Soliton Propagation in Optical Fibers with Random Parameters
We study a system of nonlinear Schrödinger equations that models propagation of optical pulses in a monomode fiber. It includes linear terms (second and third order dispersions, and attenuation) as well as nonlinear terms (cross-phase modulation,and Raman scattering). The Whitham variational (averaging) method is used to reduce the nonlinear partial differential equations to an ordinary differential system for a finite number of soliton parameters: distance between pulses, phase frequency, width and amplitude. When the random medium coefficients are turned on the reduced ODE’s becomes a stochastic system. We derive the corresponding Fokker-Planck equation and discuss its solutions in special cases. The stationary Fokker-Planck solution (equilibrium ensemble) gives the expected mean values and correlations of soliton parameters over large spatial scales and allows us to analyze the long-term effects of the random fiber on the 2-pulse system.
KeywordsManifold Attenuation Soliton Librium Vicin
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