Stochastic simulation of pulses in nonlinear-optical fibers with random birefringence

Numerical simulations of nonlinear pulse propagation in optical fibers with randomly varying birefringence are presented. For short-length-scale randomness the dominant effect is due to phase-velocity birefringence and produces a probabilistic uncertainty that increases with propagation distance for the expected value of the pulse’s polarization state. An approximate evolution equation for the probability distribution of the polarization state was derived previously [ Physica D55, 166 ( 1992)]. Comparisons between this distribution and Monte Carlo simulations are presented that demonstrate the validity of the analytical results. The simulations also show that the polarization state of a pulse is completely randomized on the longer soliton-period length scale. This provides justification for the assumption of a uniformly distributed polarization state used in previous analyses of this problem [ Opt. Lett.16, 1231 ( 1991); J. Lightwave Technol.10, 28 ( 1992)]. Furthermore, the higher-order effects of group birefringence are assessed. In particular, the polarization-state fluctuations induced by the randomness are shown to reduce significantly the effects of pulse splitting and dispersive radiation loss caused by group-velocity birefringence.

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