Nonlinear degenerate four-wave mixing in birefringent optical fibers: phase conjugation and spatial instabilities

We investigate the phase-conjugated signal reflectivity and conjugation fidelity in the degenerate four-wave mixing process in a monomode birefringent optical fiber, in the nonlinear (depleted pumps) regime. Exact solutions are displayed for linearly polarized beams in a high-birefringence fiber, whereas for a low-birefringence fiber similar results hold for a scheme employing circular polarizations. The reflectivity is found to exhibit multistable isolated branches of solutions, and the deterioration of ideal phase conjugation condition are discussed. Whenever the birefringence gives phase shifts comparable to the nonlinear ones, spatial instabilities may originate chaotic power exchange between the waves. The scale of length and the powers required for the observation of the instability are estimated.