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Optics Letters

Multigrating phase conjugation: exact results

Wieslaw Z. Krolikowski, Milivoj R. Belić

Published Feb 1, 1988• 11 citations
Publisher

Abstract

Multigrating operation of degenerate four-wave mixing in photorefractive media is considered in the strong pump regime. Closed-form expressions for the reflectivity are obtained for the cases of absorption and no absorption. An arbitrary phase mismatch between the intensity interference fringes and the refractive-index gratings is allowed.

DOI
10.1364/ol.13.000149

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Physical Review A•May 1, 1985•35 citations
Multigrating operation of degenerate four-wave mixing in photorefractive media is considered in the strong pump regime. Closed-form expressions for the reflectivity are obtained for the cases of absorption and no absorption. An arbitrary phase mismatch between the intensity interference fringes and the refractive-index gratings is allowed.
Multigrating optical phase conjugation in photorefractive media in the case of pump depletion and for arbitrary relationships among different coupling strengths is studied numerically. The role of linear absorption as well as the role of all the coupling mechanisms and their competition in the wave mixing process is examined. It is found that multigrating operation with accidental values of coupling constants leads to a decrease in the efficiency of the process. It is also shown that the presence of absorption, which is in principle detrimental, sometimes exerts a beneficial influence on multigrating phase conjugation.
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.
A method for exact solution of the stationary holographic degenerate four-wave mixing in reflection geometry in photorefractive media is presented. The effects of pump depletion and light absorption in the nonlinear dynamic medium are rigorously taken into account. Numerical steps in the procedure are reduced to the solution of one simple nonlinear first-order differential equation, or are absent altogether when the equation is linearized, or for the case of no absorption. The method of solution is applicable to other wave-mixing geometries as well.