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Topical Meeting on Optical Bistability (OB)

Bistability in intracavity resonant degenerate 4-wave mixing in Na vapor

Wulfhard K. Lange, E. Köster, J. Mlynek

Published Jan 1, 1985• 0 citations
Publisher

Abstract

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/.

DOI
10.1364/obi.1985.md14

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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.
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.
In this work the different schemes of propagation and interaction of the light beams in nonlinear Fabry-Perot interferometer have been studied theoretically and experimentally. Degenerate and non-degenerate four-wave mixing have been realized in the cavity of Fabry-Perot type using Rhodamine-6G dye and polymethine dye 3274U solution as saturable absorber. The diffraction efficiency of intracavity dynamic grating has been studied in dependence on intensity of interacting beams and parameters of resonator. The theoretical model of the processes of intracavity degenerate and non-degenerate four-wave mixing has been developed and applied to the analysis of the efficiency of light beams conversion by mean of Bragg diffraction from intracavity dynamic gratings. For theoretical description of typical experimental situations we used the round-trip model of nonlinear interferometer adapted for the geometry of degenerate four-wave mixing, which can be realized in the scheme of symmetrical oblique incidence of pump, signal and probe beams to the front and back mirrors of cavity.
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.
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.