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IEEE Journal of Quantum Electronics

Analytical theory of four-wave stimulated Brillouin scattering in the saturation regime

Chun-Ching Shih

Published Sep 1, 1987• 5 citations
Publisher

Abstract

An analytical solution of the enhanced stimulated Brillouin scattering arranged in a four-wave mixing configuration is presented. The theory includes the effect of pump depletion and is able to demonstrate the reflectivity, efficiency, and field variations in the saturation regime.
DOI
10.1109/jqe.1987.1073530

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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.
We report on a theoretical and modeling study of self-pumped four-wave mixing in a Brillouin medium. A theoretical analysis gives expressions for the threshold intensity and for the steady-state reflectivity at small input intensities. Operation over a range of input intensities is also investigated by using a computer model that predicts that, for high input intensities, the conjugate can become unstable and oscillate chaotically in time. Experimentally we observe phase conjugation with an input threshold 25 times less than that required for phase conjugation by stimulated Brillouin scattering.
It has previously been shown that Brillouin enhanced four-wave mixing can lead to large phase conjugate reflectivities for moderate laser powers.1,2 However, in the geometry considered by previous workers the pumps have equal frequency and hence the conjugate signal is shifted in frequency with respect to the probe. We have conducted an experimental and theoretical study of Brillouin-enhanced four-wave mixing for the different case in which the two pump waves differ in frequency by twice the Brillouin frequency of the four-wave mixing medium, and in which the probe wave frequency is halfway between those of the pump waves. In this case, the phase conjugate wave has the same frequency as the probe. Reflectivities > 100 % have been measured. Experimental results are compared to those of a theory that includes the effects of phase mismatch, pump depletion, and the finite response time of the medium.
The equations for plane-wave steady-state propagation of n fields interacting via four wave processes in a Raman medium have been known since at least 1962. Complete analytic solutions have only been found for the process of harmonic generation. However, solutions have been obtained in the gain regime assuming zero pump depletion. Assuming all fields satisfy the phase matching condition we have found general analytic solutions to these equations. The solutions are complete in that they describe both pump deletion and saturation. Some example problems will be studied.
An experimental and theoretical investigation of a polarization-decoupled form of Brillouin-enhanced four-wave mixing (BEFWM) is undertaken. Analytical steady-state solutions are found and numerical simulations of the transient regime including pump depletion are made. Experimental investigations of the BEFWM process were carried out in the liquids acetone and CS/sub 2/. Reflectivities, greater than unity, are readily observed. The variation of the transient reflectivity as a function of pump intensities and frequency detuning is studied. In the case of CS/sub 2/ it is shown that the Kerr effect makes a significant contribution to the interaction and numerical simulations, including Kerr effects, to produce good agreement with the experimental results.>