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Physical Review E

Counterpropagating beams in biased photorefractive crystals: Anisotropic theory

Kristian Motzek, Milivoj R. Belić, Thomas Richter, Cornelia Denz, Anton S. Desyatnikov, Ph. Jander, F. Kaiser

Published Jan 19, 2005• 9 citations
Publisher

Abstract

We formulate an anisotropic nonlocal theory of the space charge field induced by the coherent counterpropagating beams in biased photorefractive crystals. We establish that the competition between the drift and diffusion terms has to be taken into account when the crystal ĉ axis is tilted with respect to the propagation direction of the beams. We demonstrate that this configuration combines the features of both spatial soliton formation without energy exchange and two-wave mixing with energy exchange leading to pattern formation.

DOI
10.1103/physreve.71.016610

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We formulate an anisotropic nonlocal theory of the space charge field induced by the coherent counterpropagating beams in biased photorefractive crystals. We establish that the competition between the drift and diffusion terms has to be taken into account when the crystal ĉ axis is tilted with respect to the propagation direction of the beams. We demonstrate that this configuration combines the features of both spatial soliton formation without energy exchange and two-wave mixing with energy exchange leading to pattern formation.
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.
The propagation of a light beam in a photorefractive crystal in an alternating meander electric field is studied. A nonlinear equation is obtained for a spatial charge field formed in the crystal upon modulation of the light intensity synchronously with the applied electric field. It is established theoretically that the spatial charge field has two components, which make contributions to different mechanisms of a photoresponse providing self-focusing and the appearance of spatial solitons, as well as the trajectory self-bending. The conditions are found at which the soliton regime is realised and parameters affecting this regime in a greater extent are determined.
Nonreciprocal energy transfer between two coherent laser beams during two-wave mixing requires a photorefractive phase shift between the interference pattern and the resulting space charge. The symmetry of the Stark geometry photorefractive quantum wells forbids a phase shift using either dc or ac fields. We present the first experimental demonstration of nonreciprocal energy transfer during two-wave mixing using moving gratings. Optical energy exchange is observed in photorefractive p-i-n quantum well diodes with photorefractive gains approaching 1000 cm−1 and exhibiting complex spatio-temporal dynamics.
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.
The anisotropic four-wave mixing in the scheme recently proposed by S.I. Stepanov and M.P. Petrov (Opt. Commun. vol.53, p.64-8, 1985) is studied. The main feature of this interaction arrangement is that the same phase hologram (index grating) has opposite contrasts for orthogonally polarized, counterpropagating waves. The coupled nonlinear equations, in the case of transmission and reflection gratings, for the pi /2 photorefractive phase shift are exactly solved, and their properties are discussed in detail. The numerical evidence of the effects of bistability and self-oscillation is included.>