1. EE 230: Optical Fiber Communication Lecture 13
Dispersion Compensation
From the movie
Warriors of the Net

2. Pulse Dispersion

3. Definition of chirp
The chirp C is defined by the change in frequency d due to the rate of change of the phase:
 is the initial 1/e duration of the pulse

4. Spread of Gaussian Pulse

5. Dispersion Power Penalty at different Bit Rates

6. Degradation of a 40 Gb/s Signal

7. 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

8. Various Dispersion Compensation Techniques

9. Propagation of Gaussian Pulses
Input Pulse
Output Pulse
chirped and broadened
b2<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

10. Spectral Shaping at the Transmitter
Optical Fiber Telecommunications IIIA

11. 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

12. Dispersion Properties of Various Fibers

13. Chromatic Dispersion Properties of Various Fibers

14. Conventional Dispersion Compensating Fiber
Fiber Optic Communications Technology- Mynbaev & Scheiner

15. Dispersion Compensating Fiber

16. Use of Dispersion Compensating Fiber
Understanding Fiber Optics-Hecht

17. Problem with Conventional Dispersion Shifted Fiber

18. Importance of Slope Matching

19. Link Distance Dependence on Slope Matching

20. Higher order Mode DispersionProperties
LaserComm

21. High-Order-Mode Dispersion Compensation Device

22. Compensation with Optical Filters

23. Chirped fiber Bragg grating dispersion
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

24. Chirped Fiber Bragg Gratings
Optical Networks A Practical Perspective-Ramaswami & Sivarajan

25. Pulse Spreading due to Self Phase Modulation

26. Four-wave Mixing

27. Taylor Series expansion of β(ω)
Through the cubic term:
where

28. Importance of Taylor Series terms
Group velocity Vg, dispersion D, and dispersion slope S

29. Four-Wave Mixing Phase-Matching Requirement
Phase mismatch M needs to be small for FWM to occur significantly

30. 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

31. Mid-Span Spectral Inversion
Optical Fiber Telecommunications IIIA

32. Dispersion Managed Network

33. 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