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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Model Of The Phase-Conjugate Mirror

Aleksander Błȩdowski, Wieslaw Z. Krolikowski, Adam Kujawski

Published Oct 19, 1987• 0 citations
Publisher

Abstract

The solution to the boundary-value problem for a simple model of the phase-conjugate mirror is presented. The solution is based on a set of two coupled second-order wave equations and does not assume the slowly varying envelope approximation. The formulae for the amplitudes of the waves generated in the four-wave mixing process are derived and their properties are discussed in detail.

DOI
10.1117/12.943359

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The solution to the boundary-value problem for a simple model of the phase-conjugate mirror is presented. The solution is based on a set of two coupled second-order wave equations and does not assume the slowly varying envelope approximation. The formulae for the amplitudes of the waves generated in the four-wave mixing process are derived and their properties are discussed in detail.
The coupled-wave equations describing the optical phase conjugation by degenerate four-wave mixing are usually solved in the so-called slowly varying amplitude approximation, wherein only the first derivatives of the amplitudes of the probe and the conjugate waves are taken into account. Here we solve the coupled-wave equations without this approximation for nonresonance interactions. This leads to an oscillatory dependence of both reflectivity and transmittance on the normalized coupling constant, κL. Also, the intensity distributions of the probe and the conjugate waves show oscillatory beatlike behaviors around the corresponding slowly varying amplitude approximation distributions. These behaviors can be interpreted as the diffraction of the conjugate (probe) wave from a grating resulting from the superposition of the pump–pump and the pump–probe gratings.
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.