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北海道大學工學部研究報告 = Bulletin of the Faculty of Engineering, Hokkaido University

Properties of Forward Phase Conjugation by Nearly Degenerate Four Wave Mixing with Boxcar Type Phase-Matching

Teruhito Mishima, Tsugumu Hon-ma, Shinji Sasade

Published Nov 29, 1990• 0 citations
OpenAlex

Abstract

Coupled wave equations are derived and solved for analyzing properties of forward phase conjugation by nearly degenerate four wave mixing with boxcar type phase-matchin．p ． The properties are discussed in conjunction with incident angles， polarization directions of the waves and frequency detuning．

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A theoretical description for a forward degenerate four-wave mixing process in homogeneously broadened two-level absorbers with arbitrary intensities of all four beams is presented. Assuming no pump absorption and depletion, we obtain an analytical solution of forward degenerate four-wave mixing signal intensity in the limit of the strong pumps and weak probe and signal. In the case of low absorption or large detuning, this solution is shown to become equivalent to that of the phase-conjugate degenerate four-wave mixing derived by Abrams and Lind [Opt. Lett.2, 94 (1978)]. For arbitrary beam intensities and absorption parameters, the signal intensity is numerically calculated by solution of the coupled equations of complex wave amplitudes. Comparing the results of the numerical calculation with those of the analytical solution, we discuss the validity of using the analytical solution in practical experiments and show the saturation behavior that is due to the strong probe beam. The line shapes under the various ratios among the input beams and absorption parameters are also obtained and discussed.
Abstract The properties of the phase‐conjugate reflectivity are analyzed anew for the self‐pumped four‐wave mixing in which only the two waves, i.e., the forward pump wave and the probe wave, are incident on the photo‐refractive crystal and the phase‐conjugate wave of the forward pump wave is used as the backward pump wave. First, by means of a model in which a Cat‐type phase conjugator is placed outside the interaction region, the equation for the phase‐conjugate reflectivity of self‐pumped four‐wave mixing using a transmission grating is derived. Next, the numerical calculations have been used for the first time to determine the effects of the coupling strength, the probe ratio as the incident intensity ratio of the forward pump wave to the probe wave, and the reflectivity of the Cat‐type phase conjugator on the entire phase conjugate reflectivity. Since the equation describing the phase‐conjugate reflectivity has multiple solutions, the strict analysis of the equation shows that the phase‐conjugate reflectivity has multiple values. Further, the conditions for high phase‐conjugate reflectivity has been studied.