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Optics Letters

Transient analysis of nearly degenerate four-wave mixing

W. W. Rigrod, Robert A. Fisher, B. J. Feldman

Published Mar 1, 1980• 28 citations
Publisher

Abstract

Exact solutions for the impulse responses of the phase-conjugate backward wave and of the transmitted forward wave in a nonlinear four-wave mixing medium with a cw undepleted pump are derived from an earlier analysis of active contraflow systems by Bobroff and Haus [J. Appl. Phys. 38, 390 (1967)].
DOI
10.1364/ol.5.000105

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The exact theory of degenerate four-wave mixing in a Kerr-like medium in the Bragg scattering regime is used to study the reflectivity of phase-conjugate mirrors pumped by intense laser beams. The analysis takes into account pump depletion, nonlinear phase modulation and the relaxation time of the nonlinearity. The steady-state response exhibits multivalued reflectivity, hysteresis and potential bistability; however, the transient response shows that at most one value of the phase-conjugate reflectivity is stable. Periodic or chaotic pulsations are predicted beyond threshold values of pump intensity. The onset of a natural oscillation in the Kerr-like medium is also predicted in the absence of a continuous probe beam; the resulting field amplitude is stable and weakly sensitive upon the presence of external noise.
Phase conjugation of backward-and forward-wave produced by degenerate four-wave mixing using a nearly resonantly enhanced nonlinearity in four-level organic dye solutions was investigated. The conversion efficiency of 22% has been obtained in a 2.5×10-5-molar solution of chlorophyll A in methylalcohol with a 5mm interaction length and a pumping energy of ～8mj from SH of a Q-switched Nd:YAG. Degenerate four-wave mixing by two-photon resonant-enhancement in the solution of rhodamine 6G in alcohol was investigated. Measurements were performed which described the dependance of nonlinear reflectivities on the molar concentrations of the media and the intensities of the pumping and object waves. Phase conjugation characteristics of forward-wave in four-wave mixing process were theoretically analysed. Experiments have confirmed the theoretical prediction. The method of quartet degenerate four-wave mixing has been extended to the doublet degenerate casa. Using this method, image conversion from 1.06μm to 5320 A has been realized with a conversion efficiency of 25% in a 5 mm long saturable absorber made of organic dye 9740 solution in diehloroethane. Theoretical analysis shows that using a medium, which is a near resonant absorber for the infrared object wave but transparent for the visible reconstruction wave, the conversion efficiency may be well in excess of unity.
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.
Phase conjugation of backward-and forward-wave produced by degenerate four-wave mixing using a nearly resonantly enhanced nonlinearity in four-level organic dye solutions was investigated. The conversion efficiency of 22% had been obtained in a 2.5 X 10-5 - molar solution of Chlorophyll A in methylalcohol with a 5 mm interaction length and a pumping energy of ～ 8 mJ from SH of a Q-switched Nd: YAG. Degene-rate four-wave mixing by two-photon resonant-enhancement in the solution of rhodamine 6G in alcohol was studied. Measurements were performed which described the dependence of nonlinear reflectivities on the molar concentrations of the media and the intensities of the pumping and object waves. Phase conjugation characteristics of forward-wave in four-wave mixing process were theoretically analysed. Experiments have cofirmed the theoretical prediction. The method of quartet degenerate four-wave mixing had been ex-tended to the doublet degenerate case. Using this method image conversion from 1.06 μm to 5320 ? had been realized with a conversion efficiency of 25% in a 5 mm long satu-rable absorber made of organic dye 9740 solution in dichloroethane. Theoretical analy-sis showed that using a medium, which is a near resonant absorber for the infrared object wave but is transparent for the visible reconstruction wave, the conversion efficiency may be well in excess of unity.