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Journal of the Optical Society of America B

Exact solution to cross-polarization two-wave mixing in cubic photorefractive crystals

Milivoj R. Belić, Milan S. Petrović

Published Jun 1, 1994• 0 citations
Publisher

Abstract

Slowly varying envelope wave equations for cross-polarization two-wave mixing in cubic photorefractive crystals are solved exactly by a novel analytical method. The method allows both the transmission (codirectional) and the reflection (contradirectional) geometry of the process to be treated equally and yields simple explicit expressions.

DOI
10.1364/josab.11.001142

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Applied Physics Letters•Jul 25, 1988•14 citations
Slowly varying envelope wave equations for cross-polarization two-wave mixing in cubic photorefractive crystals are solved exactly by a novel analytical method. The method allows both the transmission (codirectional) and the reflection (contradirectional) geometry of the process to be treated equally and yields simple explicit expressions.
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 intensity dependence of stationary energy transfer in photorefractive codirectional cross-polarization two-wave mixing is examined. The intensity formulae remained effect both in the saturation and the intermediate regime (before saturation) are driven, and the analytical expressions with the ratio of saturation intensity to total incident intensity as their explicit variable are obtained for the case of pump depletion. It is necessary to use these formulae in some problems, such as the temperature or intensity dependence of cross-polarization two-wave mixing. A method of measuring the coupling coefficient and saturation intensity of a cubic photorefractive crystal is presented, which is suitable for cross-polarization two-wave mixing in the intermediate regime.