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Physical review. B, Condensed matter

Degenerate multiwave mixing and phase conjugation in silicon

I. C. Khoo, Richard J. F. Normandin, T. H. Liu, R. R. Michael, Robert G. Lindquist

Published Oct 15, 1989• 17 citations

Abstract

We present a detailed theory and experiment on degenerate-multiwave-mixing-mediated beam amplification in the semiconductor silicon. The theory accounts for several important factors, such as coupling to higher-order diffractions, intensity-dependent self- and mutual-phase modulations, losses, phase matchings, intensity ratio among the input beams, etc. In the silicon case under study, involving the generation of electron-hole pairs by 1.06-\ensuremath{\mu}m laser pulses, the intensity-dependent absorption loss and the temporal and/or spatial intensity profile of the input laser beam are also explicitly accounted. The experimental results for probe-gain dependences on several parameters are in good agreement with the theory. The important role played by the side diffractions in mediating the amplification of the probe is also apparent in our experiment on phase conjugation of the probe beam, where a strong dependence of the phase-conjugation reflection on the pump- to probe-beam ratio is observed, similar to the probe-gain dependence.

DOI: 10.1103/physrevb.40.7759

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We present a detailed theory and experiment on degenerate-multiwave-mixing-mediated beam amplification in the semiconductor silicon. The theory accounts for several important factors, such as coupling to higher-order diffractions, intensity-dependent self- and mutual-phase modulations, losses, phase matchings, intensity ratio among the input beams, etc. In the silicon case under study, involving the generation of electron-hole pairs by 1.06-\ensuremath{\mu}m laser pulses, the intensity-dependent absorption loss and the temporal and/or spatial intensity profile of the input laser beam are also explicitly accounted. The experimental results for probe-gain dependences on several parameters are in good agreement with the theory. The important role played by the side diffractions in mediating the amplification of the probe is also apparent in our experiment on phase conjugation of the probe beam, where a strong dependence of the phase-conjugation reflection on the pump- to probe-beam ratio is observed, similar to the probe-gain dependence.

Recent experimental observation of large probe beam gain at moderate laser power in a Kerrlike nonlinear medium demonstrated the possibility of constructing a self-pump ring oscillator and phase conjugator. We present a detailed theory, based on experimental parameters, of the working principles of such multiwave mixing mediated devices. The theory accounts for the side diffractions, which are responsible for probe beam gain in a Kerrlike medium, and other relevant parameters such as noise, loss, phase modulation, intensity dependences, etc.

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.

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.

The theory of probe beam amplification via degenerate optical wave mixing in a Kerr medium is presented. This theory includes consideration of the self-phase modulation, two-wave mixing, and multiwave mixing terms in the coupled-wave equations. Both analytical solutions, under the assumptions of a nondepleted pump beam and a transparent Kerr medium, and numerical solutions with these assumptions removed are presented. Our solutions show that under certain conditions, phase matching can be satisfied and a high probe beam gain is possible, even for a zero phase shift between the refractive index and the intensity gratings.