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Optics Letters

Symmetries of two-wave mixing in photorefractive crystals

Predrag Stojkov, Dejan V. Timotijević, Milivoj R. Belić

Published Oct 15, 1992• 8 citations
Publisher

Abstract

We consider symmetries of two-wave mixing equations in photorefractive crystals, using group theoretical methods. Symmetry groups for both the equations and conserved quantities are determined, and the corresponding generators are written explicitly. Results obtained for plane-parallel polarized two-wave mixing are used to introduce the method for solution and the form of solutions for cross-polarized two-wave mixing.

DOI
10.1364/ol.17.001406

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We consider symmetries of two-wave mixing equations in photorefractive crystals, using group theoretical methods. Symmetry groups for both the equations and conserved quantities are determined, and the corresponding generators are written explicitly. Results obtained for plane-parallel polarized two-wave mixing are used to introduce the method for solution and the form of solutions for cross-polarized two-wave mixing.
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We present an eight-dimensional matrix formulation of vector four-wave mixing. We study the case of a nonoptically active photorefractive for the transmission grating. The coupled equations are represented in a group formalism and irreducible forms are found. We show that when cross-polarization coupling is neglected, the system of equations is governed by two coupled SU(2) groups. We develop a theory that allows for pump depletion and electric-field-induced bulk birefringence. Analytical solutions are found when cubic 4¯3m materials are considered in two standard experimental geometries, i.e., electric fields perpendicular to the (110) crystal faces and electric fields perpendicular to the (001) crystal faces. Results are presented that show the effects of linear and circular polarized beams, and the use of these materials for vector phase conjugation is discussed. Solution routes to other geometries and noncubic photorefractive materials are also presented.
The stability of the steady-state solutions of four-wave mixing in photorefractive crystals has been studied. Two complementary methods have been used: linear stability analysis and time integration of the nonlinear equations. A critical dependence of the stability on the phase of the perturbation has been revealed. The existence of two stable solutions for certain values of some parameters has been found. Also, regimes of unstable behavior in cases with a unique steady-state solution for large values of the pump ratio have been found.