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Annual Meeting Optical Society of America

Photorefractive wave mixing with finite beams

Wieslaw Z. Krolikowski, Mark Cronin‐Golomb

Published Jan 1, 1991• 1 citation

Abstract

While the interaction of optical beams in photorefractive crystals can often be accurately described in terms of 1-D plane-wave approximation, 2-D models are sometimes more suitable, as suggested by recent work.1 Here we discuss some aspects of photorefractive interaction of finite size optical beams. We have solved the system of partial differential equations governing two- and four-wave mixing numerically by using iterative procedures. Simulations of beam amplification in two-beam coupling show strong beam deformation even without any spatial information imposed on them. Spatially nonuniform energy transfer is responsible for this effect. The pump beam loses energy during propagation and at the end of its passage through the beam intersection region (which was completely inside the crystal) it is strongly depleted and cannot contribute significantly to beam amplification. As the pump beam crosses through the probe, it amplifies most strongly that side of the probe that it meets first. By the time the pump has reached the far side of the probe, it is strongly depleted and less effective at probe amplification. In the case of phase conjugation through four-wave mixing, we found that the conjugate beam is strongly deformed only when the coupling constant is negative (corresponding to deamplification of the probe input beam). For positive coupling constants the output conjugate beam is a good replica of the input probe beam.

DOI: 10.1364/oam.1991.mu1

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A slowing down of light pulses using backward-wave four-wave mixing is achieved in photorefractive crystals with different coupling strength. The delay and width of the output pulse are studied as a function of the input pulse width and pump intensity ratio for the amplified transmitted beam and for the phase-conjugated beam. The delay characteristics are compared with those of the two-beam coupling. It is demonstrated that the four-wave mixing process ensures a larger slowing down of short pulses (pulses with width shorter than the photorefractive response time) as compared to the photorefractive two-beam coupling scheme and guarantees the elimination of forerunners. The delay of long pulses in the four-wave mixing configuration is almost the same as the one that can be reached with two-beam coupling. The effect of absorption on the nonlinear shape transformation of the output pulses is discussed qualitatively.

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Effects of cross-polarization coupling have been investigated in the case of degenerate four-wave mixing (DFWM) in absorbing semi-insulating compound semiconductor photorefractive (PR) crystals in transmission geometry. Considering pump beam depletion, and the slowly varying approximation, nonlinear coupled wave equations are obtained and have been solved numerically by a shooting method. Numerical results obtained from computer calculation are presented in graphical form. It is seen that if all the input beams are of the same polarization, cross-polarization coupling generates a phase-conjugate beam which is polarized in a plane orthogonal to that of the input beam.