Threshold conditions for generation in a photorefractive crystal with counterpropagating mutually incoherent pump beams

The threshold conditions for generation are found for media with a nonlinear response of a mixed type. The possibility of cavity-free generation in a photorefractive crystal with a purely local initial response, by virtue of a shift of the generation frequency away from the pump frequency, is analyzed. The frequency shift and the wave-vector mismatch are derived as a function of the interaction constant.