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Annual Meeting Optical Society of America

1.06-μm nanosecond laser amplifications via degenerate multiwave mixing in Si

I. C. Khoo, Richard J. F. Normandin, R. R. Michael, T. H. Liu, G. M. Finn

Published Jan 1, 1987• 0 citations
Publisher

Abstract

The process of degenerate four-wave and multiwave mixing in a nonlinear medium (with an intensity-dependent refractive index) is reexamined in the context of probe beam amplification and related phase conjugation. In general, such multiwave mixing processes (involving pump, probe, and various diffracted beams) require a self-consistent solution of several coupled Maxwell wave equations to explain and quantitatively fit the experimental observations with the theory.

DOI
10.1364/oam.1987.wr8

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The process of degenerate four-wave and multiwave mixing in a nonlinear medium (with an intensity-dependent refractive index) is reexamined in the context of probe beam amplification and related phase conjugation. In general, such multiwave mixing processes (involving pump, probe, and various diffracted beams) require a self-consistent solution of several coupled Maxwell wave equations to explain and quantitatively fit the experimental observations with the theory.
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.
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.
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 transient model of degenerate four-wave mixing in saturable amplifiers is developed for calculation of the phase-conjugate reflectivity in the weak-probe-beam limit. Our model takes into account the laser amplification of all the interacting beams together with the wave-mixing process between the two counterpropagating pump waves. Experimental investigations are made in a flash-lamp-pumped Nd:YAG amplifier with nanosecond pulses at 1.06 microm. A reflectivity of 22% is achieved when all the waves interfere within the laser medium.