or Isused for the propagation of signals, usually in theform of modulated radio, light, acoustic waves, orelectric currents, from one point to another, suchas an optical fiber, cable, or bundle; a wire; adielectric slab; water; or air. Free space can alsobe considered as a transmission medium for electro-magnetic waves.

transmitted power. The energy per unit time usuallyexpressed in watta, propagated through a specifiedcroas sectional area, such as a fiber cable or otherwaveguide, or a specified cross-sectional area per-pendicular to the direction of propagation, such asin a specified solid angle, or through a fictitioussphere completely surrounding the transmitter. Sinceinstantaneous transmitted power can vary with timeand the specified croas-sectional area can change,the power can assume various forms of measurement,such as the peak envelope power, the power in a givendirection, the power averaged over time, the poweraveraged over an area or solid angle, the total car-rier power delivered to an antenna, the total powerradiated and integrated over all directions, or itmay be the power limited to a specified portion ofa frequency spectrum or bandwidth.

trapping. See ray trapping.

21

vvacancy defect. In the somewhat ordered array of atoms

and molecules in optical-fiber material, a site atwhich an atom or molecule is missing in the array.The defect can serve as a scattering center, causingdiffusion, heating, absorption and resultant atten-uation. Also see interstitial defect.

valence band. In a semiconductor, the range of elec-tron energy, lower than that of the conductionband, possessed by electrons that are held bound toan atom of the material, thus reducing conductivityfor electric currents even under the influence ofan applied electric field. When electron engergiesare raised, e.g., by thermal excitation or by pho-nons, electrons with the highest energy levels ofthe valence band are raised to the lower energylevels of the conduction band, thus leaving holesin the atoms whose electrons remain in the valenceband.

velocity. See phase velocity.

V-parameter. A parameter that can be used to calculateor express the number of propagating modes that astep-indexed optical fiber is capable of supporting,expressed mathematically as:

fn = (2na/k)(n12 - n22)1/2

where fn is the V-parameter (V-value or normalizedfrequency), a is the optical fiber core radius, Aisthe source wavelength, and nl and n2 are the refrac-tive indices of the core and cladding of the opticalfiber. For a large number of modes, the mode volumeis given by:

N = fn2/2

where N is the number of modes, or mode volume, andfn Is the V-parameter (V-value or normalized fre-quency) above. Synonymous with normalized frequency;V-value.

V-value. Synonym for V-parameter.

wwave. See electromagnetic wave; evanescent wave.

wave equation. The equation, based on Maxwell’s equa-tions, the constitutive relations, and the vectoralgebra, that relates the electromagnetic field ofan electromagnetic wave time and space derivativeswith the transmission medium electrical permittivityand magnetic permeability in a region without elec-trical charges or currents. The solution of the waveequation yields the electric and magnetic fieldstrength everywhere as a function of time and spacecoordinates, field strengths, and transmission mediaparameters. The wave equation is given as either:

72H- ~ca2H/at2 = o ‘r

v2E - vEa2E/at2 = o

in a current- and charge-free nonconducting medium,where E is the electric field intensity, H is themagnetic field intensity, c is the electric permit-

A-22

tivity, and p is the magnetic permeability. V is thevector spatial derivative operator. The wave equa-tion applies in optical waveguides.

wavefront. A surface normal to an electromagnetic rayas it propagates from a source, the surface of thewavefront passing through those parts of the wavesthat are in the same phase. For parallel rays, thewavefront is a plane. For rays diverging from orconverging toward a point, the wavefront is spher-ical. The wavefront is perpendicular to the direc-tion of propagation of the wave, and the electricand magnetic field vectors of the wave define aplane that is tangent to the wavefront surface atthe point that the field vectors are determined.The front is a three-dimensional surface all thepoints on which are the same optical path lengthfrom the wave source.

waveguide. Any structure capable of confining and sup-porting the energy of an electromagnetic wave to aspecific relatively narrow controllable path that iscapable of being altered, such as a rectangularcross-section metal pipe, an optical fiber of cir-cular cross section, or a coaxial cable. See slabdielectric waveguide.

waveguide delay distortion. In an optical waveguide,the distortion in received signal caused by the dif-ferences in propagation time for each wavelength,(i.e., the delay versus wavelength effect for eachpropagating mode), causing a spreading of a receivedsignal pulse at the detector. Waveguide delay dis-tortion contributes to group-delay distortion asdoes material dispersion and multimode group-delayspread.

waveguide dispersion. The part of the total dispersionattributable to the dimensions of the waveguide. Thecross-section dimensions are critical. They deter-mine the modes that are allowed and not allowed topropagate. Waveguide dispersion increases as thespectral width of the source increases due to theactual dimensions and their variation along thelength of the guide.

wavelength. The length of a wave measured from anypoint on a wave to the corresponding point on thenext cycle of the wave, such as from crest to crest.Wavelength determines the nature of the variousforms of radiant energy that comprise the electro-magnetic spectrum, e.g., it determines the color oflight. For a sinusoidal wave, the wavelength is thedistance between points of corresponding phase oftwo consecutive cycles of the wave. The wavelengthk, iS related to the phase velocity v, and the fre-quency f, by the relation i= vlf.

wavelength-division multiplexingg (WDM). In optical com-munication systems, the multiplexing of lightwaves ina single transmission medium or channel, such thateach of the waves are of a different wavelength andare modulated separately before insertion into themedium. Usually, several sources are used, such asa laser, or several lasera, or a dispersed whitelight source or aources, each having a distinctlydifferent center wavelength. WDM is the same asfrequency-division multiplexing (FDM) applied tovisible light frequencies of the electromagneticspectrum.

wave number. The value of 2n times the reciprocal ofthe wavelength of a single-frequency sinusoidal wavesuch as a singlefrequency uniform plane-polarized

w

W—

3

electromagnetic wave, e.g. , a monochromatic light-wave. The wave number is usually used for waves inor near the visible spectrum, since wavelength ismore readily measured than frequency, but it is fre-quency, or wave number, that iS directly related toto energy. For example, photon energy is given by:

P.E. = hkc/2n = hf = hcl~

where h is Planck’s constant, k is the wave number,c is the velocity of the light, f 1S the frequency,and k is the wavelength. The wave number is thenumber of wavelengths per unit distance in the direc-tion of propagation. Also see wave parameter.

aveguide switch. A mechanically or electrically con-trolled device that is capable of stopping, atten-uating, or diverting the propagation of electromag-netic energy at a specific point in a waveguide.

wave parameter. 1. Any feature of a wave, such as itsamplitude, phase or shape. 2. A unit that is usedin regard to periodic waves, such as electromagneticwaves. The wave parameter, p, is given by the rela-tion p = 2n/A, where A is the wavelength. Also seewave number.

DM. See wavelength-division multiplexing.

-dB coupler. In fiberoptic, a coupler that splitsthe optical energy in an optical waveguide into twoequal parts and couples each part into a separatewaveguide. The 3-dB coupler ideally distributea 50%of the input optical power to each of the outputchannels. However, in actual practice, the ratiomay vary, for example, 45% into one and 55% into theother output channel. Some optical energy may belost or absorbed by the coupler.

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