Nonlinear polarization-mode dispersion in optical fibers with randomly varying birefringence

Randomly varying birefringence leads to nonlinear polarization-mode dispersion (PMD) in addition to the well-known linear PMD. Here we calculate the variance of the field fluctuations produced by this nonlinear PMD. Knowing the size of these fluctuations is useful for assessing when nonlinear PMD is important and for its proper incorporation in fast numerical algorithms. We also derive the equilibrium probability distributions for the PMD coefficients, and we track the evolution of the polarization state's probability distribution from its initial delta-function distribution to its steady-state uniform distribution on the Poincaré sphere.