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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Absolute instability of phase conjugation at four-wave mixing in SBS media

Michail G. Galushkin, Konstantin V. Mitin, A. M. Seryogin

Published Sep 10, 2010• 0 citations
Publisher

Abstract

For the phase conjugated wave at four-wave mixing at SBS the transient analytical solution is obtained. A rate of the reflected wave amplitude increasing and a range of values of coupled waves parameters in which time instability is most essential are determined. Conditions of attenuation of absolute instability influence on considered process of phase conjugation are noted.

DOI
10.1117/12.881833

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For the phase conjugated wave at four-wave mixing at SBS the transient analytical solution is obtained. A rate of the reflected wave amplitude increasing and a range of values of coupled waves parameters in which time instability is most essential are determined. Conditions of attenuation of absolute instability influence on considered process of phase conjugation are noted.
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Transient phase conjugation by degenerate four-wave mixing in saturable dyes is investigated theoretically and experimentally. Two special cases are examined: (1) the case in which two pump waves and a probe wave are simultaneously turned on and (2) the case in which the pump waves are turned on well before the incidence of the probe wave. For case (1) a peak appears in the transient reflectivity for high pump intensity, while for case (2) the reflectivity increases monotonically with time up to the steady-state value irrespective of the value of the pump intensity.
The phase-conjugate reflectivity produced by degenerate four-wave mixing in a Kerr medium in the Bragg scattering regime is shown to be unstable when the intensity of the external pump beams is greater than a threshold value that can be predicted analytically. Below this threshold, a single branch of the reflectivity curve is stable, eliminating any possibility for bistability. A numerical simulation indicates that the unstable regime is characterized by fast oscillations with a period related to the transit time in the nonlinear medium. A finite relaxation time of the nonlinearity eliminates the high-frequency oscillations but can increase the amplitude of the low-frequency components. The insertion of a phase-conjugate mirror into an optical cavity leads to an instability whose threshold can be evaluated analytically. The temporal evolution of the field intensity in the cavity is shown to change from a stable regime to periodic oscillations and then to quasi-periodic oscillations as the pump intensity is increased.
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.