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Journal of Modern Optics

Effects of Absorption on Multivalued Solutions in Photorefractive Four-wave Mixing with Complex Coupling Constant

Kenneth D. Shaw

Published Aug 1, 1993• 0 citations
Publisher

Abstract

The steady-state coupled wave equations describing anisotropic photorefractive four-wave mixing with absorption in cubic crystals are solved for the general case where the coupling constant is complex. The effects of absorption on the behaviour of the multivalued solutions that occur under these conditions are examined, and the consequences for the dynamical behaviour are discussed.

DOI
10.1080/09500349314551621

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The steady-state coupled wave equations describing anisotropic photorefractive four-wave mixing with absorption in cubic crystals are solved for the general case where the coupling constant is complex. The effects of absorption on the behaviour of the multivalued solutions that occur under these conditions are examined, and the consequences for the dynamical behaviour are discussed.
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We develop a numerical method to solve the coupled-wave equations for four-wave mixing phase conjugation in a photorefractive crystal with unequal complex coupling constants; by this method we can obtain both the intensities and the phases of various beams. We discuss the intensities and the phases of the interacting beams in a photorefractive crystal for the cases in which the phase shifts between the refractive-index gratings and the interference pattern are all π/2 and in which they are not all π/2.
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.
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