<title>Nonunidirectional energy exchange at the two-wave interaction in cubic photorefractive crystals under a square-wave electric field</title>

Abstract

We demonstrate experimentally and theoretically that the sign of two-wave coupling gain in sillenite crystal at some polarization of light changes with the increase of the amplitude of square-wave field applying along the [1 1 0] axis. it is shown that the nonunidirectional energy exchange is the reason of this effect in Bi2TiO20 single crystal. Also strong influence of this effect on the polarization properties of the two-wave coupling gain was it revealed at the experimental investigations of the efficiency of the two-wave interaction in Bi12SiO20 single crystal. At the theoretical analysis we used the model obtained on the basic of the mode approach. Made the numerical calculation of dependencies of the two-wave coupling gain has good agreement with the experimental data. This calculation has allowed estimating the material parameters ofthe investigated samples ofthe crystal.Keywords: photorefraction, two-wave interaction, nonunidirectional energy exchange I . INTRODUCTIONSillenite crystals Bi12SiO20, Bi2GeiO20, and Bi12TiO20 are promising photorefractive materials for many applications, e.g., volume holographic storage, phase conjugation, optical information processing, and holographic interferometry 2 because of their small response time and high photosensitivity. The applying of alternating electric field of a square-wave form to these crystals can significantly increase their photorefractive response to a light pattern '.This becomes possible because the efficiency of division of charges at the formation of photorefractive response increases when increasing of value applied field. Herewith alternating external electric field can stimulate the gain as unlocal so and local components of the space charge field. Local component becomes the negligible small value if the frequency of the ac-applied field becomes much more than time of Maxwell's relaxation. Also, in this case time periodically modulation of the efficiency of the two-wave interaction in the stationary regime practically is absence, so two-wave mixing is steady state.Authors of majority of paper consider (see example 5.8), that energy exchange under steady state two-wave mixing is unidirectional if can neglect by the photovoltaic effect and absorption grating. In experiments this means, that directional of energy exchange between the interaction beam not dependencies from the ratio its intensity and from the value of the coupling constant Fm ' which increases when, increasing of amplitude of the external ac field. However, it is shown in that contribution of the effect of self-diffraction gyration, as it is called in , may be the reason of the nonunidirectional energy exchange at the two-wave mixing in a cubic photorefractive crystal under external ac electric field.In this work we report the experimental observation and numerical results of the nonunidirectional energy exchange in Bi12TiO20 and Bi12SiO20:Cd crystals. To explain this effect we consider the gain coefficient as a function ofthe amplitude of applied field and entrance polarization vec...