Perturbative analysis of self-oscillation in degenerate four-wave mixing

Self-oscillation of two counterpropagating waves in four-wave mixing under orthogonal pump configuration is analyzed perturbatively, taking into account the pump depletion and the refractive-index variation. A number of threshold pump intensities corresponding to different oscillating field distributions are obtained. Certain values of pump intensity permit multiple solutions for the oscillating field distribution and the corresponding output power of the oscillating waves, indicating a possibility of multistability.