Effect of the phase of the coupling constant on the self-organization of light in potassium niobate

We investigate self-organization of a laser beam into a scattering ring in photorefractive potassium niobate when the phase of the coupling constant is arbitrary. We find that for a range of values of the phase and amplitude of the coupling gain, the calculated forward and backward scattered ratios are in reasonable agreement with experimental observations. The phase of the coupling constant is determined by an interplay of both diffusive and photovoltaic nonlinearities, as well as phase shifts in the induced grating profile with only photovoltaic nonlinearities but for strong modulation depths of the intensity grating.