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Soviet Journal of Quantum Electronics

Kinetics of the evolution of an absolute instability due to the Brillouin nonlinearity under four-wave mixing conditions

I Yu Anikeev, Dmytro Glazkov, Iosif G. Zubarev, С И Михайлов

Published Jun 30, 1991• 5 citations
Publisher

Abstract

A four-wave hypersonic phase-conjugate mirror was proposed and implemented to observe the evolution of an absolute instability under conditions of continuous variation of the wave mismatch δ k . Kinetic equations describing four-wave mixing under conditions of an absolute instability of counterpropagating reference waves are solved numerically taking into account the group delay effect. Strong modulation of all the waves at the exit from a medium of length L is predicted theoretically and observed experimentally when δ kL = 0. This disappears with increasing wave mismatch δ kL ≈ 2π. Estimates are obtained of the maximum theoretical sensitivity and the maximum reflection coefficient of the signal wave incident on such four-wave hypersonic phase-conjugate mirrors.

DOI
10.1070/qe1991v021n06abeh003910

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A four-wave hypersonic phase-conjugate mirror was proposed and implemented to observe the evolution of an absolute instability under conditions of continuous variation of the wave mismatch δ k . Kinetic equations describing four-wave mixing under conditions of an absolute instability of counterpropagating reference waves are solved numerically taking into account the group delay effect. Strong modulation of all the waves at the exit from a medium of length L is predicted theoretically and observed experimentally when δ kL = 0. This disappears with increasing wave mismatch δ kL ≈ 2π. Estimates are obtained of the maximum theoretical sensitivity and the maximum reflection coefficient of the signal wave incident on such four-wave hypersonic phase-conjugate mirrors.
We present a theoretical treatment of four-wave mixing (FWM) in a Brillouin-active medium for the case in which the pump waves differ in frequency by approximately twice the Brillouin frequency shift of the medium and in which the probe-wave frequency is approximately the arithmetic mean of the frequencies of the two pump waves. Under these conditions, the conjugate wave produced by the FWM process has the desirable property of being at the same frequency as the probe. We derive the coupled amplitude equations describing this interaction. We solve these equations analytically in the limit of negligible pump depletion and find that large phase conjugate reflectivities are readily achievable. The coupled amplitude equations are solved numerically for the general case, and it is found that large power transfer from the pumps to the output wave is possible. The output wave is shown to be a nearly perfect phase conjugate of the probe wave, even far into the regime where pump depletion effects are important. Our formalism predicts the existence of a parametric instability in the propagation of the pump waves, but good performance is predicted before the onset of this instability.
Four-wave mixing mediated by Brillouin scattering in the transient regime exhibits an instability which results in large phase conjugate reflectivities [A. M. Scott and K. D. Ridley, IEEE J Quantum Electron. QE-25, 438 (1989)]. In this paper we compare measurements of the threshold for the instability both as a function of the ratio of the second pump beam to the first pump beam and as a function of the phase mismatch. Phase conjugation in Brillouin enhanced four-wave mixing occurs through the interaction of a signal with two counterpropagating pump beams. In our experiments, the frequencies of all three input beams are different, and a small phase mismatch results. The magnitude of this mismatch was varied both by changing one of the input frequencies and the interaction length. The frequency of the second pump beam was changed by using stimulated Brillouin scattering in various mixtures. Thus we were able to vary the phase mismatch from four to thirteen resulting in a 50% change in the threshold intensity, in agreement with theoretical models. The ratio of the backward-to-forward pump beam intensities also affects the threshold, and measurements of this agree with the model.
We report on an investigation of Brillouin-enhanced four-wave mixing which provides phase conjugate reflectivities greater than 104. Theoretical modeling shows that the phase conjugate intensity grows with time until limited by pump depletion, and the main effect of varying the signal power is to increase the time delay before the conjugate beam reaches peak intensity. This is confirmed experimentally, and the maximum peak reflectivity is limited by the length of the laser pulses used in the experiment.
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.