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IEEE Journal of Quantum Electronics

Fanning and photorefractive self-pumped four-wave mixing geometries

A. A. Zozulya

Published Jan 1, 1993• 28 citations

Abstract

Results of recent experimental and theoretical investigations on the role of fanning in the operation of several popular photorefractive self-pumped FWM geometries, including the double phase conjugate mirror (DPCM), the ring oscillator, the semilinear mirror, the system of two coupled DPCMs, and the total internal reflection (TIR) mirror, are presented. The results can be divided into two groups. Geometries of the first group (the DPCM and the ring oscillator) have soft excitation thresholds. Geometries of the second group (the semilinear mirror, the system of the two DPCMs and the TIR mirror) have hard excitation thresholds. Geometries of the first group experience a noticeable influence of fanning only when the level of fanning of a single pumping beam passing through a crystal, is high. Geometries of the second group, such as the semilinear mirror, the system of two DPCMs, and the TIR mirror without fanning, are not self-starting.>

DOI: 10.1109/3.199308

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Results of recent experimental and theoretical investigations on the role of fanning in the operation of several popular photorefractive self-pumped FWM geometries, including the double phase conjugate mirror (DPCM), the ring oscillator, the semilinear mirror, the system of two coupled DPCMs, and the total internal reflection (TIR) mirror, are presented. The results can be divided into two groups. Geometries of the first group (the DPCM and the ring oscillator) have soft excitation thresholds. Geometries of the second group (the semilinear mirror, the system of the two DPCMs and the TIR mirror) have hard excitation thresholds. Geometries of the first group experience a noticeable influence of fanning only when the level of fanning of a single pumping beam passing through a crystal, is high. Geometries of the second group, such as the semilinear mirror, the system of two DPCMs, and the TIR mirror without fanning, are not self-starting.>

Effects of stimulated photorefractive backscattering (SPB) interactions in both stimulated photorefractive backscattering and four-wave mixing (SPB-FWM) and total internal reflection (TIR) self-pumped phase conjugators have been analyzed theoretically. SPB interactions in the four-wave mixing regions are neglected. Calculations show that the operational threshold and the phase conjugation reflectivity of both phase conjugators are very sensitive to the backscattering two-wave mixing gain coefficient of the crystals. From these results the mechanism transition phenomenon of a self-pumped phase conjugator between SPB-FWM and TIR can be explained if the backscattering gain coefficient of the crystal varies with doping concentration or with wavelength.

The double phase-conjugate mirror (DPCM) is a stimulated four-wave mixing effect, mediated by either a chi(3) mechanism or a photorefractive effect. The type of grating that operates in the DPCM can be a transmission or reflection grating, depending on the wave-mixing configuration. Any combination of nonlinearity and grating geometry is possible, so that four general DPCM classes emerge. An analytic solution of the last unsolved class, the photorefractive reflection DPCM, is presented. With these results, general observations concerning the four categories of double phase conjugation are made. An important conclusion is that the type of grating geometry and its associated boundary conditions dictate many of the basic features of the DPCM, regardless of the nonlinearity involved.

The effects of linear absorption on the degenerate and nondegenerate self-oscillation of a photorefractive phase-conjugate mirror under condition of anisotropic four-wave mixing are considered. The phase conjugation results from nonlinear mixing of two strong undepleted orthogonally polarized counterpropagating pump waves with a probe wave. We consider two types of situation for orthogonally polarized pump beams corresponding to two crystal families: one such as the Bi12SiO20 crystal family (sillenite family) and the other such as the BaTiO3 and strontium barium niobate crystal family. In both of these crystal families the degenerate and nondegenerate self-oscillations are shown to occur in the presence of linear absorption, which tends to increase the value of the coupling coefficient required for self-oscillation. Numerical results are presented that exhibit various features of degenerate and nondegenerate self-oscillation in both crystal families for different values of the phase ϕb of the backward grating.

We present a plane-wave analysis of a recently demonstrated self-pumped phase conjugator. This device uses four-wave mixing to produce the phase-conjugate replica of an incident optical wave. All the waves are derived from the single incident wave: there are no externally supplied pumping beams. We consider the case of four-wave mixing in two interaction regions coupled by simple reflection. We calculate the phase-conjugate reflectivity as a function of coupling strength, taking into account imperfect coupling between the two interaction regions, and show that there is a threshold coupling strength below which the reflectivity is zero and above which the reflectivity is multiple valued. We also compute the coupling strength per unit length for a photorefractive crystal of barium titanate.