Photorefractive wave mixing with finite beams

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.