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Intermode Dispersion (MMF)
Group Delay  = L / vg
 
L
v gmin

 n1  n2

L
c
L
vgmax
vgmin  c/n1. (Fundamental)
vgmax  c/n2. (Highest order mode)
/L  - 50 ns / km
Depends on length!
Intramode Dispersion (SMF)
Dispersion in the fundamental mode
Group Delay  = L / vg
Group velocity vg depends on
Refractive index = n(l)
V-number= n(l)
 = (n1  n2)/n1 = (l)
Material Dispersion
Waveguide Dispersion
Profile Dispersion
Material Dispersion
All excitation sources are inherently non-monochromatic and emit within a spectrum ∆l of
wavelengths. Waves in the guide with different free space wavelengths travel at different
group velocities due to the wavelength dependence of n1. The waves arrive at the end of
the fiber at different times and hence result in a broadened output pulse.

 Dm l
L
Dm = material dispersion coefficient, ps nm-1 km-1
Waveguide Dispersion
Waveguide dispersion: The group velocity vg(01) of the fundamental mode depends
on the V-number which itself depends on the source wavelength l even if n1 and n2
were constant. Even if n1 and n2 were wavelength independent (no material dispersion),
we will still have waveguide dispersion by virtue of vg(01) depending on V and V
depending inversely on l. Waveguide dispersion arises as a result of the guiding
properties of the waveguide which imposes a nonlinear -lm relationship.

 Dw l
L
Dw = waveguide dispersion coefficient
Dw depends on the waveguide structure, ps nm-1 km-1
Chromatic Dispersion
Material dispersion coefficient
(Dm) for the core material
(taken as SiO2), waveguide
dispersion coefficient (Dw) (a =
4.2 mm) and the total or
chromatic dispersion coefficient
Dch (= Dm + Dw) as a function
of free space wavelength, l
Chromatic = Material + Waveguide

 (Dm  Dw )l
L
Dispersion coefficient (ps km-1 nm-1)
20
Dm
10
SiO2-13.5%GeO2
0
a (mm)
Dw
4.0
3.5
3.0
–10
2.5
–20
1.2
1.3
1.4
1.5
1.6
l (mm)
Material and waveguide dispersion coefficients in an
optical fiber with a core SiO 2-13.5%GeO 2 for a = 2.5
to 4 mm.
© 1999 S.O. Kasap,Optoelectronics(P rentice Hall)
Polarization Dispersion
n different in different directions due to
induced strains in fiber in manufacturing,
handling and cabling. n/n < 10-6
  Dpol L
Dpol = polarization dispersion coefficient
Typically Dpol = 0.1 - 0.5 ps nm-1 km-1/2
Self-Phase Modulation Dispersion : Nonlinear Effect
At sufficiently high light intensities, the refractive index of glass n is
n = n + CI
where C is a constant and I is the light intensity. The intensity of light
modulates its own phase.
For   1 ps km-1
Imax  3 W cm-2.
n is 310-7.
2a  10 mm,
A  7.8510-7 cm2.
Optical power  23.5 W in
the core
Zero Dispersion Shifted Fiber
Dispersion
Material
Dispersion
Zero at 1.55mm
0
1.2 mm
Total Dispersion
1.4 mm
1.6 mm
l
Total dispersion is zero in the
Er-optical amplifier band
around 1.55 mm
Waveguide Dispersion
Zero-dispersion
shifted fiber
Disadvantage: Cross
talk (4 wave mixing)
Nonzero Dispersion Shifted Fiber
For Wavelength Division Multiplexing (WDM) avoid 4 wave mixing: cross talk.
We need dispersion not zero but very small in Er-amplifer band (1525-1620 nm)
Dch = 0.1 - 6 ps nm-1 km-1.
Nonzero dispersion shifted fibers
Nonzero Dispersion Shifted Fiber
Nonzero dispersion shifted fiber (Corning)
Fiber with flattened
dispersion slope
Dispersion Flattened Fiber
Dispersion flattened fiber example. The material dispersion
coefficient (Dm) for the core material and waveguide dispersion
coefficient (Dw) for the doubly clad fiber result in a flattened
small chromatic dispersion between l1 and l2.
Dispersion and Maximum Bit Rate
0.5
B
 1/ 2
Return-to-zero (RTZ) bit rate or data rate.
Nonreturn to zero (NRZ) bit rate = 2 RTZ bitrate
Output optical power
T = 4
1
0.61
0.5


t
A Gaussian output light pulse and some tolerable intersymbol
interference between two consecutive output light pulses ( y-axis in
relative units). At time t =  from the pulse center, the relative
magnitude is e -1/2 = 0.607 and full width root mean square (rms)
spread isrms = 2.
© 1999 S.O. Kasap,Optoelectronics(Prentice Hall)
Dispersion and Maximum Bit Rate
Maximum Bit Rate
0.25
0.59
B


