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Applied Physics Letters

Bistable reflectivity of phase-conjugated signal through intracavity degenerate four-wave mixing

Govind Prasad Agrawal, Christos Flytzanis, Robert Frey, F. Pradère

Published Apr 1, 1981• 28 citations
Publisher

Abstract

Through intracavity degenerate four-wave interaction the reflectivity of the phase-conjugated signal is shown to exhibit bistability and hysteresis when the driving pump field is varied in a continuous matter. The nonlinear medium inside the Fabry-Perot cavity may be in one- or two-photon resonance with the pump. We suggest suitable materials and discuss possible applications of the bistable response of the reflectivity.

DOI
10.1063/1.92429

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Through intracavity degenerate four-wave interaction the reflectivity of the phase-conjugated signal is shown to exhibit bistability and hysteresis when the driving pump field is varied in a continuous matter. The nonlinear medium inside the Fabry-Perot cavity may be in one- or two-photon resonance with the pump. We suggest suitable materials and discuss possible applications of the bistable response of the reflectivity.
An externally driven nonlinear Fabry-Perot interferometer with bistable transmission characteristics is probed through a weak optical field. The nonlinear interaction among the counterpropagating pump beams and the probe beam generates the phase-conjugated beam through intracavity degenerate four-wave mixing. It is shown that the phase-conjugated reflectivity displays bistability and that hysteresis as the driving field is varied in a continuous manner. The analysis is carried out in the mean-field approximation and is valid for the case of low absorption and a high-Qcavity. Both the dispersive and the absorptive effects arising due to saturation of the one-photon resonance are included, and their effect on the phase-conjugated reflectivity is discussed. The results show that, when a bistable device switches on, the reflectivity decreases by a few orders of magnitude. We discuss possible applications and suggest materials where the proposed effects can be seen.
A general formalism is developed to study intracavity phase conjugation through resonant degenerate four-wave mixing. The effects of spatial hole burning, arising from interference of the counterpropagating pump waves, are fully incorporated. The analysis is applied to discuss intracavity phase conjugation in nonlinear media that can be modeled using either a two-level system or a Λ-type three-level system. In both cases, the phase-conjugate reflectivity exhibits bistability for an appropriate choice of the input parameters. For a two-level system, the tuning characteristics of the Fabry–Perot cavity significantly affect the phase-conjugate spectrum that displays hysteresis when the cavity is detuned from the applied laser frequency.
Resonant degenerate 4-wave mixing (DFWM) has proven to be a powerful technique to generate phase conjugate (PC) wave fronts. In this contribution we consider the situation where the nonlinear medium is placed inside a Fabry-Perot cavity (Fig. 1). In this geometry, the intracavity pump intensity and, as a consequence, also the PC emission are expected to exhibit bistable switching /1,2/. With respect to practical applications, intracavity PC might be of interest, e.g., for probing an optical memory element or for Q-switching a resonator with a phase conjugating mirror. Only recently, however, first experimental studies on bistability in intracavity PC have been performed /3,4/.
Many important effects such as optical bistability or periodic and chaotic self-pulsations have their origin in the interaction of two counterpropagating optical beams of the same frequency in a nonlinear medium. The investigation of the actual behavior of the standing waves set up inside a nonlinear Fabry-Perot etalon by an external pump beam is generally performed by observation of the transmitted beam. As predicted theoritically(1), intracavity phase conjugation is another way to test this interaction between the two counterpropagating pump waves inside the nonlinear cavity.
Experimental results are presented regarding the generation and bistable behavior of a conjugated signal obtained through intracavity nearly degenerate four-wave mixing in a semiconductor laser amplifier injected with both pump ($\ensuremath{\omega}$) and probe ($\ensuremath{\omega}\ensuremath{-}\ensuremath{\delta}\ensuremath{\omega}$) frequencies. Conjugated reflectivities at $\ensuremath{\omega}+\ensuremath{\delta}\ensuremath{\omega}$ larger than 500% with 35% efficiency together with bistable behavior in the three signals (pump, probe, and conjugated) are reported.
Theoretical calculations regarding the collinear intracavity nearly degenerate four-wave mixing are presented when a Fabry-Perot cavity is externally driven by a strong pump and probed by a weak signal. The calculations are performed for two different limits: the mean-field and the small-signal gain approximations. The results suggest the bistable behavior for all the three signals (pump, probe, and conjugate) with several different shapes of the hysteresis loops. Furthermore, for certain values of the parameters in the mean-field approximation, calculations show a resonance behavior of probe and conjugate signals with respect to the incident pump intensity, with probe and conjugate transmittance as high as 103{10}^{3}103--104{10}^{4}104 in the case when the pump transmission does not exhibit bistability. In the small-signal gain approximation, theory also demonstrates strong dependence of probe amplification on the normalized detuning when it is smaller than the probe-cavity mistuning.