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Journal of the Optical Society of America B

Origin of frequency shift and temporal instability in photorefractive self-pumped phase conjugators

Ping Xie, Peng‐Ye Wang, Jian-Hua Dai

Published Jul 1, 2000• 0 citations
Publisher

Abstract

The physical origin of frequency shift and dynamic instability in a photorefractive self-pumped phase conjugator is analyzed by use of four-wave mixing and multi-four-wave mixing. We show that the frequency shift and the instability result from the requirement of the maximal energy transfer between the interacting beams. Two examples of numerical results in a cat self-pumped phase conjugator are given, which are in good agreement with previous experimental results. A simple method is proposed to change an unstable phase-conjugate output to a stable one.

DOI
10.1364/josab.17.001182

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The physical origin of frequency shift and dynamic instability in a photorefractive self-pumped phase conjugator is analyzed by use of four-wave mixing and multi-four-wave mixing. We show that the frequency shift and the instability result from the requirement of the maximal energy transfer between the interacting beams. Two examples of numerical results in a cat self-pumped phase conjugator are given, which are in good agreement with previous experimental results. A simple method is proposed to change an unstable phase-conjugate output to a stable one.
When the phase-conjugate replica of an optical beam is generated by traditional four-wave mixing with external pumping beams, the frequency of the phase-conjugate beam is fixed by the frequencies of the three input beams. In self-pumped phase conjugation, there is only one input beam, and the frequency of the output beam is free to roam. In photorefractive materials, this frequency difference between the incident and output beams is typically a few hertz. We present a method for controlling this frequency shift in the self-pumped phase-conjugate mirror that uses a ring configuration1 in photorefractive barium titanate. We show that two-beam coupling of an additional control beam with either of the optical beams already present in the ring cavity can alter the frequency of the phase-conjugate beam. We show that the control beam can alter the nonreciprocal phase shift2 of light propagating around the ring and thereby alter the frequency of the phase-conjugate beam. We also calculate the magnitude and the sign of the expected frequency shift as a function of the intensity, direction, and frequency of this control beam.
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.
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.
We present theory and experiments to show that the efficiency of four-wave mixing in photorefractive materials can be enhanced by use of optical waves of slightly different frequencies. The optimum frequency shift scales inversely with the response time of the material. We show that the \ensuremath{\sim}1-Hz frequency shift previously observed in the output of a self-pumped phase conjugator that used photorefractive BaTiO3{\mathrm{O}}_{3}O3​ is the result of this inherent property of four-wave mixing.
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.