EE 230: Optical Fiber Communication Lecture 2

EE 230: Optical Fiber Communication Lecture 2

From the movieWarriors of the Net

Fibers from the view of Geometrical Optics

Total Internal Reflection

1 1 2 2

1 3

1 2 1 2

21 2

1

1

:sin sin

Re

90 deg

sin sin

c c

c

c

Snells Lawn nflection Condition

When n n and as increases eventuallygoes to rees and

nn n or nis called the Critical angle

For there is no pro pagating refracted ray

Reflection as a function of angle

Fiber Optics Communication Technology-Mynbaev & Scheiner

This additional Phase Shift is not accounted for

in geometrical wave approach

The reflectivities of waves polarizedparallel and perpendicular to the plane of incidence as given by the Fresnel equations

Principal Types of Optical Fiber

Understanding Fiber Optics-Hecht

Types of Fibers•Single mode/Multi-mode•Step Index/Graded Index•Dispersion Shifted/Non-dispersion shifted•Silica/fluoride/Other materials

•Major Performance Concerns for Fibers•Wavelength range•Maximum Propagation Distance•Maximum bitrate•Crosstalk

Fabrication of Optical Fiber

• Fabrication of fiber preform: macroscopic version with correct index profile

• Drawing of preform down into thin fiber• Jacketing and cabling

Step-Index Fiber• Cladding typically pure silica• Core doped with germanium to increase

index• Index difference referred to as “delta” in

units of percent (typically 0.3-1.0%)• Tradeoff between coupling and bending

losses• Index discontinuity at core-clad

boundary

Basic Step index Fiber Structure


Ray Trajectories in Step Index fiber

Meridional Rays

Skew Rays

Coupling Light into an Optical Fiber


Acceptance Angle

Optics-Hecht & Zajac

The acceptance angle (i) is the largest incident angle ray that can be coupled into a guided ray within the fiber

The Numerical Aperature (NA) is the sin(i) this is defined analagously to that for a lens

#

tan

1 2

f ffD FullAccep ceAngle

NA

º =

= ×

1 1 12 2 22 2 2

1 2

1 2 1 2

( ) (2 ) (2 )

and 2

NA n n n n

n n n nWhere nn

= - = D = D

- +D º º

φ1

φ2

θ1

θ2

nCO

nCL

n0

From Snell’s Law, 21 sinsin CLCO nn

For total internal reflection, θ2=90º

CO

CLc n

n11 sin

What value of φ1 corresponds to θc? That is the maximum acceptance angle for the fiber. φ2 = 90º-θc sinφ2 = cos θc

CO

CLc n

nsin , so

CO

CLCOc n

nn 22

cos

NAnnn

nnnn CLCO

CO

CLCOCOCO

22

22

2sin

Again from Snell’s Law,

21 sinsin COo nn

(= NA), so

0

11 sin

nNA

c

Numerical Aperture

210 sinsin COnn

For Corning SMF-28 optical fiber

nco=1.4504, nCL=1.4447 at 1550 nm

NA = 0.13

Acceptance angle = 7.35 degrees

Geometrical View of Modes


•Ray approximation valid in the limit that goes to zero

•Geometrical Optics does not predict the existance of discrete modes

•Maxwells Equations and dielectric boundary conditions give rise to the requirement that the fields and phase reproduce themselves each “cycle”

Rays and Their E-field Distribution

Origin of Modal Dispersion• Straight path along fiber axis has distance L and velocity c/nCO for

transit time of LnCO/c

• Path at maximum acceptance angle φc has distance L/cosφ2 where φ2=90º-θc and thus a longer transit time.

• Transit time difference equal to

• Dispersion limits rate of signals that fiber can handle• If spread can be up to 70% of bit period, then maximum bit rate is

1.4cnCO/L(NA)2

2

22

2 1sin1cos

COnNA

112

CL

COCO

nn

cLn

tt

Intermodal Dispersion


1SI 2

1 2SI2

SI

Lt cLt for c

( )Lt c 2

n nn

n n nNAn

D = D

D @ D @D @

Bandwidth for Various Fiber Types


21

21 8

4

1Bit Rate BR< 4

14 4

2

2

SI

SISI

GI

GIcBRLn

t

cBR t Ln

cBRn L

cBR n L

= =DD

D

= =D D

= D

D

No intermodal time shift for single Mode Fiber

Graded Index Fiber

Fiber Optic Communication Systems-Agarwal

1

1 2

212

1

21

( ) 1 for <a

( ) 1 =n for >a

for 2 a "parabolic profile"

NA=n 2 1 which varies with

8GI

n na

n n

a

Lntc

Fiber Optic Communications-Palais

Ray Propagation in Graded-Index Fiber

Graded Index Slab Uniform in X and Z

Fundamentals of Photonics - Saleh and Teich

Ray spreading comparison

3

4

8 COGI cn

NALt

CO

SI cnNALt

2

2

Comparison, continued

If NA=0.13 and nCO=1.45,

∆tSI/L=19 ps/m

∆tGI/L=0.039 ps/m

Graded-index fiber has substantially less modal dispersion

EE 230: Optical Fiber Communication Lecture 2

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