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Quantum Electronics

Self-diffraction of light waves by a local photorefractive grating in a crystal of the symmetry group bar 43min the transverse configuration

Rudolf V. Litvinov

Published Feb 28, 2007• 0 citations
Publisher

Abstract

The exact solution of nonlinear equations describing the symmetric stationary interaction of two light waves of an arbitrary polarisation on a local photorefractive grating in a crystal of the symmetry group 3 m in the transverse configuration of crystal faces is obtained in the paraxial limit. The polarisation of light waves and efficiency of energy transfer between them are studied as functions of the reduced length of a sample and the intensity ratio of incident waves.

DOI
10.1070/qe2007v037n02abeh013349

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The exact solution of nonlinear equations describing the symmetric stationary interaction of two light waves of an arbitrary polarisation on a local photorefractive grating in a crystal of the symmetry group 3 m in the transverse configuration of crystal faces is obtained in the paraxial limit. The polarisation of light waves and efficiency of energy transfer between them are studied as functions of the reduced length of a sample and the intensity ratio of incident waves.
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We derive the threshold conditions for the instability of counterpropagating waves in a nonlinear medium with local photorefractive response against the excitation of transverse small-angle structures. These conditions allow for all the important types of diffraction from refractive-index reflection gratings and are not limited to the case of strict frequency degeneracy of the waves. We study the dependence of the crystal-thickness threshold and the secondary wave emission angle on the crystal parameters and the pump conditions. We show that when the pump wave intensities differ considerably, excitation of standing light structures is replaced by excitation of traveling structures. Finally, we discuss the applications of the theory to experiments with the photorefractive crystals LiNbO 3 and LiTaO 3 .
Here we present four wave mixing configuration as one of the most important methods of generation and explanation of process of generation phase conjugation light the coupled equation was solved by three methods: undepleted pump approximation exact solution and two wave mixing approximation. Although exact solutions can be derived for four-wave mixing, the results are difficult to use because of the complicated transcendental equation involved. Solved the coupled equations and introduce an approximation in which two-wave mixing is the dominant process.
It is known that two-wave coupling in photorefractive crystal may result in an intensity-dependent phase shift as well as energy transfer between the two waves without phase crosstalk. In a sense, this kind of phase shift is similar to the intensity-dependent refractive-index effects in Kerr media. Consequently, optical bistability can be established in an optical cavity with a photorefractive crystal. We formulate the model and get the expected bistable transmission with numerical simulations. Several cases, including that of the codirectional coupling and the contradirectional coupling, are considered. The effects of the photorefractive crystal’s distribution absorption and the spatial phase shift between the index grating and the light interference pattern in the crystal on the nonlinear transmission characteristics have also been studied. It is interesting to note that the output of the pumping wave is dependent on the cavity intensity and thus shows bistable behavior with respect to the cavity input as well.
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.>