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Journal of Applied Physics

Phase conjugation by degenerate four-wave mixing in a planar waveguide with a nonlinear cladding

Bao Xue Chen, Shunsuke Kobayashi

Published Sep 1, 1992• 6 citations
Publisher

Abstract

A novel analytical consideration is presented for dealing with phase conjugation by degenerate four-TE wave mixing in a planar waveguide bounded by a nonlinear cladding, in which both phase-conjugate power coupling and intensity-dependent field distributions are discussed. New wave solutions for signal and phase-conjugation reflections are obtained with anomalous power-dependent field distributions, and are used to specific numerical example based on a nematic liquid crystal.

DOI
10.1063/1.351691

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A novel analytical consideration is presented for dealing with phase conjugation by degenerate four-TE wave mixing in a planar waveguide bounded by a nonlinear cladding, in which both phase-conjugate power coupling and intensity-dependent field distributions are discussed. New wave solutions for signal and phase-conjugation reflections are obtained with anomalous power-dependent field distributions, and are used to specific numerical example based on a nematic liquid crystal.
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We derive an exact solution for both amplitude and phase of a signal that is back-reflected by collinear nonlinear degenerate mixing of four circularly polarized waves of arbitrary intensity in a Kerr-like medium. Our analysis suggests that taking pump depletion into account may spoil the ideal phase-conjugation condition, even in the limit of weak nonlinear coupling, and indicates that substantial deterioration of the probe phase-reversal property may occur for strongly interacting waves in a manner that is highly sensitive to the anisotropy of the nonlinear susceptibility.
We have derived an analytic expression for the intensity distribution of two counterpropagating waves of arbitrary input intensity in a saturable absorber. We use this distribution to extend the theory of degenerate four-wave mixing to include the effects of pump wave absorption. In particular, the spatial variation of the nonlinear absorption and coupling constants that appear in the coupled-amplitude equations for the probe and the signal (i.e., conjugate) waves are determined. These coupled-amplitude equations are solved numerically in a noniterative manner, leading to a prediction for the phase-conjugate reflectivity. The nature of the predictions differs qualitatively from those1,2 derived from theories that ignore pumpwave absorption, especially for the case of off-line-center excitation. At large values of the input pump intensities, the phase conjugate reflectivity can be larger than that predicted by theories that ignore pump-wave absorption.
The phase-conjugate field fidelity in backward-going four-wave mixing, based on the diffraction model solvable analytically, is investigated. The method assumes interaction of the non-depleted infinite plane pump waves with the spatially limited probe and signal waves inside the nonlinear medium. Solutions are obtained applying the Fourier transformation and the Green function technique under various boundary conditions for coupled wave equations. The probe and its phase-conjugate waves are defined by using a complex phase formulation including both the phase variation and amplitude modulation. It is shown that the analysed approach can involve assumptions leading to the ideal or distorted phase conjugation.
An analytic solution for the intensity distribution of two counterpropagating pump waves within a saturable absorber is derived. From this distribution, the spatial variation of the nonlinear absorption and coupling constants that appear in the coupled-amplitude equations for the probe and the signal (i.e., conjugate) waves are determined. These coupled-amplitude equations are solved numerically in a noniterative manner, leading to a prediction for the phase-conjugate reflectivity. The results of the exact theory are compared with those of previously published theories. It is found that at large values of the input-pump intensities, the predicted phase-conjugate reflectivity is larger when pump-absorption effects are included in the theory.