1. Power Considerations in Optical Transmission Systems in Presence of Nonlinear Phase Noise Alan Pak Tao Lau Department of Electrical Engineering, Stanford University May 26, 2006

2. Outline Kerr nonlinearity induced nonlinear phase noise in coherent communication systems Kerr nonlinearity induced nonlinear phase noise in coherent communication systems Optimal and practical power profile design for variance minimization Optimal and practical power profile design for variance minimization Power profile design in WDM systems Power profile design in WDM systems

3. Kerr Nonlinearity Centro-symmetric materials Centro-symmetric materials induced intensity dependent refractive index induced intensity dependent refractive index

4. Nonlinear effects in coherent communications systems Kerr induced nonlinear phase shift Kerr induced nonlinear phase shift where where Self Phase Modulation (SPM) Self Phase Modulation (SPM) Cross Phase Modulation (XPM) Cross Phase Modulation (XPM) Typical ranges of : 1~5 /(W km) Typical ranges of : 1~5 /(W km)

5. Nonlinear phase noise ASE from inline amplifiers generate Gaussian noise ASE from inline amplifiers generate Gaussian noise Random power of signal plus noise produce random nonlinear phase shift -- Gordon- Mollenauer effect Random power of signal plus noise produce random nonlinear phase shift -- Gordon- Mollenauer effect overall length L with N spans Opt. Amp. Fiber L=3000 km, N=30, = 0dBm

6. Phase Noise for coherent systems Linear Phase Noise Linear Phase Noise Optical Amp. Fiber Optical Amp. Fiber Optical Amp. Fiber Nonlinear Phase Noise Nonlinear Phase Noise

7. System design for variance minimization Total variance of phase noise Total variance of phase noise Last time, looked at how we can design the gain and spacings of inline amplifiers to minimize variance of phase noise Last time, looked at how we can design the gain and spacings of inline amplifiers to minimize variance of phase noise We’ll look at how signal power at different points in the system affects We’ll look at how signal power at different points in the system affects

8. Factors affecting Power Levels Design High power – Nonlinear phase noise, amplifier gain saturation High power – Nonlinear phase noise, amplifier gain saturation Low power – Linear phase noise, input coupling loss, shot noise and thermal noise, quantum effects Low power – Linear phase noise, input coupling loss, shot noise and thermal noise, quantum effects Allowable Range of Power levels Allowable Range of Power levels

9. Optimal Operating Power Transmitted Power = Received Power = P

10. Optimal Operating Power Mean nonlinear phase shift Mean nonlinear phase shift Corresponds with literature findings Corresponds with literature findings

11. Unequal Input and Received Power Amplifiers over or under compensate the signal loss along the link Amplifiers over or under compensate the signal loss along the link Study a linearly increasing/decreasing power profile along the link. Study a linearly increasing/decreasing power profile along the link.

12. Unequal Input and Received Power

13. Linear Power Profile Good to have a drop in received power Good to have a drop in received power

14. Optimal Power Profile Power profile Power profile Let Let Phase noise variance Phase noise variance Euler Characteristic Equation Euler Characteristic Equation

15. Optimal Power Profile

16. Power profile design in WDM systems Cross-phase modulation (XPM) Cross-phase modulation (XPM) Difference in group velocity -- Walk Off Effect Difference in group velocity -- Walk Off Effect Pulse waveform distortion negligible compared to walk off in modeling Pulse waveform distortion negligible compared to walk off in modeling

17. XPM induced nonlinear phase noise Assumptions: Flat gain amplifiers and noise spectrum Assumptions: Flat gain amplifiers and noise spectrum Typical spacing: 10Gb/s, 50 GHz, D=4 ps/(km-nm) --> Lw=62.5 km Typical spacing: 10Gb/s, 50 GHz, D=4 ps/(km-nm) --> Lw=62.5 km

18. Power Profile Design in WDM systems

19. Objective Objective

20. Power drop profile requires less pump energy Power drop profile requires less pump energy Future Work Real systems aren’t point to point Real systems aren’t point to point Signal path routed by RODAM Signal path routed by RODAM Power drop profile should still provide benefits Power drop profile should still provide benefits Power Profile Design in WDM systems

21. Acknowledgements Prof. Kahn Prof. Kahn Dany, Ezra and Rahul =) Dany, Ezra and Rahul =) Thank you !