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Physical Review A

Phase transfer in optical phase conjugation

Wieslaw Z. Krolikowski, Milivoj R. Belić, Aleksander Błȩdowski

Published Mar 1, 1988• 10 citations
Publisher

Abstract

Phase variations during a phase-conjugation process are considered in detail, following our own method of analytical solution of the degenerate four-wave mixing including pump depletion and arbitrary phase mismatch between the light interference and the refractive-index gratings. Closed-form expressions are obtained for the phase transfer, and some apparent misconceptions concerning phase changes in optical phase conjugation are discussed.

DOI
10.1103/physreva.37.2224

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Phase variations during a phase-conjugation process are considered in detail, following our own method of analytical solution of the degenerate four-wave mixing including pump depletion and arbitrary phase mismatch between the light interference and the refractive-index gratings. Closed-form expressions are obtained for the phase transfer, and some apparent misconceptions concerning phase changes in optical phase conjugation are discussed.
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 calculation procedure and various large-signal and numerical solutions are presented for degenerate four-wave mixing in optical Kerr media, and for phase conjugate resonators using degenerate four-wave mixing. The solutions presented take full account of nonlinear refractive index changes, pump depletion, signal saturation, distributed losses, and possible external mirrors with laser gain. We find that including the nonlinear index change generally causes little change in the reflectivity or power output of degenerate four-wave mixing devices, at least with symmetric pumping. The optimum power output from a phase conjugate resonator with and without a laser gain medium is calculated. The results provide some theoretical guidance for designing phase conjugate resonators. PACS Code 42. 65. Bp; 42. 60. Da
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.