Multivalued phase conjugate reflectivity in the reflection-type photorefractive four-wave mixing; strong coupling regime

Optical multistability based on the theory of four-wave mixing (FWM) is considered for the case of reflection geometry in photorefractive crystals. The resultant nonlinear algebraic equation obtained from the initial nonlinear coupled differential equations, is solved numerically by using a successive bisection method which can predict repeated zeros (roots) as well as discontinuities (jumps). We show that apart from the effects of photorefractive phase shift, the strong nonlinear coupling itself is sufficient to bring about multivalued branching behaviour of the phase conjugate reflectivity (PCR). As the coupling strength increases, the solutions become richer and more complex. We find that for certain values of pump and probe ratios and owing to the nature of strong nonlinear coupling the appearance of multiple solutions has a close connection with the phenomenon of bistability and self-oscillation.