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Physical Review A

Transient multiwave mixing in a nonlinear medium

Iam Choon Khoo, Ping Zhou

Published Feb 1, 1990• 17 citations
Publisher

Abstract

We present a detailed quantitative theory of transient multiwave mixing effects in a nonlinear medium produced by two incident coherent laser beams. Our theory accounts for all the relevant parameters such as laser pulse widths, medium response times, nonlinearities, interaction length, intensities, beam ratio, phase-modulation effects, losses, side diffractions, and explicitly shows how the dynamics and the multiwave mixing processes are interrelated with these parameters. The crucial role played by the diffracted beams and the time-dependent phase shifts among the beams and the interplay among the various intensity and index gratings are explicitly evaluated. In particular, the gain experienced by a weak incident probe beam via these mixing effects from the incident strong pump beam is investigated as a function of the aforementioned parameters.

DOI
10.1103/physreva.41.1544

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We present a detailed quantitative theory of transient multiwave mixing effects in a nonlinear medium produced by two incident coherent laser beams. Our theory accounts for all the relevant parameters such as laser pulse widths, medium response times, nonlinearities, interaction length, intensities, beam ratio, phase-modulation effects, losses, side diffractions, and explicitly shows how the dynamics and the multiwave mixing processes are interrelated with these parameters. The crucial role played by the diffracted beams and the time-dependent phase shifts among the beams and the interplay among the various intensity and index gratings are explicitly evaluated. In particular, the gain experienced by a weak incident probe beam via these mixing effects from the incident strong pump beam is investigated as a function of the aforementioned parameters.
We present a detailed general theory of multiwave mixing effects in a nonlinear medium produced by two incident coherent laser beams. Calculations are performed for localized as well as diffusive types of nonlinearities. The theory accounts for all the relevant parameters such as laser pulse widths, medium response times, nonlinearities, interaction length, intensities, beam ratio, phase modulation effects, losses, and side diffractions. The interrelationship between two- and multiwave mixing effects and the evolution of transient to stationary behavior is explicitly worked out. In particular, the gain experienced by a weak incident probe beam via these mixing effects is quantitatively analyzed as a function of the aforementioned parameters.
In a highly nonlinear thin film, the presence of the diffracted beams from the pump-probe-beam-induced refractive-index grating modifies considerably the energy coupling between the pump and the probe beams. Using coupled amplitude and phase equations, the roles of various factors such as phases and phase shifts, phase modulations, pump-beam intensity, intensity ratio, interaction length, and losses in the medium in the multiwave-mixing processes are clearly identified. We also present experimental results on the dependence of the probe gain on the pump-probe-beam ratio, the pump intensity, and on the interaction length, using a nematic liquid-crystal film as the nonlinear medium.
A systematic study of degenerate two-wave mixing in the stationary regime in thin nonlinear local-response media is presented. The model is based on the coherent interaction of four waves, the two incident beams, and the two main diffracted waves. Analytical results are obtained in all cases investigated under the assumption of weak-beam amplification. It is demonstrated that the energy transfer arises only from the forward degenerate four-wave mixing terms. In particular, the theoretical results show two new features: (1) the gain factor of the interaction is substantially reduced because of the phase change associated with the two-wave mixing terms and (2) a phase mismatch can compensate for this phase change, leading to an appreciable gain enhancement. Moreover, the general case is solved numerically. Particular attention is given to the influence of separate two-wave and forward degenerate four-wave mixing terms. Self-diffraction effects and the gain dependence versus the ratio of the pump-beam intensity to the signal-beam intensity are investigated.
Further theoretical observations and a new analysis of stationary degenerate and nearly degenerate optical wave mixing effects in a Kerr-like nonlinear medium are presented. The effects of phase modulations, beam ratio, intensity, wave mixing angle and frequency differences and other physical and optical parameters in multiwave mixing mediated probe gain and their application in ring oscillation devices are analyzed in detail. New experimental studies of the intensity and the angular dependence of the probe beam amplification and side diffractions in liquid crystal provide further insights into the phenomena.