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Soviet Journal of Quantum Electronics

Stability of stationary nonlinear states of optical waves in a system of two coupled double phase-conjugating mirrors based on photorefractive crystals

M. G. Zhanuzakov, A. A. Zozulya, Vladimir T Tikhonchuk

Published Nov 30, 1990• 2 citations
Publisher

Abstract

An investigation is reported of the stability of stationary nonlinear states of the fields of optical waves in a system comprising two coupled regions of a degenerate four-wave interaction pumped by two mutually incoherent optical beams. The importance of allowing for the finite values of scattered-wave seeds in the excitation of the scattering in such a system is demonstrated.

DOI
10.1070/qe1990v020n11abeh007572

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Quantum Electronics•Aug 31, 1997•4 citations
An investigation is reported of the stability of stationary nonlinear states of the fields of optical waves in a system comprising two coupled regions of a degenerate four-wave interaction pumped by two mutually incoherent optical beams. The importance of allowing for the finite values of scattered-wave seeds in the excitation of the scattering in such a system is demonstrated.
Development of scattered radiation in the geometry of a double phase-conjugate mirror is investigated numerically in the framework of a two-dimensional model that accounts for both diffraction and noncollinearity of the interacting beams. The large-scale structure of the scattered beams is found to be distorted because of the convective flow of energy out of the interaction region. We show that the output characteristics of the double phase-conjugate mirror depend strongly on the level of seed radiation in the direction of the scattered beams. The seed radiation may be due to incoherent scattering of the pumping beams inside the medium or to self-broadening of the pumping beams’ spectra because of nonlinear self-interaction.
Phase conjugate reflectivity of the photorefractive four-wave mixing system is usually quite unstable and it is serious issue for practical use of these systems. The cause of this instability is mainly combination of the fluctuation of the phases of input signal and pump beams and the slow response time of the photorefractive crystal. When all input beams in the four-wave mixing system are mutually coherent and the phases of the input beams are not stable, four kinds of gratings are compete each other and the phase conjugate output becomes quite unstable. To avoid this problem, we can make one of the pump incoherent to the signal and another pump1. The phase conjugate output is, however, still unstable due to the rewriting of the grating caused by the fluctuation of the phase of the input beams. In this paper, we report our feedback system to stabilize the power of the phase conjugate output from the four-wave mixing system by controlling the phase of the signal beam. In this system, we detect the phase difference between signal and forward pump beam with lock-in amplifier and control the phase of the signal with a piezoelectric mirror to stabilize the phase difference.
The effects of linear absorption on the degenerate and nondegenerate self-oscillation of a photorefractive phase-conjugate mirror under condition of anisotropic four-wave mixing are considered. The phase conjugation results from nonlinear mixing of two strong undepleted orthogonally polarized counterpropagating pump waves with a probe wave. We consider two types of situation for orthogonally polarized pump beams corresponding to two crystal families: one such as the Bi12SiO20 crystal family (sillenite family) and the other such as the BaTiO3 and strontium barium niobate crystal family. In both of these crystal families the degenerate and nondegenerate self-oscillations are shown to occur in the presence of linear absorption, which tends to increase the value of the coupling coefficient required for self-oscillation. Numerical results are presented that exhibit various features of degenerate and nondegenerate self-oscillation in both crystal families for different values of the phase ϕb of the backward grating.