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Journal of the Optical Society of America A

Optical hysteresis and bistability in phase conjugation by degenerate six-photon mixing

Anatoly A. Borshch, М. С. Бродин, V. I. Volkov, Nikolai V. Kukhtarev, Vyacheslav N. Starkov

Published Jan 1, 1984• 10 citations
Publisher

Abstract

The exact solution of the nonlinear phase-conjugation equations in the case of fifth-order nonlinearity is presented. The theoretical dependence of the backward-wave intensity on that of the interacting waves with Gaussian time shape exhibit well-pronounced hysteresis that is in agreement with experimental results performed on CdS crystals (nanosecond laser pulses). The physical nature of the phenomenon is discussed using the concept of scattering diagrams in terms of dynamic holography.

DOI
10.1364/josaa.1.000040

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The exact solution of the nonlinear phase-conjugation equations in the case of fifth-order nonlinearity is presented. The theoretical dependence of the backward-wave intensity on that of the interacting waves with Gaussian time shape exhibit well-pronounced hysteresis that is in agreement with experimental results performed on CdS crystals (nanosecond laser pulses). The physical nature of the phenomenon is discussed using the concept of scattering diagrams in terms of dynamic holography.
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.
The exact theory of degenerate four-wave mixing in a Kerr-like medium in the Bragg scattering regime is used to study the reflectivity of phase-conjugate mirrors pumped by intense laser beams. The analysis takes into account pump depletion, nonlinear phase modulation and the relaxation time of the nonlinearity. The steady-state response exhibits multivalued reflectivity, hysteresis and potential bistability; however, the transient response shows that at most one value of the phase-conjugate reflectivity is stable. Periodic or chaotic pulsations are predicted beyond threshold values of pump intensity. The onset of a natural oscillation in the Kerr-like medium is also predicted in the absence of a continuous probe beam; the resulting field amplitude is stable and weakly sensitive upon the presence of external noise.
In this paper, we provide a complete mathematical model of the phenomenon of optical bistability (OB) resulting from the degenerate two-wave mixing (TWM) process of laser beams interacting with a single nonlinear layer of ferroelectric material. Starting with the electromagnetic wave equation for optical wave propagating in nonlinear media, a nonlinear coupled wave (CW) system with both self-phase modulation (SPM) and cross-phase modulation (XPM) sources of nonlinearity are derived. The complete CW system with full nonlinearity is solved numerically and a comparison between both the cases of with and without SPM at various combinations of design parameters is given. Furthermore, to provide a reliable theoretical model for the OB via TWM process, the results obtained theoretically are compared with the available experimental data. We found that the nonlinear system without SPM fails to predict the bistable response at lower combinations of the input parameters. However, at relatively higher values, the solution without SPM shows a reduction in the switching contrast and period in the OB response. A comparison with the experimental results shows better agreement with the system with full nonlinearity.