Evolution of phase-conjugate waves in stimulated photorefractive backscattering

Stimulated photorefractive backscattering produces a phase-conjugate wave under some conditions. Numerical solutions to the time-dependent wave equation for the backscattered field are obtained that indicate what conditions are required. The key parameters that control conjugation fidelity are the product of the photorefractive coupling coefficient and the length of the crystal; the ratio of the absorption coefficient to the coupling coefficient; the ratio of pump irradiance to dark irradiance; and the Fresnel number, defined by the angular extent of the pump beam and the inverse of the coupling coefficient. Backseeding with randomly phased plane waves whose amplitudes are proportional to the amplitudes of the pump plane-wave-expansion coefficients results in greatly improved conjugation fidelity if the backseeding intensity exceeds the intensity scattered from noise.