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Journal of the Optical Society of America B

Exact solution of a nonlinear model of two-wave mixing in Kerr media

Pochi Yeh

Published May 1, 1986• 63 citations
Publisher

Abstract

The coupling of two electromagnetic waves in Kerr media is considered. An exact solution of the coupled-mode equations is derived in the most general case when both pump depletion and material absorption are considered.
DOI
10.1364/josab.3.000747

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This paper presents an exact solution to the slowly varying envelope equations for the probe and signal fluxes in degenerate four-wave mixing in Kerr media. The analysis is performed for a noncollinear geometry, and all beams have the same linear polarization in the nonlinear medium. It is assumed that the angle separating the directions of the counterpropagating pumps and probe and signal beams is large enough so that cross-coupled waves do not contribute to the envelope equations describing the spatial evolution of the pump, probe, and signal beams. Multiple values of the transmitted probe are obtained for equal pump fluxes above a threshold determined by the nonlinear phase shift in the medium. Significant pump depletion occurs in this regime, but it can also occur without the appearance of multiple solutions. Since exact optical phase conjugation occurs only in the limit where the pumps are undepleted in Kerr media, this result implies that there are fundamental upper limits on the pump intensity that can be used to increase signal reflectivities in optical phase conjugation.