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Journal of the Optical Society of America B

Phase conjugation by four-wave mixing with a nonstationary pumping wave

Jozsef S. Bakos, Gagik P. Djotyan, T. Juhánz

Published Aug 1, 1989• 3 citations
Publisher

Abstract

Collinear schemes of transient phase conjugation during degenerate four-wave mixing are investigated in inertion-less Kerr-like media. The analytical solution of this problem is presented for the case when one of the pumping waves is monochromatic but the other one is an ultrashort laser pulse.
DOI
10.1364/josab.6.001540

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Optical phase conjugation by four-wave mixing in a Kerr medium is considered. Two strong counterpropagating lasers pump a nonlinear medium in which they excite the third-order polarization. Mixing with a weak incident field then generates the phase-conjugated image of that field. It is shown how the polarization of the pumps and the tensorial nature of the nonlinear interaction can be accounted for by a geometrical polarization tensor. The electric field is shown to obey two coupled wave equations, which couple a positive- and negative-frequency component of the field. These wave equations allow plane-wave solutions, and we derive the dispersion relation for the wave vectors of these modes. By matching the field of such a mode across the boundaries of the medium to an external incident field, we are able to obtain analytically the Fresnel coefficients for reflection and transmission. Our expressions reduce to earlier results in the appropriate limits.
We derive an exact solution for both amplitude and phase of a signal that is back-reflected by collinear nonlinear degenerate mixing of four circularly polarized waves of arbitrary intensity in a Kerr-like medium. Our analysis suggests that taking pump depletion into account may spoil the ideal phase-conjugation condition, even in the limit of weak nonlinear coupling, and indicates that substantial deterioration of the probe phase-reversal property may occur for strongly interacting waves in a manner that is highly sensitive to the anisotropy of the nonlinear susceptibility.
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