The statistics of Intrachannel Four Wave Mixing IFWM
- Slides: 14
The statistics of Intra-channel Four Wave Mixing (IFWM) in Coherent Communication Systems Alan Pak Tao Lau Department of Electrical Engineering, Stanford University June 6, 2007
Outline Kerr nonlinearity induced nonlinear phase noise in coherent communication systems l Statistics of IFWM phase noise l Phase noise reduction through exploiting correlation of IFWM l Ongoing/Future work l
Phase noise in coherent communication systems l Laser phase noise • Laser linewidth • Carrier recovery mechanisms l Linear phase noise • ASE noise from inline amplifiers l Nonlinear phase noise • Phase fluctuations from randomness of data • Interaction of ASE noise and signal with Kerr nonlinearity l Shot noise / Thermal noise
Kerr Nonlinearity l induced intensity dependent refractive index l Self phase modulation induced Nonlinear Phase Shift
Signal propagation in optical fibers Pulse trains l Nonlinear Schordinger Equation (NLSE) l l Pertubation l l l SPM on IXPM on IFWM on Linear solution to NLSE : : :
What we know about IFWM l l IFWM technically information, but hard to fully exploit (requires complexity exp(K) for optimal detection) IFWM phase noise are correlated Wei and Liu, Optics Lett. , Vol. 28, Issue 23, pp. 2300 -2302 Ho, PTL vol. 17, no. 4, Apr. 2005, pp. 789 -791 l Basically, know nothing about IFWM
Real part negatively correlated Empirical distribution 1 pic of Liu corr… 1 pic of Ho empirical pdf
Correlation of IFWM induced phase noise for QPSK systems
Variance goes with N^2 Fiber overall length L with N spans Opt. Amp.
Pairwise independent
Typical fiber types and dispersion maps (db/km) D(ps/nm-km) S(ps/nm^2 -km) SMF 0. 25 DCF 0. 6 ~17 0. 25 Typical dispersion maps: l SMF/DCF l NZDSF-/SMF l SMF/IDF 1. 3 ~-0. 43 NZDSF 0. 25 IDF ~0. 06 (/W-km) ~-40 ~0. 05 ~2 ~-0. 13 ~3
Multiplicative perturbation to NLSE l NRZ pulse with power 0 d. Bm, 45 km of NZDSF D=-2 ps/nm-km,
Conclusions/Future Work l l Verify analytical predictions through simulation results Quantify the benefits of sequential detection and pulse shape design Acknowledgements l Sahand Rabbani
- Jablonského diagram
- Introduction to statistics what is statistics
- Longitudinal vs transverse wave
- Short wave vs long wave radiation
- Difference between full wave and half wave rectifier
- Transverse and longitudnal waves
- Half wave rectifier definition
- Piv of full wave bridge rectifier
- P and s wave arrival time chart
- Rectified sine wave fourier series
- Wave wave repeating
- The wave chapter 10
- Half wave symmetry examples
- Electromagnetic and mechanical waves
- Mechanical and electromagnetic waves similarities