Troubleshooting fiber Bragg grating fabrication with modelingFBG with light launched into long...

AOPC Sept. 10, 1999Fiber Optics and ElectronicsTechnology Center

Troubleshooting fiber Bragggrating fabrication with modeling

Alessandra Chiareli

Fiber Optics & ElectronicsTechnology Center

Collaborators: Jim Brennan (TSD), Dwayne LaBrake (TSD), Charles Haggans


AbstractSeveral approaches are available for modelingfiber Bragg gratings, each having their ownstrengths and weaknesses. In this talk, we willdiscuss how different techniques for solvingcoupled mode theory equations can providecomplementary information that is not easilyattainable by using one technique alone. Thiswork is particularly applicable to very longlength fiber Bragg gratings.


Outline• Motivation

• What is a fiber Bragg grating

• Reviewing chromatic dispersion

• FGB as dispersion compensator

• We made one and it does not look good

• Using modeling to understand why and toset fabrication tolerances

• Conclusion


dispersioncompensation WDM

erbium doped fibersfor fiber amplifiers

bandwidth

Telecommunications has abandwidth problem


Introduction

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Wavelength (nm)

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Tra

nsm

issi

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Wavelength (nm)

∆n = 10 to 10-5 -2Λ1.46

Cor

e R

efra

ctiv

e In

dex

Fiber Axis

L

Fiber Core Index ModulationOptical Fiber

Signal In

TransmissionReflection

= 2n b e

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Wavelength (nm)1558


Phase Mask: Direct Imprinting

+1 order

-1 order

UV Beam

Phase Mask

Optical Fiber


Bragg Gratings:Basic Definitions

Apodization : Tailored Spatial Exposure.

Chirp : Non-UniformBragg Grating Period.

Uniform Profile : UniformBragg Grating Period (typical).

∆n

∆n

∆n

∆n

Apodization : Tailored Spatial Exposure.


Detection Scheme Does NotResolve Pulses

Optical Fiber

> 400 km

Chromatic Dispersion ProblemChromatic Dispersion Problem

Optical Fiber

> 400 km


Dispersion Compensation• The Problem

– Standard single-mode fiber has zero dispersion at the 1310nm transmissionband. It is not corrected at the 1550nm band. Dispersion broadens opticalpulses as they travel in single-mode fiber, limiting the ultimate data ratesupported by fiber.

• A Solution– Recompress the optical pulses using chirped gratings.

Input: Long λ lags short λ

Output: Compressed Pulse

Decreasing grating period(Chirp)

Long λ

Short λ


Fiber Bragg GratingDispersion Compensator


• to compensate the large bandwidth ∆λ of erbiumfiber amplifiers for long distances of fiber links Lf

with dispersion D (D=17ps/nm/km @ 1550 nm)

DLL n

cf

g eff=

2

∆

Dispersion Compensator Goal

D - dispersion per unit lengthLf - fiber link lengthLg - grating lengthneff - effective indexc - speed of light∆λ - grating bandwidth

•For a 80 km link, need to compensate 1360 ps/nm•For a bandwidth of 7 nm, need about 1 m granting


Approach to FBG SpectrumSimulation: coupled-mode theory

()()()()()()()()dRizRzizSzdzdSizSzizRzdz=+=−−

•Good quantitative predictor of diffraction efficiencyand spectral dependence of fiber gratings

CoupleModeamplitudeequations

Where R and S are the forward and backward propagatingmodes, respectively, and σ and κ are coupling coefficients


Some Solution Approaches

• Direct numericalintegration ofcoupled mode eqs.– advantage - can

resolve effect of smallscale fabricationerrors

– disadvantage - notfast

• Transfer matrix(piecewise-uniformapproach)– advantage -

reasonable simulationtimes for longgratings

– disadvantage -smallest section mustbe about 50 periods inlength


Main Modeling ParametersInput

• fiber geometry(dimension, refractiveindices,photosentivity)

• grating length

• central period

• chirp/bandwidth

• grating strength

• apodization

• phase shifts

Output

• reflection

• transmission

• delay (ripple factor)

• dispersion


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reflection (d

delay (ps)

wavelength (m)

What is an ideal dispersioncompensating grating spectrum?


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Grating showing instability infabrication process


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Analysis Resultdirect numerical integration

Measurement in blue & Simulation in Red


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reflection (d

delay (ps)

wavelength (nm)

Another fabricated DCG: whythe fuzz?

deviation from linear delay is called delay ripple


Transfer Matrix piecewise-uniform approach

We imposed stochastic phase shifts and studied their effecton grating spectra as we varied their max. amplitude andtheir frequency along the grating.


Figure of merit

Ripple standard deviation

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reflection (d

delay (ps)

wavelength (nm)

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delay ripple (

wavelength (nm)


Delay ripple amplitude as a function of...

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ripple amplitud

phase shift amplitude (degrees)

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0 2000 4000 6000 8000 10000 12000

ripple amplitu

number of phase shifts, N

...random phase maximumamplitude

... number of random phase shiftsalong the grating length

The simulation results (circles) follow apower law relationship (line).

Analysis Resulttransfer matrix approach


Delay ripple

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delay ripple (

wavelength (nm)

measurement: delay ripple across chirpedFBG with light launched into long

wavelength side.

simulation: delay ripple acrosschirped FBG with light launched

into long wavelength side

Delay ripple for chirped FBG with periodic phase shifts across its length is shownbelow. The ripple increases with the optical path length through the grating. The

wavelengths on the launch side show the least amount of ripple both in thesimulations and measurements.

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Ripple Amplitu


Conclusion

A variety of modeling & computational tools isneeded to get the work done.

Troubleshooting fiber Bragg grating fabrication with modelingFBG with light launched into long...

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