1/2
BL 
0.25L

Dispersion
1/2
 Dch l1/2
L
0.25
0.59


Dch  l Dch l1/2
Bit Rate = constant
inversely proportional to dispersion
inversely proportional to line width of laser
(single frequency lasers!)
Electrical signal (photocurrent)
1
0.707
Fiber
Sinuso idal signal
Emitt er
t
Optical
Input
f = Modulation frequency
Pi = Input light power
0
Ph oto detect or
Optical
Output
Po = Output light power
t
0
1 kHz
1 MHz
1 GHz
1 MHz
1 GHz
f
f el
Sinuso idal elect rical sign al
Po / Pi
0.1
0.05
t
1 kHz
fop
f
An optical fiber link for transmitting analog signals and the effect of disp ersion in the
fiber on the bandwidth, fop.
© 1999 S.O. Kasap,Optoelectronics (Prentice Hall)
Relationships between dispersion parameters, maximum bit rates and bandwidths. RZ = Return
to zero pulses. NRZ = Nonreturn to zero pulses. B is the maximum bit rate for NRZ pulses.
Dispersed pulse shape
Gaussian with rms
deviation 
Rectangular with fu ll
width T
1/2 =
FWHM width
 = 0.4251/2
B
(RZ)
0.25/
B
(NRZ)
0.5/
fop
fel
0.75B = 0.19/
0.71fop = 0.13/
 = 0.29T =
0.291/2
0.25/
0.5/
0.69B = 0.17/
0.73fop = 0.13/
Example: Bit rate and dispersion
Consider an optical fiber with a chromatic dispersion coefficient 8 ps km-1 nm-1 at an operating
wavelength of 1.5 mm. Calculate the bit rate distance product (BL), and the optical and electrical
bandwidths for a10 km fiber if a laser diode source with a FWHP linewidth l1/2 of 2 nm is used.
Solution
For FWHP dispersion,
1/2/L = |Dch|l1/2 = (8 ps km-1 nm-1)(2 nm) = 16 ps km-1
Assuming a Gaussian light pulse shape, the RTZ bit rate  distance product (BL) is
BL = 0.59L/t1/2 = 0.59/(16 ps km-1) = 36.9 Gb s-1 km.
The optical and electrical bandwidths for a 10 km distance is
fop = 0.75B = 0.75(36.9 Gb s-1 km) / (10 km) = 2.8 GHz.
fel = 0.70fop = 1.9 GHz.
Combining intermodal and intramodal dispersions
Consider a graded index fiber with a core diameter of 30 mm and a refractive index of 1.474 at the
center of the core and a cladding refractive index of 1.453. Suppose that we use a laser diode emitter
with a spectral linewidth of 3 nm to transmit along this fiber at a wavelength of 1300 nm. Calculate,
the total dispersion and estimate the bit-rate  distance product of the fiber. The material dispersion
coefficient Dm at 1300 nm is 7.5 ps nm-1 km-1. How does this compare with the performance of a
multimode fiber with the same core radius, and n1 and n2?
Solution
The normalized refractive index difference  = (n1n2)/n1 = (1.4741.453)/1.474 =
0.01425. Modal dispersion for 1 km is
intermode = Ln12/[(20)(31/2)c] = 2.910-11 s 1 or 0.029 ns.
The material dispersion is
1/2 = LDm l1/2 = (1 km)(7.5 ps nm-1 km-1)(3 nm) = 0.0225 ns
Assuming a Gaussian output light pulse shaper,
intramode = 0.4251/2 = (0.425)(0.0225 ns) = 0.0096 ns
Total dispersion is
2
2
 rms   intermode
  intramode
 0.0292  0.00962  0.030 ns
B = 0.25/rms = 8.2 Gb
Comparison of typical characteristics of multimode step-index, single-mode step-index, and
graded-index fibers. (Typical values combined from various sources; 1997
Property
 = (n1n2)/n1
Core diameter (mm)
Cladding diameter (mm)
NA
Bandwidth  distance or
Dispersion
Multimode step-index
fiber
0.02
100
140
0.3
20 - 100 MHzkm.
Attenuation of l ight
4 - 6 dB km-1 at 850 nm
0.7 - 1 dB km-1 at 1.3 mm
Typical light source
Light emi tting diode
(LED)
Short haul or subscriber
local network
communications
Typical applications
Single-mode step-index
Graded Index
0.003
8.3 (MFD = 9.3 mm)
125
0.1
< 3.5 ps km-1 nm-1 at 1.3 mm
> 100 Gb s-1 km in common
use
1.8 dB km-1 at 850 nm
0.34 dB km-1 at 1.3 mm
0.2 dB km-1 at 1.55 mm
Lasers, single mode
injection lasers
Long haul commu nications
0.015
62.5
125
0.26
300 MHz km - 3 GHz km
at 1.3 mm
3 dB km-1 at 850 nm
0.6 - 1 dB km-1 at 1.3 mm
0.3 dB km-1 at 1.55 mm
LED, lasers
