18
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

16.711 Lecture 3 Optical fibers

  • Upload
    oro

  • View
    91

  • Download
    2

Embed Size (px)

DESCRIPTION

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. 16.711 Lecture 3 Optical fibers. Today. - PowerPoint PPT Presentation

Citation preview

Page 1: 16.711 Lecture 3 Optical fibers

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

Page 2: 16.711 Lecture 3 Optical fibers

16.711 Lecture 3 Optical fibers

Today

• Fiber modes• Fiber Losses• Dispersion in single-mode fibers• Dispersion induced limitations• Dispersion management• The Graded index fibers

Page 3: 16.711 Lecture 3 Optical fibers

16.711 Lecture 3 Optical fibers

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

V-number

,22

21

22

2

nn

nnb eff

,)/996.01428.1( 2Vb

,)(2 2/12

221 nn

aV

,41.2)(2 2/12

221 nn

aV

ccutoff

Number of modes when V>>2.41

,2

2VM

Normalized propagation constant

for V between 1.5 – 2.5.

Mode field diameter (MFD)

),1

1(22V

aw

Page 4: 16.711 Lecture 3 Optical fibers

16.711 Lecture 3 Optical fibers

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

221 nn

aV

,41812

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

221 nn

aV

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:

Page 5: 16.711 Lecture 3 Optical fibers

16.711 Lecture 3 Optical fibers

Fiber loss• Material absorption

silica electron resonance <0.4mOH vibrational resonance ~ 2.73 mHarmonic and combination tones ~1.39 m1.24 m, 0.95 m

• Rayleigh scattering

Local microscopic fluctuations in density

,4

C C~ 0.8dB/km m4

0.14dB loss @ 1.55m

• Bending loss and Bending radius

),/exp( cRR ,32

21 nn

aRc

Page 6: 16.711 Lecture 3 Optical fibers

16.711 Lecture 3 Optical fibers

Dispersions in single mode fiber

• Material dispersion

,|0

d

dvg ,

gg v

L ,)()(

2

2

d

nd

cd

d

Lg

),(2

2

d

nd

cDm , LDmg

Example --- material dispersion

Calculate the material dispersion effect for LED with line width of 100nm and a laser with a line width of 2nm for a fiber with dispersion coefficient of Dm = 22pskm-1nm-1 at 1310nm.

,2.2 nsLDm

Solution:

,44psLDm

for the LED

for the Laser

Page 7: 16.711 Lecture 3 Optical fibers

16.711 Lecture 3 Optical fibers

Dispersions in single mode fiber

• Waveguide dispersion

,|0

d

dvg ,

gg v

L

,2)2(

984.1)(

22

2

2

cna

N

d

d

Lgg

, LDmg

Example --- waveguide dispersionn2 = 1.48, and delta n = 0.2 percent. Calculate Dw at 1310nm.

Solution:

,)()(

)(2

2212

dV

VbdV

c

nnn

d

d

Lg

,)()(

2

2212

dV

VbdV

c

nnnDw

,)/996.01428.1( 2Vb for V between 1.5 – 2.5.

,26.0)(

2

2

dV

VbdV

),/(9.1)()(

2

2212 kmnmps

dV

VbdV

c

nnnDw

Page 8: 16.711 Lecture 3 Optical fibers

16.711 Lecture 3 Optical fibers

• chromatic dispersion (material plus waveduide dispersion)

,)(

wmg DDL

• material dispersion is determined by the material composition of a fiber.

• waveguide dispersion is determined by the waveguide index profile of a fiber

Page 9: 16.711 Lecture 3 Optical fibers

16.711 Lecture 3 Optical fibers

• Polarization mode dispersion

,

pg DL

• 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

Page 10: 16.711 Lecture 3 Optical fibers

16.711 Lecture 3 Optical fibers

• Dispersion induced limitations

,2

1

2/1B

• For RZ bit With no intersymbol interference

,1

2/1B

• For NRZ bit With no intersymbol interference

Page 11: 16.711 Lecture 3 Optical fibers

16.711 Lecture 3 Optical fibers

Dispersion induced limitations

,2

1

2/1B

• Optical and Electrical Bandwidth

,7.03 Bf dB

• Bandwidth length product

,25.0

D

BL

Page 12: 16.711 Lecture 3 Optical fibers

16.711 Lecture 3 Optical fibers

Dispersion induced limitations

,16/ 12/1

pskmDL

,8.27.03 GHzBf dB

,9.3625.0 1kmGbs

DBL

Example --- bit rate and bandwidth

Calculate 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

Page 13: 16.711 Lecture 3 Optical fibers

16.711 Lecture 3 Optical fibers

Dispersion Management

],)(2

1exp[),0( 2

00 T

tAtA ),

2exp()2(),0(

~ 20

22/12

00

TTAA

,1

00 T

• Pre compensation schemes

1. Prechirp

Gaussian Pulse:

...,|2

1)(|)(

000 2

2

0

d

kd

d

dkkk

...,)(2

1...|)(|

)()( 2

2102

2

00 00

d

d

d

d

c

k

),2

exp(),0(~

),(~

2 zi

AzA

],)(2

1exp[

)()

2exp(),0(

~

2

1),(

20

020 zQTzQ

Adz

iAtzA

,1)(2

0

2

T

zizQ

,])(1[)( 0

2/122

0

2 TT

zzT

Page 14: 16.711 Lecture 3 Optical fibers

16.711 Lecture 3 Optical fibers

Dispersion Management

],)(2

)1(exp[),0( 2

00 T

tiCAtA

),

)1(2exp()

1

2(),0(

~ 20

22/1

20

0 iC

T

iC

TAA

• Pre compensation schemes

1. Prechirp

Prechirped Gaussian Pulse:

],)1()1(2

exp[)1

2()

2exp(),0(

~),(

~2

22

022

20

22/1

20

02

2 C

iCT

C

T

iC

TAz

iAzA

],)(2

1exp[

)()

2exp(),0(

~

2

1),(

20

020 zQTzQ

Adz

iAtzA

,)(

1)(2

0

2

T

ziCzQ

,])()1[()( 0

2/122

0

222

0

2 TT

z

T

zCzT

,1

)1(0

2/120 T

C

Page 15: 16.711 Lecture 3 Optical fibers

16.711 Lecture 3 Optical fibers

Dispersion Management

1. Prechirp

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

,1

212

2

DLC

CCL

,/ 22

0 TLD

Page 16: 16.711 Lecture 3 Optical fibers

16.711 Lecture 3 Optical fibers

Dispersion Management

Examples:

),(1052

1 11 sB

TFWHM

1. What’s 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/ 110 sTT FWHM

,1

)1(0

2/120 T

C ,9.5C

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

20

222

0

2 TTT

z

T

zCzT

,2

22

c

D ,/24 22 kmps

,12kmz

Page 17: 16.711 Lecture 3 Optical fibers

16.711 Lecture 3 Optical fibers

Dispersion compensation fiber or dispersion shifted fiber

• Why dispersion compensation fiber:

02211 LDLD

• for long haul fiber optic communication. • All–optical 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.

Page 18: 16.711 Lecture 3 Optical fibers

16.711 Lecture 3 Optical fibers

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( 2/12ap ,/2 pz

,320

21 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 1kmGbsL

BL

Solution:

,026.0320

21 nsc

nL