EE 230: Optical Fiber Communication Lecture 13
Dispersion Compensation
From the movie
Warriors of the Net
Pulse Dispersion
Definition of chirp
The chirp C is defined by the change in
frequency d due to the rate of change of
the phase:
d Ct
d  
 2
dt 
 is the initial 1/e duration of the pulse
Spread of Gaussian Pulse
2
2
 3 L 
 C 2 L    2 L 

2 2









1



1

C
 4 3 2 
 02 
2 02   2 02 
 0

2
2
Dispersion Power Penalty at different
Bit Rates
Degradation of a 40 Gb/s Signal
Ideal Dispersion Compensation Device
•
•
•
•
•
•
•
•
Large negative dispersion coefficient
Low attenuation
Minimal nonlinear contributions
Wide bandwidth
Corrects dispersion slope as well
Minimal ripple
Polarization independent
Manufacturable
Various Dispersion Compensation
Techniques
Propagation of Gaussian Pulses
Input Pulse
Output Pulse
chirped and broadened
2<0 for standard single mode silica fiber
and Ld ~ 1800 km at 2.5 Gb/s and ~115 km at 10 Gb/s
Input Pulse
Already Positively
Chirped
After some distance
the chirp is removed
and the pulse assumes its
minimum possible width
Upon further propagation
the pulse will continue to broaden
and acquire chirp.
Optical Networks a Practical Perspective-Ramaswami and Sivarajan
Spectral Shaping at the Transmitter
Optical Fiber Telecommunications IIIA
Compensation at Receiver
• Adjust decision point on the fly based
on previous few bits
• Mathematically extrapolate signal back
to what it presumably was at origin
• These techniques can be used only if
calculations can be done much faster
than bit rate
Dispersion Properties of Various
Fibers
Chromatic Dispersion Properties of
Various Fibers
Conventional Dispersion
Compensating Fiber
Fiber Optic Communications Technology- Mynbaev & Scheiner
Dispersion Compensating Fiber
Use of Dispersion Compensating
Fiber
Understanding Fiber Optics-Hecht
Problem with Conventional
Dispersion Shifted Fiber
Importance of Slope Matching
Link Distance Dependence on Slope
Matching
Higher order Mode
DispersionProperties
LaserComm
High-Order-Mode Dispersion
Compensation Device
Compensation with Optical Filters
1
AL, t  
2

i

2
 A' 0,  H  exp  2  2 L  it d
Chirped fiber Bragg grating dispersion
2n
D
c 
where  is the difference between Bragg
wavelengths at ends of grating.
For n=1.45 and =0.2 nm, D=4.8x107
ps/(km-nm) as compared to 18 for fiber
Chirped Fiber Bragg Gratings
Optical Networks A Practical Perspective-Ramaswami & Sivarajan
Pulse Spreading due to Self Phase
Modulation
Four-wave Mixing
Taylor Series expansion of β(ω)
Through the cubic term:
   0  1   
where
2
d 
i 
i
d
i
2
 
2

3
6
 
3
 ...
Importance of Taylor Series terms
Group velocity Vg, dispersion D, and
dispersion slope S
Vg 
1
1
 2c
D
2
2

dD  2c 
 4c 
S
  2   3   3  2
d   
  
2
Four-Wave Mixing Phase-Matching
Requirement
Phase mismatch M needs to be small for
FWM to occur significantly
M   3     4    1     2 
Spectral Inversion
• Add pump signal whose wavelength is
ideally at zero-dispersion point
• Four-wave mixing generates phase
conjugate signal at 2p-s
• Phase conjugate undoes both GVD and
SPM over second half of link
• Filter out pump beam at end
Mid-Span Spectral Inversion
Optical Fiber Telecommunications IIIA
Dispersion Managed Network
Summary of Techniques
• At transmitter: prechirping, coding
• At receiver: signal analysis, decision
point adjustment
• Fiber: DCF, DSF, dual-mode fiber
• Filters: Bragg gratings, Mach-Zehnders
• Spectral inversion