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Journal of Applied Physics

Polarimetric determination of the ratio between the constituent phase conjugate signals in degenerate four-wave mixing

Sok Won Kim, Sang Soo Lee

Published Sep 15, 1987• 0 citations
Publisher

Abstract

We have derived the polarization dependent coupling constants for transmission and reflection gratings in degenerate four-wave mixing, measured phase-conjugate signals for various polarization conditions, and determined the relative contribution of the two gratings to the signal. The results obtained with cryptocyanine dissolved in methanol as the nonlinear medium show that the signal from transmission grating is 1.53–2.14 times larger than that from a reflection grating depending on the angle between the wave vectors of the forward pump beam and the probe beam.

DOI
10.1063/1.339521

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Abstract We present a study of optical phase conjugation through degenerate four-wave mixing in CuCl, as a function of light frequency, intensity, polarization and sample temperature. The phase-conjugate signal exhibits two maxima at the frequencies of the T5 exciton (one-photon resonance) and of the biexciton (two-photon resonance). By appropriate combinations of the input beam polarizations, it is possible to single out the various terms contributing to the signal (small-spaced, large-spaced population grating and two-photon coherent excitation). The absolute value of X(3) responsible for the two-photon resonance has been determined ( x(3) (-w,w,w, -w) = 3.10-7 e.s.u.). It leads to ‘mirror’ efficiencies of the order of 10% for input pump intensities I0 » 105 W cm -2 and sample thickness d» 10-4 cm. At higher I0, a saturation of the reflection takes place. The variation of the conjugate beam with temperature has been studied in the range 15 K < T <70 K. Finally, the phase-conjugate nature of the signal has been verified by inserting an aberrator in the path of the input probe beam, and by checking the reconstruction of the reflected beam.

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IEEE Journal of Quantum Electronics•Jan 1, 1988•8 citations
We have derived the polarization dependent coupling constants for transmission and reflection gratings in degenerate four-wave mixing, measured phase-conjugate signals for various polarization conditions, and determined the relative contribution of the two gratings to the signal. The results obtained with cryptocyanine dissolved in methanol as the nonlinear medium show that the signal from transmission grating is 1.53–2.14 times larger than that from a reflection grating depending on the angle between the wave vectors of the forward pump beam and the probe beam.
We consider degenerate four-wave mixing in a Kerr medium with a standard noncollinear geometry and the polarization directions of all the beams parallel to one another. The two pump beams, the probe beam, and the phase-conjugate beam are denoted by the subscripts 1,2,4 and 3, respectively. The nonlinear medium is placed between z = 0 and z = 1; the values of the intensities of the beams at z = 0 and 1 are denoted by Ii0 andIi1, where i = 1,2,3,4. Beams 2 and 4 are incident at z = 1; and beam 1 is incident at z = 0. We have determined the dependence of the phase-conjugate reflectivity R = I31/I41 and the pump transmission T = I11/I10 on the following parameters: the probe ratio, q=I41/(I10 + I21); the pump ratio, r = I21/I 1 0; the absorption coefficient–path length product, al; and the coupling constant of the medium, q. In the absence of nonlinear refraction, pump depletion, and linear absorption in the medium, R = tan2q. When all of these effects are taken into account, the maximum value of R is given by Rmax = exp (-2α1)/(q(1 + r)). The minimum value that T can reach is proportional to q for q < 1. Even for small values of q, multistable solutions for R and T are obtained when q is greater than a threshold value, which we denote by qth. We have determined the dependence of qth on the parameters q and r.
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.
A degenerate four-wave mixing experiment is performed in the saturable absorber of cryptocyanine. When the pump-beam intensity is below the saturation intensity, the reflectivity of the probe beam does not change, even though the probe-beam intensity is increased; however, the reflectivity begins to decrease slowly for moderate pump-beam intensity and finally decreases as l/q (q is the ratio of probe-to-forward pump-beam intensity) for pump-beam intensity far above the saturation intensity. The results are explained by extending Kogelnik's coupled-wave theory of volume grating to the four-wave case.
Abstract The properties of the phase‐conjugate reflectivity are analyzed anew for the self‐pumped four‐wave mixing in which only the two waves, i.e., the forward pump wave and the probe wave, are incident on the photo‐refractive crystal and the phase‐conjugate wave of the forward pump wave is used as the backward pump wave. First, by means of a model in which a Cat‐type phase conjugator is placed outside the interaction region, the equation for the phase‐conjugate reflectivity of self‐pumped four‐wave mixing using a transmission grating is derived. Next, the numerical calculations have been used for the first time to determine the effects of the coupling strength, the probe ratio as the incident intensity ratio of the forward pump wave to the probe wave, and the reflectivity of the Cat‐type phase conjugator on the entire phase conjugate reflectivity. Since the equation describing the phase‐conjugate reflectivity has multiple solutions, the strict analysis of the equation shows that the phase‐conjugate reflectivity has multiple values. Further, the conditions for high phase‐conjugate reflectivity has been studied.
Abstract We present a study of optical phase conjugation through degenerate four-wave mixing in CuCl, as a function of light frequency, intensity, polarization and sample temperature. The phase-conjugate signal exhibits two maxima at the frequencies of the T5 exciton (one-photon resonance) and of the biexciton (two-photon resonance). By appropriate combinations of the input beam polarizations, it is possible to single out the various terms contributing to the signal (small-spaced, large-spaced population grating and two-photon coherent excitation). The absolute value of X(3) responsible for the two-photon resonance has been determined ( x(3) (-w,w,w, -w) = 3.10-7 e.s.u.). It leads to ‘mirror’ efficiencies of the order of 10% for input pump intensities I0 » 105 W cm -2 and sample thickness d» 10-4 cm. At higher I0, a saturation of the reflection takes place. The variation of the conjugate beam with temperature has been studied in the range 15 K < T <70 K. Finally, the phase-conjugate nature of the signal has been verified by inserting an aberrator in the path of the input probe beam, and by checking the reconstruction of the reflected beam.