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Optics Letters

On the equality of stimulated Brillouin scattering reflectivity to conjugate reflectivity of a weak probe beam

Richard L. Abrams, Concetto R. Giuliano, Juan Francisco Lam

Published Mar 1, 1981• 18 citations
Publisher

Abstract

If a strong pump wave, with energy that is above threshold for stimulated Brillouin scattering, and a weak probe wave are incident into a nonlinear medium, then it has been shown by others that the reflectivity of the weak probe is equal to the reflectivity of the strong pump and that the probe is phase conjugated provided that the pump is phase conjugated. We present an analysis that predicts an exact equality of the reflectivities and identifies the parametric limitations.

DOI
10.1364/ol.6.000131

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Journal of the Optical Society of America B•Sep 1, 1989•11 citations
If a strong pump wave, with energy that is above threshold for stimulated Brillouin scattering, and a weak probe wave are incident into a nonlinear medium, then it has been shown by others that the reflectivity of the weak probe is equal to the reflectivity of the strong pump and that the probe is phase conjugated provided that the pump is phase conjugated. We present an analysis that predicts an exact equality of the reflectivities and identifies the parametric limitations.
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.
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.
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.