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Applied Optics

Cross-polarized photorefractive four-wave mixing with extraordinary writing beams and an ordinary reading beam

Yoshihisa Takayama, Atsushi Okamoto, Motoki Saito, Kunihiro Sato

Published May 10, 1998• 4 citations
Publisher

Abstract

In parallel-polarized photorefractive four-wave mixing the phase-matching condition can be achieved automatically if the pump beams are allowed to propagate in directions opposite to each other. However, in cross-polarized photorefractive four-wave mixing, the incident angles of the beams should be adjusted to maintain the phase-matching condition. We analyze the phase-matching properties of cross-polarized four-wave mixing with extraordinary writing beams and an ordinary reading beam and obtain the phase-conjugate reflectivity in consideration of phase mismatching. We also perform an experiment in which a phase-conjugate beam is generated in cross-polarized four-wave mixing and confirm the analyses.

DOI
10.1364/ao.37.002967

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In parallel-polarized photorefractive four-wave mixing the phase-matching condition can be achieved automatically if the pump beams are allowed to propagate in directions opposite to each other. However, in cross-polarized photorefractive four-wave mixing, the incident angles of the beams should be adjusted to maintain the phase-matching condition. We analyze the phase-matching properties of cross-polarized four-wave mixing with extraordinary writing beams and an ordinary reading beam and obtain the phase-conjugate reflectivity in consideration of phase mismatching. We also perform an experiment in which a phase-conjugate beam is generated in cross-polarized four-wave mixing and confirm the analyses.
We analyze the phase-conjugate reflectivity and the amplification property of cross-polarized four-wave mixing with a photorefractive BaTiO3 crystal in consideration of the pump-beam depletion. The coupled-wave equations of cross-polarized four-wave mixing with ordinary writing beams and an extraordinary reading beam are derived and solved with the grating-integral method. The results of calculations of the reflectivity and the amplification factors will be compared with the result under the undepleted-pumps approximation. In addition, to achieve high conversion efficiency, the optimum conditions for the intensity ratio and the angle configurations of the probe and pump beams are also discussed.
Summary form only given. Four-wave mixing with photorefractive crystals has been an active area, and cross-polarized four-wave mixing (CPFWM) has attracted much attention due to its advantage of efficient utilization of the phase conjugate beam. Recently, multi-valued phase conjugate reflectivity has been studied and its availability for optical applications such as optical memories and switches has been suggested, however the studies have been restricted to the case of parallel-polarized four-wave mixing, or even the existence of the multi-valued property of CPFWM has not been found so far. We prove the existence of multi-valued property of the phase conjugate reflectivity in CPFWM and reveal a threshold value of the coupling strength of beam interaction to turn it up. As a result, we show a method to control the threshold value and suggest the utilities of multi-valued property for optical applications.
The demonstration of optical phase conjugation in photorefractive materials has been accomplished by numerous methods, including i) externally-pumped four-wave mixing,1ii) self-pumped (passive) phase conjugation,24iii) stimulated backscattering,5,6and iv) mutually-pumped phase conjugation.7-10Stimulated backscattering and self-pumped phase conjugators have only a single incident beam. On the other hand, externally-pumped four-wave mixing has two auxiliary pumping beams in addition to the incident probe beam. Different still is the cross-conjugation of the two incident beams in mutually pumped phase conjugators. To use these conjugators in a given application, the compatibility between the processes generating the phase-conjugate wave(s) and the application must be considered. The distinguishing features of the different conjugators translate to advantages or disadvantages for certain applications.
A recent theory of polarization switching and beam amplification effect in Kerr-like media is extended to birefringent photorefractive crystals. In this class of material, the birefringence allows a new mechanism for coherent nonlinear mixing effects among the extraordinary and ordinary waves, leading to amplification and polarization switching effects. Analytic solutions of the parametric equations governing these interacting waves are solved for both the phase-matched and phase-mismatched geometries. The authors also present an experimental confirmation of the predicted polarization switching effect.>
Phase conjugate reflectivity of the photorefractive four-wave mixing system is usually quite unstable and it is serious issue for practical use of these systems. The cause of this instability is mainly combination of the fluctuation of the phases of input signal and pump beams and the slow response time of the photorefractive crystal. When all input beams in the four-wave mixing system are mutually coherent and the phases of the input beams are not stable, four kinds of gratings are compete each other and the phase conjugate output becomes quite unstable. To avoid this problem, we can make one of the pump incoherent to the signal and another pump1. The phase conjugate output is, however, still unstable due to the rewriting of the grating caused by the fluctuation of the phase of the input beams. In this paper, we report our feedback system to stabilize the power of the phase conjugate output from the four-wave mixing system by controlling the phase of the signal beam. In this system, we detect the phase difference between signal and forward pump beam with lock-in amplifier and control the phase of the signal with a piezoelectric mirror to stabilize the phase difference.