Wave mixing in photorefractive crystals with stable solutions and instabilities

Two-wave and four-wave mixing in photorefractive media with saturable gain and saturable absorption is analyzed. Solutions to wave equations are found in terms of quadratures and implicitly given functions. Different models of saturation are compared. It is found that for weak couplings energy transfer between waves is less effective in the strong unsaturated regime as compared to the saturated, while for strong couplings both regimes are equally effective. The existence of multiple solutions in four-wave mixing is established. It is shown that the unsaturated system is more stable than the saturated.