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Optics Letters

Effects of signal detuning on phase conjugation

Tao-Yi Fu, M. Sargent

Published Nov 1, 1979• 94 citations
Publisher

Abstract

The formulations of degenerate three-wave and four-wave phase conjugation are generalized to include signalpump detuning. The theory is an extension of grating-dip spectroscopy. The reflection bandpass is shown to be limited by the power-broadened bandwidth (proportional variant 1/T(1)) of the two-level population difference. Unlike for runningwave saturation, the signal-absorption coefficient saturated by a standing wave shows virtually no gain regions.

DOI
10.1364/ol.4.000366

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Journal of Modern Optics•May 1, 1988•0 citations
The formulations of degenerate three-wave and four-wave phase conjugation are generalized to include signalpump detuning. The theory is an extension of grating-dip spectroscopy. The reflection bandpass is shown to be limited by the power-broadened bandwidth (proportional variant 1/T(1)) of the two-level population difference. Unlike for runningwave saturation, the signal-absorption coefficient saturated by a standing wave shows virtually no gain regions.
The Abrams-Lind formulation of degenerate four-wave phase conjugation is generalized to treat signal-pump detuning. The theory is an extension of two-wave grating-dip spectroscopy. We find that the reflection passband of phase conjugation is limited by the power-broadened bandwidth of the population difference, a width that can be very narrow. Unlike the running-wave saturator case, the signal absorption saturated by a standing wave shows no gain. This is due to the presence of appreciable amounts of unsaturated medium between spatial holes. We also generalize the degenerate three-wave mixing coefficients of Heer to include signal-pump detuning.
The phase-conjugate reflectivity attainable by degenerate four-wave mixing in an idealized saturable absorbing medium is calculated for arbitrary values of the laser intensity, laser frequency, and absorption path-length of the nonlinear medium. The influence of pump-wave absorption, including saturation and standing-wave effects, is included in the theory. The treatment is based on an analytic expression for the intensity distribution of the counterpropagating waves. The theoretical predictions differ substantially from those based on theories that ignore pump absorption effects. The results of the present calculation are used to predict the minimum laser intensity, absorption path-length, and detuning required to obtain unit reflectivity and self-oscillation.
The theory of resonant four‐wave mixing using one and two‐photon transitions is described in terms of saturation spectroscopy. Detuning the signal wave from the pump wave in the one‐photon case leads to a narrow‐band reflection spectrum, with width given by 1/T1, where T1 is the lifetime of the population difference. In the corresponding time‐domain picture (the fourth dimension), this produces a reflected pulse at least as long as T1, regardless of the signal. This time‐domain picture also leads to a novel kind of coherent transient spectroscopy. In the two‐photon case, an infinite number of levels are involved in principle, i.e., phase conjugation in infinite dimensions! In this case, two kinds of mechanisms compete in generating conjugate waves leading to two phenomena that do not occur in two‐level media: 1) a double‐peaked reflection spectrum and 2) coupled‐mode oscillation in absorbing media. In addition, due to the dynamic‐Stark shifted line center, the reflection coefficient approaches a constant value at large intensities, unlike the two‐level coefficient which bleaches to zero.
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.
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.