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Topical Meeting on Optical Bistability (OB)

Theory of Optical Bistability in Collinear Degenerate Four-Wave Mixing

Richard S. Lytel

Published Jan 1, 1983• 0 citations
Publisher

Abstract

Optical bistability occurs in many all-optical devices with non-linear couplings and feedback mechanisms. Thus, bistability is predicted for phase conjugate resonators,1 Fabry-Perot interferometers,2 and, generally wave mixing devices with a source of feedback. Bistability is therefore expected in four-wave mixing, where the Maxwell equations provide nonlinear feedback through the nonlinear susceptibility.

DOI
10.1364/obi.1983.thb35

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Optical bistability occurs in many all-optical devices with non-linear couplings and feedback mechanisms. Thus, bistability is predicted for phase conjugate resonators,1 Fabry-Perot interferometers,2 and, generally wave mixing devices with a source of feedback. Bistability is therefore expected in four-wave mixing, where the Maxwell equations provide nonlinear feedback through the nonlinear susceptibility.
A mean field theory of nearly-degenerate four-wave mixing is developed for the optical bistability, which has recently been found in a phase-conjugate resonator consisting of a normal mirror and a phase-conjugate mirror under relatively strong pumping. The bistability in transmission of the probe beam occurs as the mirror separation or the probe offset frequency is changed, but for a limited range of probe beam intensity. This behavior is explained as occurring under injection-locked conditions because of combined effects of tilting and broadening, or narrowing of the resonance curves due to nonlinearities in the phase-conjugate reflectivity arising from pump depletion.
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.
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.