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IEEE Journal of Quantum Electronics

High-efficiency scattering in transient Brillouin-enhanced four-wave mixing

A. Scott, M. S. Hazell

Published Aug 1, 1986• 41 citations
Publisher

Abstract

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.

DOI
10.1109/jqe.1986.1073135

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The theory of phase conjugation in laser amplifiers by saturable-gain degenerate four-wave mixing with copolarized beams is developed for pulses of arbitrary temporal shape and duration in the limit of a weak signal beam. The influence of the input pulse’s characteristics (energy, temporal pulse shape, duration) on the phase-conjugate reflectivity and on the conjugate pulse shape is analyzed. A sharp instantaneous peak of phase-conjugate reflectivity is predicted at high intensities of the four-wave mixing beams. This effect is experimentally demonstrated at λ0 = 1064 nm in a Nd:YVO4 amplifier pumped by a cw Ti:sapphire laser. A transient peak reflectivity of R ∼ 50% is thus obtained, corresponding to an enhancement of 1.6× compared with the maximum steady-state reflectivity. The experimental results and the theoretical predictions are in good agreement.

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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.
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.
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 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.
Brillouin enhanced four-wave mixing (BEFWM) is a judicious combination of SBS and FWM processes. Very high phase conjugate reflectivity (>106) has been reported. Various conditions have been presented that lead to these high reflectivities, but all those discussions are based on a single mode laser. Here we report the experimental results of BEFWM with a multimode laser. The laser mode spacing is 0.15 GHz, which is larger than the linewidth of the acoustic phonon (0.1 GHz), so we can neglect the gratings that are not resonant with the acoustic frequency. We observed that the phase conjugate reflectivity is smaller for the multimode pump. Assume there is no coupling between modes through BEFWM and each mode interacts with the nonlinear medium independently. It has been shown that the reflectivity will decrease as the input pump power decreases. Thus the reflectivity of a single mode pump is higher than the resultant reflectivity from a multimode pump. Further examination of the temporal profiles of the probe and phase conjugate pulses in the multimode case shows that the pulse modulation depth is decreased in the phase conjugate pulse.
The theory of phase conjugation in laser amplifiers by saturable-gain degenerate four-wave mixing with copolarized beams is developed for pulses of arbitrary temporal shape and duration in the limit of a weak signal beam. The influence of the input pulse’s characteristics (energy, temporal pulse shape, duration) on the phase-conjugate reflectivity and on the conjugate pulse shape is analyzed. A sharp instantaneous peak of phase-conjugate reflectivity is predicted at high intensities of the four-wave mixing beams. This effect is experimentally demonstrated at λ0 = 1064 nm in a Nd:YVO4 amplifier pumped by a cw Ti:sapphire laser. A transient peak reflectivity of R ∼ 50% is thus obtained, corresponding to an enhancement of 1.6× compared with the maximum steady-state reflectivity. The experimental results and the theoretical predictions are in good agreement.