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Light Beam Propagation in a Photorefractive Environment: Beam-Fanning Effect and Amplification of Weak Beams

Arturo Zúñiga-Segundo, M. A. Arvizu-Coyotzi, José Luis López-Bonilla, Blanca E. Carvajal-Gámez

Published Jul 1, 2006• 0 citations
OpenAlex

Abstract

We investigate the propagation of light in photorefractive media by direct numerical simulation. The two dimensional model is based on solution of nonlinear material equations in steady-state and the equations governing propagation of the optical fields. We present results on fanning effect of a single beam and two-wave amplification in an applied alternating field.

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We investigate the propagation of light in photorefractive media by direct numerical simulation. The two dimensional model is based on solution of nonlinear material equations in steady-state and the equations governing propagation of the optical fields. We present results on fanning effect of a single beam and two-wave amplification in an applied alternating field.
We investigate asymmetric stimulated photorefractive scattering (fanning) in the framework of a two-dimensional model, based on the solution of nonlinear material equations and parabolic equations for electromagnetic radiation. We focus on the spatial distribution of electromagnetic fields and the nonlinear refractive index generated by fanning. In the region of developed fanning the structure of the refractive index corresponds to regions of relatively smooth index with abrupt transitions between them. These transitions trace lines of zero field.
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.
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.
A recent theory of polarization switching and beam amplification effect in Kerr-like media is extended to birefringent photorefractive crystals. In this class of material, the birefringence allows a new mechanism for coherent nonlinear mixing effects among the extraordinary and ordinary waves, leading to amplification and polarization switching effects. Analytic solutions of the parametric equations governing these interacting waves are solved for both the phase-matched and phase-mismatched geometries. The authors also present an experimental confirmation of the predicted polarization switching effect.>
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.