Stochastic polarization instability: limitation to optical switching using fibers with modulated birefringence

We show that the standard map governs near-separatrix evolution of the polarization state for an intense light wave traveling along a fiber whose linear birefringence has a periodic modulation. This allows us to estimate analytically, in good agreement with numerical experiments, the minimum angle to the unstable axis of a linearly polarized input beam in order to avoid chaotic power-dependent switching of the output polarization state.