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.
KeywordsOptical Pulse Hamiltonian Structure Stationary Random Process Nonlinear Schrodinger Equation Order Dispersion
Unable to display preview. Download preview PDF.
- A.B. Aceves, Soliton Turbulence in Nonlinear Optical Phenomena, this volume, p. 199.Google Scholar
- M.J. Ablowitz, H. Segur, Solitons and the inverse scattering transform, SIAM, Philadelphia, 1985.Google Scholar
- H. Haken, Advanced Synergetics: Instability Hierarchies of Self-Organizing Systems and Devices, Springer-Verlag, New-York 1983.Google Scholar
- A.C. Newell, Solitons in Mathematics and Physics, Society for Industrial and Applied Mathematics,1985.Google Scholar
- G.B. Whitham, Linear and Nonlinear Waves, John Wiley and Sons, New York, 1974.Google Scholar
- V.E.Zakharov, A.B. Shabat, Zh. Eksp. Teor. Fiz. 61, 118 (1971) (Soviet Physics JETP 34, 62 (1972)).Google Scholar