lecture3_16

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16.711 Lecture 3 Optical fibers

Last lecture

Geometric optic view of waveguide, numeric aperture Symmetric planar dielectric Slab waveguide

Modal and waveguide dispersion in palnar waveguide

Rectangular waveguide, effective index method

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Today

Fiber modes Fiber Losses

Dispersion in single-mode fibers

Dispersion induced limitations

Dispersion management

The Graded index fibers

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Fiber modes --- single mode and multi-mode fibers

V-number

,2

2

2

1

2

2

2

nn

nnb

eff

,)/996.01428.1( 2Vb

,)(2 2/12

2

2

1 nna

V

,41.2)(

2 2/122

2

1 nna

Vc

cutoff

Number of modes when V>>2.41

,2

2

VM

Normalized propagation constant

for V between 1.52.5.

Mode field diameter (MFD)

),11(22

Vaw

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Examples --- single mode and multi-mode fibers

1. Calculate the number of allowed modes in a multimode step index fiber, a = 100 m, core

index of 1.468 and a cladding index of 1.447 at the wavelength of 850nm.

,44.91)(2 2/12

2

2

1 nna

V

,4181

2

2

V

M

Solution:

a < 2.1m

2. What should be the core radius of a single mode fiber that has the core index of 1.468 and the

cladding index of 1.447 at the wavelength of 1.3m.

,4.2)(2 2/12

2

2

1 nna

V

Solution:

3. Calculate the mode field diameter of a single mode fiber that has the core index of 1.458 and

the cladding index of 1.452 at the wavelength of 1.3m.

,1.10)/11(22 0 mVaw

Solution:

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Dispersions in single mode fiber

Waveguide dispersion

,|0

d

dvg ,

g

gv

L

,

2)2(

984.1)(

2

2

2

2

cna

N

d

d

L

gg

, LDmg

Example --- waveguide dispersion

n2 = 1.48, and delta n = 0.2 percent. Calculate Dw at 1310nm.

Solution:

,)()(

)(2

2

212

dV

VbdV

c

nnn

d

d

L

g

,)()(2

2

212

dV

VbdV

c

nnnDw

,)/996.01428.1( 2Vb for V between 1.52.5.

,26.0)(2

2

dV

VbdV

),/(9.1)()(2

2

212 kmnmps

dV

VbdV

c

nnnDw

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chromatic dispersion (material plus waveduide dispersion)

,)(

wm

gDD

L

material dispersion is determined by

the material composition of a fiber.

waveguide dispersion is determined

by the waveguide index profile of a

fiber

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Polarization mode dispersion

, pg D

L

fiber is not perfectly symmetric,

inhomogeneous.

refractive index is not isotropic.

dispersion flattened fibers:

Use waveguide geometry and

index profiles to compensate

the material dispersion

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,

2

1

2/1

B

For RZ bit With no intersymbol interference

,1

2/1B

For NRZ bit With no intersymbol interference

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,212/1

B

Optical and Electrical Bandwidth

,7.03 Bf dB

Bandwidth length product

,25.0

D

BL

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,16/ 12/1 pskmDL

,8.27.03 GHzBf dB

,9.3625.0 1kmGbsD

BL

Example --- bit rate and bandwidthCalculate the bandwidth and length product for an optical fiber with chromatic dispersion

coefficient 8pskm-1nm-1 and optical bandwidth for 10km of this kind of fiber and linewidth of

2nm.

Solution:

Fiber limiting factor absorption or dispersion?

,5.21025.0 dBkmdBLoss

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Dispersion Management

],)(2

1exp[),0(

2

0

0T

tAtA ),

2exp()2(),0(

~2

0

22/12

00

TTAA

,

1

0

0T

Pre compensation schemes

1. Prechirp

Gaussian Pulse:

...,|2

1)(|)(

000 2

2

0

d

kd

d

dkkk

...,)(2

1...|)(|

)()( 22102

2

00 00

d

d

d

d

c

k

),2

exp(),0(~),(

~2 z

iAzA

],)(2

1exp[)(

)2

exp(),0(~

2

1),(

2

0

020

zQTzQ

Adz

iAtzA

,1)( 20

2

TzizQ ,])(1[)( 0

2/122

0

2 TTzzT

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],)(2

)1(exp[),0(

2

0

0T

tiCAtA

),

)1(2exp()

1

2(),0(

~2

0

22/1

2

00

iC

T

iC

TAA

Pre compensation schemes

1. Prechirp

Prechirped Gaussian Pulse:

],)1()1(2

exp[)1

2()

2exp(),0(

~),(

~2

2

2

02

2

2

0

22/1

2

00

2

2C

iCT

C

T

iC

TAz

iAzA

],)(2

1exp[)(

)2

exp(),0(~

2

1),(

2

0

020

zQTzQ

Adz

iAtzA

,)(

1)(2

0

2

T

ziCzQ

,])()1[()(

0

2/12

2

0

22

2

0

2 TT

z

T

zCzT

,1)1(0

2/12

0T

C

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1. Prechirp

With T1/T0 = sqrt(2), the transmission distance is:

,1

212

2

DLC

CCL

,/ 2

2

0 TLD

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Examples:

),(1052

1 11

sBTFWHM

1. Whats the dispersion limited transmission distance for a 1.55m light wave system making

use of direct modulation at 10Gb/s? D = 17ps(km-nm). Assume that frequency chirping

broadens the guassian-shape by a factor of 6 from its transform limited width.

Solution:

,10366.1/11

0 sTT FWHM

,1)1(0

2/12

0T

C ,9.5C

,])()1[()( 002/12

2

0

22

2

0

2 TTT

z

T

zCzT

,2

22

cD ,/24

2

2 kmps

,12kmz

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Dispersion compensation fiber or dispersion shifted fiber

Why dispersion compensation fiber:

02211 LDLD

for long haul fiber optic communication.

Alloptical solution

Approaches

),(2

2

d

nd

cDm

longer wavelength has

a larger index.

make the waveguide

weakly guided so that

longer wavelength has a

lower index.

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The Graded index fibers

02211 LDLD

Approaches

,;)1(1

,];)/(1[)(

2

1

ann

aann

General case Intermode dispersion

,1

2

2

d

dn

ndz

d

),sin(')cos( 00 pzpz

,)/2(2/12

ap ,/2 pz

,32021

c

nL

Only valid for paraxial approximation

Calculate the BL product of a grade index filber of 50m core with refractive index of n1 =

1.480 and n2 = 1.460. At 1.3 m.

,6.925.0 1kmGbsLBL

Solution:

,026.032021 ns

cnL

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