Optical bistability and multistability in a photorefractive bidirectional ring oscillator

We consider optical bistability and multistability based on the theory of bidirectional oscillations induced by four-wave mixing (FWM) in a photorefractive (PR) phaseconjugate ring resonator model. Bistable and multistable effects of the intensity of oscillation have been established numerically using a successive bisection method that can predict repeated roots as well as discontinuities.Oscillation intensities are studied as a function of parameters such as the nonlinear coupling strength (gL), the ratio of pump beam intensities (R) and the product of reflection coefficients of three cavity mirrors (|r|). It is shown that for certain combinations of these parameters and assuming that gL exceeds its threshold value, the oscillation intensity becomes double-valued or multivalued corresponding to the number of oscillating modes in the cavity. The multiplicity of solutions as well as the possible regions of bistable/multistable branches are greatly affected by the sign of gL and also depend on whether R and |r| are greater than or less than unity.