Solitons in birefringent optical fibers and polarization mode dispersion

The early work on solitons in optical fibers was all done using single-mode fibers, and these fibers remain important for many applications. The modes in single-mode fibers are for all practical purposes weakly confined plane waves and have two polarizations. The basic equation that describes light evolution in these fibers is the coupled nonlinear Schro center dot dinger equation. The soliton robustness hypothesis and its origins, which were the original motivation for studying these equations, is first described. Limits on robustness due to birefringent walkoff and the impact of random birefringence variations in stabilizing solitons is then described. Questions and controversies that arose shortly after the publication of these equations are addressed. These include their relationship to the Maker and Terhune coefficients, the requirements for the validity of the nonlinear Schro center dot dinger equation and the impact of polarization mode dispersion, and the conditions under which the birefringence can be considered linear. It is a consequence of the fluctuation-dissipation theorem that the birefringence must be linear in any homogeneous, low-loss optical medium with a local dielectric response. Any ellipticity is associated with non-locality, as would occur for example in a twisted optical fiber. This important result, which is not well-known in the optics community, is reviewed.