Stability analysis of steady state solutions of anisotropic four-wave mixing in cubic photorefractive crystals
Four-wave mixing (FWM) in cubic photorefractive crystals is considered in a geometry in which two counterpropagating pump beams have orthogonal polarizations, and the grating constrast has a different sign for each of them. For purely diffusive photorefractive nonlinearities the shape of the graphs of phase conjugate intensity versus signal intensity suggests the possibility of bistable operation for a positive and self-oscillations for a negative coupling constant. To confirm these predictions, the full time-dependent equations governing the dynamics of FWM in photorefractive crystals have been solved. It was found that for the negative coupling constant and coupling strength satisfying the threshold condition, a phase conjugate wave is generated without a probe beam (self-oscillation). The time needed to build up this oscillation depends on the value of the initial noise. From three branches given by the steady-state solution for this case the upper two are stable. Studies of the case with a positive coupling constant in the region of parameters giving multiple solutions for the conjugate wave have shown that the middle branch is always unstable, suggesting the possibility of bistable behavior. However, part of the lower branch is unstable too. Moreover, there is a region where the intensity of the conjugate wave exhibits self-pulsations in time.