Theory of nonlinear loop mirrors with twisted low-birefringence fiber

We analyze propagation in a nonlinear, birefringent optical fiber with twis t. The results show that the polarization evolution is periodic, and they a re applied to the analysis of a Sagnac interferometer. The period is calcul ated by using perturbation theory, and we find a condition for it to be ind ependent of the initial polarization state. We derive a simplified set of e quations 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 f unction of birefringence, twist, length, and input polarization) in terms o f the Poincare sphere. (C) 2001 Optical Society of America.