Theory of nonlinear loop mirrors with twisted low-birefringence fiber

Abstract

We analyze propagation in a nonlinear, birefringent optical fiber with twist. The results show that the polarization evolution is periodic, and they are applied to the analysis of a Sagnac interferometer. The period is calculated by using perturbation theory, and we find a condition for it to be independent of the initial polarization state. We derive a simplified set of equations to describe the nonlinear evolution of the phase. We give a useful way to visualize the behavior of the nonlinear optical loop mirror (as a function of birefringence, twist, length, and input polarization) in terms of the Poincaré sphere.