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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
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
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
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:
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
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
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
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
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
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
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
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
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
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
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
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
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.
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