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Journal of the Optical Society of America B

Saturation in Degenerate Four-Wave Mixing

G. Grynberg, M. Pinard, Philippe Verkerk

Published Jan 1, 1984• 0 citations
OpenAlex

Abstract

In atomic vapors, the variation of the phase-conjugate reflectivity versus frequency has been a subject of interest these recent years. At low incident intensity for the pump and probe waves, a Lorentzian curve centered at the atomic resonance frequency is observed. At high pump intensity a splitting is observed, and the phase-conjugate reflectivity tends toward zero at the atomic resonance frequency.1 A correct treatment for this complex situation has been derived recently by Bloch and Ducloy.2 However, their theory leads to intricate calculations for which it is difficult to find physical interpretations. A great simplification is obtained by using the dressed-atom approach. The calculations are easier to derive and lead to clear physical interpretations. New results are predicted, some of them have already been observed experimentally.

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•May 21, 1990•1 citation
In atomic vapors, the variation of the phase-conjugate reflectivity versus frequency has been a subject of interest these recent years. At low incident intensity for the pump and probe waves, a Lorentzian curve centered at the atomic resonance frequency is observed. At high pump intensity a splitting is observed, and the phase-conjugate reflectivity tends toward zero at the atomic resonance frequency.1 A correct treatment for this complex situation has been derived recently by Bloch and Ducloy.2 However, their theory leads to intricate calculations for which it is difficult to find physical interpretations. A great simplification is obtained by using the dressed-atom approach. The calculations are easier to derive and lead to clear physical interpretations. New results are predicted, some of them have already been observed experimentally.
We have derived an analytic expression for the intensity distribution of two counterpropagating waves of arbitrary input intensity in a saturable absorber. We use this distribution to extend the theory of degenerate four-wave mixing to include the effects of pump wave absorption. In particular, the spatial variation of the nonlinear absorption and coupling constants that appear in the coupled-amplitude equations for the probe and the signal (i.e., conjugate) waves are determined. These coupled-amplitude equations are solved numerically in a noniterative manner, leading to a prediction for the phase-conjugate reflectivity. The nature of the predictions differs qualitatively from those1,2 derived from theories that ignore pumpwave absorption, especially for the case of off-line-center excitation. At large values of the input pump intensities, the phase conjugate reflectivity can be larger than that predicted by theories that ignore pump-wave absorption.
Summary form only given.The present summary reports about a dressed-state approach to optical phase conjugation (OPC) by resonant nearly degenerate four-wave mixing in vapors. The basic idea is to decouple the pump fields from the probe field by first treating the problem of the pump fields interacting with the atom and then consider the interaction with the probe field. From this model, the dip, observed in the OPC yield when the pump fields are tuned to an atomic resonance, can be interpreted as an interference effect between contributions to the polarization originating from two dressed-state transitions.
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 effect of an intense pump beam on the intensity of the phase-conjugated emission is studied in the case of a three-level atom. We first extend to the case of cross-polarized pump beams the dressed-atom model that we have presented previously [Phys. Rev. A 34, 4008 (1986)] for the case of two-level atoms. The range of validity of our theory is \ensuremath{\Gamma} (natural width) ${\ensuremath{\Omega}}_{1}$ (Rabi frequency of the intense pump) ku (Doppler width). We have studied the line shape in degenerate four-wave mixing, the influence of a static magnetic field, and the resonances that appear in nondegenerate four-wave mixing. Experiments are done in a neon discharge using cw dye lasers. The experimental results are in good agreement with the theoretical predictions. In degenerate four-wave mixing, we have shown that the saturating dip disappears when the weak beams have orthogonal polarizations. In the presence of a static magnetic field and in the nearly degenerate case, narrow resonances corresponding to transitions between energy levels of the dressed atom are observed. The intensity and the width of these resonances are in very good agreement with the predictions of the theoretical model.
We present in this paper a theory of the saturation effects in degenerate four-wave mixing which makes use of the dressed-atom method. We mainly study the case of a Doppler-broadened line, but several results can be applied to the case of nearly degenerate four-wave mixing for a Doppler-free medium. We show that a close relationship does exist between the two problems : the generated beam is mainly created when the detuning between two incident beams is equal to the Rabi frequency. In the degenerate case, this condition is fulfilled by two velocity groups because of the Doppler shift. We analytically calculate the lineshapes for two-level atoms in the case of forward saturation (the intense pump beam propagates in the same direction than the probe beam) and in the case of backward saturation (the intense pump beam and the probe beam propagate in opposite directions). We also study collisional effects and the influence of the intensity of the weak pump beam when perturbation theory can no longer be applied.