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Journal of the Optical Society of America B

Theory of intracavity-pumped photorefractive phase-conjugate mirror

Ram Yahalom, Avigail Yariv

Published Aug 1, 1988• 9 citations
Publisher

Abstract

We present a new type of phase-conjugate mirror that is based on an externally driven Fabry–Perot interferometer with intracavity-pumped photorefractive material, which is probed by the signal beam. It is shown theoretically that such a configuration leads to multivalued solutions and possibly to bistability. This configuration also permits optical control of the resonator output and electrical control of the phase-conjugate reflectivity.

DOI
10.1364/josab.5.001783

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We present a new type of phase-conjugate mirror that is based on an externally driven Fabry–Perot interferometer with intracavity-pumped photorefractive material, which is probed by the signal beam. It is shown theoretically that such a configuration leads to multivalued solutions and possibly to bistability. This configuration also permits optical control of the resonator output and electrical control of the phase-conjugate reflectivity.
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/.
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.
Phase-conjugate resonators have several attractive properties for image processing and storage. In the work described here, we demonstrate improved thresholding and storage properties of a phase-conjugate resonator (PCR) by the addition of an intracavity saturable absorber. It can be shown that the resonator will be bistable if (1) the small-signal absorption of the saturable absorber exceeds the small-signal gain of the phase-conjugate mirror, and (2) the absorption saturates more readily than the gain (i.e., reflectivity) of the PCM. Recently, a saturable absorber was used inside a PCR to control the transverse modes,1 but no evidence of bistability was obtained. In our experiment, we used a PCR bounded at one end by a conventional mirror and at the other end by an externally pumped BaTiO3 PCM. The saturable absorber was a solid film of fluorescein- doped boric acid glass.2 By adjustment of the total intensity and beam ratio at the PCM, we were able to demonstrate bistability. The input in our experiment was an incoherent control beam incident noncollinearly onto the intracavity saturable absorber. In the absence of a control beam, no oscillation was observed. When the control beam was turned on, the resonator switched to the on state in ~5 sec. The control beam could then be removed, and the cavity oscillation continued. To return to the off state, the resonator path was blocked.
One of the typical methods to generate the phase-conjugate beam is four-wave mixing with a photorefractive crystal. It is known that the phase-conjugate reflectivity shows the bistability in some cases. Analyzing the temporal property of four-wave mixing, we offer a new method to control the bistable phase-conjugate reflectivity, and we perform an experiment of the bistability control by the method. An equation to obtain the threshold value of the coupling strength for showing the bistability is derived by a steady-state analysis of four-wave mixing, and the temporal property of four-wave mixing is studied with two different initial conditions that are used for letting the phase-conjugate reflectivity R converge to an off state (R=0) or to an on state (R>0). The initial condition for the converging off state is that the forward pump beam is turned off throughout. The condition for the converging on state is that the forward pump beam is turned on in advance, and after enough time passes, it is turned off. In both conditions, the backward pump beam and the probe beam continue to illuminate throughout. Whereas both optical arrangements are equivalent after setting up these initial conditions, each phase-conjugate reflectivity converges to different stationary values, R=0 and R>0. Besides, an experiment is performed and we actually control the bistability by this method. Furthermore, the temporal and the spatial variation of the refractive-index grating in the photorefractive crystal is investigated, and the process of the bistability is explained.