Local and wide-area
networks. Medium haul
communications
Dispersion Compensation
Total dispersion = DtLt + DcLc = (10 ps nm-1 km-1)(1000 km) +
(100 ps nm-1 km-1)(80 km)
= 2000 ps/nm for 1080 km or 1.9 ps nm-1 km-1
Dispersion Compensation and Management
 Compensating fiber has higher attenuation.
Doped core. Need shorter length
 More susceptible to nonlinear effects.
Use at the receiver end.
 Different cross sections. Splicing/coupling losses.
 Compensation depends on the temperature.
 Manufacturers provide transmission fiber spliced to
inverse dispersion fiber for a well defined D vs. l
Dispersion Managed Fiber
The inverse dispersion slope of dispersion managed fiber cancels the detrimental
effect of dispersion across the a wide spectrum of wavelength. More DWDM
channels expected in ultralong haul transmission. (Courtesy of OFS Division of
Furukawa.)
Attenuation
Attenuation = Absorption + Scattering
Attenuation coefficient  is defined as the fractional decrease in
the optical power per unit distance.  is in m-1.
Pout = Pinexp(L)
 dB
 Pin 
1
 10log 
L
Pout 
dB 
10
  4.34
ln(10)
Lattice Absorption (Reststrahlen Absorption)
A solid with ions
Ex
Light direction
k
z
Lattice absorption through a crystal. The field in the wave
oscillates the ions which consequently generate "mechanical"
waves in the crystal; energy is thereby transferred from the wave
to lattice vibrations.
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
Rayleigh Scattering
Rayleigh scattering involves the polarization of a small dielectric particle or a region
that is much smaller than the light wavelength. The field forces dipole oscillations in
the particle (by polarizing it) which leads to the emission of EM waves in "many"
directions so that a portion of the light energy is directed away from the incident beam.
2
8 3 2
R  4 n 1 T kBTf
3l
 = isothermal compressibility (at Tf)
Tf = fictive temperature (roughly the
softening temperature of glass) where
the liquid structure during the cooling
of the fiber is frozen to become the
glass structure
Example: Rayleigh scattering limit
What is the attenuation due to Rayleigh scattering at around thel = 1.55 mm window
given that pure silica (SiO2) has the following properties: Tf = 1730°C (softening
temperature); T = 710-11 m2 N-1 (at high temperatures); n = 1.4446 at 1.5 mm.
Solution
We simply calculate the Rayleigh scattering attenuation using
8 3 2
R  4 (n 1) 2 T kBTf
3l
8 3
2
2
11
23
R 
(1.4446
1)
(7
10
)(1.38
10
)(1730  273)
6 4
3(1.55 10 )
R = 3.27610-5 m-1 or 3.27610-2 km-1
Attenuation in dB per km is
dB = 4.34R = (4.34)(3.73510-2 km-1) = 0.142 dB km-1
This represents the lowest possible attenuation for a silica glass core fiber at
1.55 mm.
Corning low-water-peak fiber has no OH- peak
E-band is available for communications with this fiber
[Photonics Spectra, April 2002 p.69]
Bending Loss
Field dist ribution
Microbending
Escaping wave
Cladding
<
Core
 

c

R
Sharp bends change the local waveguide geometry that can lead to waves
escaping. The zigzagging ray suddenly finds itself with an incidence
angle  that gives rise to either a transmitted wave, or to a greater
cladding penetration; the field reaches the outside medium and some light
energy is lost.
© 1999 S.O. Kasap,Optoelectronics(Prent ice Hall)
Microbending Loss
 R 
 R 
  exp  exp 3/ 2 
  
 Rc 
Bending loss for three different fibers. The cut-off wavelength is 1.2 mm. All three
are operating at l = 1.5 mm.
Example: Microbending loss It is found that for a single mode fiber with a cut-off
wavelength lc = 1180 nm, operating at 1300 nm, the microbending loss reaches 1 dB m-1
when the radius of curvature of the bend is roughly 6 mm for  = 0.00825, 12 mm for  =
0.00550 and 35 mm for  = 0.00275. Explain these findings?
Solution: Maybe later?
WDM Illustration