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Philosophical Transactions of the Royal Society of London Series A Mathematical and Physical Sciences

Optical phase conjugation via degenerate four-wave mixing in copper chloride

M. L. Claude, Lloyd L. Chase, Daniele Hulin, A. Mysyrowicz

Published Dec 18, 1984• 2 citations

Abstract

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.

DOI: 10.1098/rsta.1984.0124

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Mar 8, 1989•0 citations

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.

Summary form only given. Previously, we have used four-wave mixing via coherent population trapping to achieve optical phase conjugation (OPC) with high gain, using two dye lasers and a sodium vapor cell. The /spl Lambda/ transition used involved the two hyperfine ground states and one excited state, so that two different optical frequencies were needed to satisfy the two-photon resonant condition between the probe and one of the pump beams. Later, we demonstrated in rubidium that a single hyperfine transition with Zeeman sublevels is enough to achieve OPC with equally high gain, thus eliminating the need for high-frequency sideband generation. However, in order to guarantee that the diffraction from the grating is primarily dispersive, the backward pump beam had to be detuned by about 60 MHz from the probe and the forward pump. One of the key disadvantages of such a nondegenerate scheme is that applications such as phase-conjugate mirrors are hard to implement. Here, we report the observation of optical phase conjugation in rubidium with equally high gain, but all the frequencies are degenerate.

The phase-conjugation in crystalline CuCl has been studied at 1.6 K. It has been found that the two-photon resonance of the

\varGamma_{1}

-excitonic molecule and the one-photon resonance of the

\varGamma_{5}

-exciton contribute to the generation of the phase-conjugated wave. Each contribution has been separated spectroscopically by adjusting the polarization configuration of the incident fields adequately and has been compared qualitatively with the theory. The efficiency of the phase-conjugated reflection has become maximum at around the two-photon resonance of the excitonic molecule, 3.186 eV and has been ∼1% at the maximum.

Nondegenerate four-wave mixing on the j=0\ensuremath{\rightarrow}j=1 transition, in a ``V '' system, using orthogonal, circularly polarized pump beams is used to study theoretically the generation of the phase-conjugate signals. The efficiency of generation of the conjugate wave is studied as a function of the various system parameters such as pump-probe detuning, Zeeman splitting, pump-atom detuning, collisional parameters, and the intensities of the pump beams. The origin of the various resonances in the reflectivity is explained. For weak pump fields, some resonances are shown to have subnatural linewidths. In the degenerate case, the reflectivity as a function of pump-atom detuning has, in contrast to a two-level system, a doublet structure for moderate absorption-length parameters and field strengths. The reflectivity is shown to have additional resonances due to pump imbalance. The phase-conjugate signal is also shown to exhibit the pressure-induced extra resonances.

Considers phase conjugation through degenerate four-wave mixing in a Λ-type three-level system under certain simplifying assumptions, the most restrictive among them being the assumption of symmetrical detuning of the pump from the two lower lying sublevels. When compared to an absorbing resonant two-level system, it is found that significantly higher values of the phase-conjugate reflectivity are possible at pump intensities well below saturation provided the sublevel splitting is less than a homogeneous linewidth. The physical mechanism responsible for phase conjugation is coherent population trapping arising from two-photon-induced atomic coherence between the two sublevels.

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.