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Journal of the Optical Society of America

Effects of separated absorption and emission spectra on degenerate four-wave mixing in organic dyes

John A. Buck, A. Dienes, J. R. Whinnery

Published Nov 1, 1981• 12 citations
Publisher

Abstract

Degenerate four-wave mixing in a separated absorption-gain system, such as that of an organic dye, is studied by using a four-level model. The effects of the nonlinearity arising from the displaced emission spectrum are found and compared with the results of the two-level model of Abrams and Lind [ Opt. Lett.2, 94 ( 1978); Opt. Lett.3, 205 ( 1978)]. A nonsymmetric saturation behavior over the width of the absorption line is shown to exist that can be detrimental to the phase-conjugate reflectivity. Otherwise, minor differences are seen from the two-level case.

DOI
10.1364/josa.71.001381

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Acta Physica Sinica•Jan 1, 1981•2 citations
Degenerate four-wave mixing in a separated absorption-gain system, such as that of an organic dye, is studied by using a four-level model. The effects of the nonlinearity arising from the displaced emission spectrum are found and compared with the results of the two-level model of Abrams and Lind [ Opt. Lett.2, 94 ( 1978); Opt. Lett.3, 205 ( 1978)]. A nonsymmetric saturation behavior over the width of the absorption line is shown to exist that can be detrimental to the phase-conjugate reflectivity. Otherwise, minor differences are seen from the two-level case.
Two-frequency four-wave mixing in a dye is demonstrated, in which degenerate four-wave mixing is performed simultaneously within the absorption and emission frequency spectra, with two separate sets of beams. The coupling between the two bands gives rise to backward output waves at both frequencies, which are proportional to the phase conjugate of a single probe which can be at either of the two frequencies. Forward-propagating waves which are not conjugated are also generated at both frequencies. The frequency shifted outputs are tunable over the bandwidth of the spectrum in which they lie. A theoretical analysis is performed which is based on a four-level system model of the ground and first excited singlet states in a dye. Resulting are coupled equations, which are solved to yield the efficiencies of the various outputs. Experiments give results in good agreement with the theory.
A theoretical description for a forward degenerate four-wave mixing process in homogeneously broadened two-level absorbers with arbitrary intensities of all four beams is presented. Assuming no pump absorption and depletion, we obtain an analytical solution of forward degenerate four-wave mixing signal intensity in the limit of the strong pumps and weak probe and signal. In the case of low absorption or large detuning, this solution is shown to become equivalent to that of the phase-conjugate degenerate four-wave mixing derived by Abrams and Lind [Opt. Lett.2, 94 (1978)]. For arbitrary beam intensities and absorption parameters, the signal intensity is numerically calculated by solution of the coupled equations of complex wave amplitudes. Comparing the results of the numerical calculation with those of the analytical solution, we discuss the validity of using the analytical solution in practical experiments and show the saturation behavior that is due to the strong probe beam. The line shapes under the various ratios among the input beams and absorption parameters are also obtained and discussed.
Phase conjugation by degenerate four-wave mixing in a saturable absorbing medium with a relatively long-lived excited state is analyzed; the analytical results are compared with experimental results. We propose a four-level model and take into account the effects of both excited-state absorption and pump propagation to explain the experimental results, which could not be explained by the models proposed previously. The numerical result predicts that the value of the phase-conjugate reflectivity as a function of the pump intensity is maximum at a certain absorbance (as absorbance increases) that is dependent on the cross section of the excited-state absorption. The present analysis explains most observations in the experiment, which was performed with a saturable-dye-doped polymer film as the saturable absorbing medium.
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.
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.
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.