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Journal of the Optical Society of America B

Dynamics of multiple two-wave mixing and fanning in photorefractive materials

Michael Snowbell, Moshe Horowitz, Baruch Fischer

Published Oct 1, 1994• 14 citations

Abstract

We investigate the dynamics of multiple two-wave mixing in photorefractive materials. This is the first time to our knowledge that a study of the dynamics of many pairs of two-wave mixing interactions has taken place. A basic case with three waves undergoing multiple two-wave mixing is studied numerically. A numerical study is also performed in which many waves are used to model the time development of the fanning effect. Comparison of this numerical model with a basic experiment involving fanning in the presence of a two-wave mixing interaction is given. A qualitative agreement is exhibited. In addition, it is found that effectively reducing the coupling constant of a two-wave mixing interaction by the addition of an incoherent background beam can, under certain circumstances, significantly reduce the fanning without lowering the signal level.

DOI: 10.1364/josab.11.001972

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We investigate the dynamics of multiple two-wave mixing in photorefractive materials. This is the first time to our knowledge that a study of the dynamics of many pairs of two-wave mixing interactions has taken place. A basic case with three waves undergoing multiple two-wave mixing is studied numerically. A numerical study is also performed in which many waves are used to model the time development of the fanning effect. Comparison of this numerical model with a basic experiment involving fanning in the presence of a two-wave mixing interaction is given. A qualitative agreement is exhibited. In addition, it is found that effectively reducing the coupling constant of a two-wave mixing interaction by the addition of an incoherent background beam can, under certain circumstances, significantly reduce the fanning without lowering the signal level.

A theoretical analysis is presented of two-wave mixing in photorefractive materials in which the complex amplitude of a weak signal beam has slowly varying but otherwise arbitrary spatial dependence and arbitrary time variation. The set of coupled partial differential equations that couple the dynamics of the optical fields to the photorefractive medium is solved analytically to give the complex amplitude of the transmitted signal in the undepleted pump regime. The results are compared with known results for the transient two-wave mixing of plane waves.

In a biased photorefractive crystal, the process of two one-dimensional waves mixing, i.e., the dynamical evolution of both pump beam and signal beam, is traced by numerically solving the coupled-wave equation. Direct simulations show that the propagation and stability of the two beams are completely determined by the system parameters, such as the external bias field, the intensity and the beam waist of the pump beam. By adjusting these parameters, one can control the state of two Gaussian waves mixing. The numerical results are helpful for performing a two-wave mixing experiment.

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.