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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Stabilization of the phase conjugate reflectivity in photorefractive four-wave mixing

Tsutomu Shimura, Atsushi Nakamura, Kazuo Kuroda, Hiroyuki WAKIMOTO, Mikiro TSUKAKOSHI

Published Jan 1, 1996• 0 citations
Publisher

Abstract

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.

DOI
10.1364/cleo_europe.1996.ctuk40

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A typical method of generating phase conjugate light using photorefractive crystals is four-wave mixing. It is known that the phase conjugate reflectivity is multivalued in a steady state. In this paper, a time domain response analysis of four-wave mixing is carried out and the method for controlling the bistability of the phase conjugate reflectivity is described. First, a steady-state analysis of the four-wave mixing is carried out and the condition is derived for bistability of the phase conjugate reflectivity. Next, by using two different initial conditions, the time response analysis is carried out for the four-wave mixing. Under one of the conditions, no forward pump beam is incident before and after observation of the bistability for measurement of phase conjugate reflectivity. Under another condition, the forward pump is incident before observation of the bistability. The phase conjugate reflectivity is measured after this pump is cut off when a steady state is reached. For each case, the numerical calculations are carried out. It is shown for the first time that the bistability of the phase conjugate reflectivity can be controlled by the initial condition. Further, the temporal and spatial variations of the diffraction grating generated in the crystal are studied and the process of the phase conjugate reflectivity to exhibit bistability is clarified. © 1998 Scripta Technica, Electron Comm Jpn Pt 2, 81(2): 1–8, 1998

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Photorefractive Effects, Materials, and Devices•Jan 1, 1999•0 citations
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.
A typical method of generating phase conjugate light using photorefractive crystals is four-wave mixing. It is known that the phase conjugate reflectivity is multivalued in a steady state. In this paper, a time domain response analysis of four-wave mixing is carried out and the method for controlling the bistability of the phase conjugate reflectivity is described. First, a steady-state analysis of the four-wave mixing is carried out and the condition is derived for bistability of the phase conjugate reflectivity. Next, by using two different initial conditions, the time response analysis is carried out for the four-wave mixing. Under one of the conditions, no forward pump beam is incident before and after observation of the bistability for measurement of phase conjugate reflectivity. Under another condition, the forward pump is incident before observation of the bistability. The phase conjugate reflectivity is measured after this pump is cut off when a steady state is reached. For each case, the numerical calculations are carried out. It is shown for the first time that the bistability of the phase conjugate reflectivity can be controlled by the initial condition. Further, the temporal and spatial variations of the diffraction grating generated in the crystal are studied and the process of the phase conjugate reflectivity to exhibit bistability is clarified. © 1998 Scripta Technica, Electron Comm Jpn Pt 2, 81(2): 1–8, 1998
One of the typical methods to generate the phase-conjugate beam is four-wave mixing with a photorefractive crystal. It is known that the phase-conjugate reflectivity shows the bistability in some cases. Analyzing the temporal property of four-wave mixing, we offer a new method to control the bistable phase-conjugate reflectivity, and we perform an experiment of the bistability control by the method. An equation to obtain the threshold value of the coupling strength for showing the bistability is derived by a steady-state analysis of four-wave mixing, and the temporal property of four-wave mixing is studied with two different initial conditions that are used for letting the phase-conjugate reflectivity R converge to an off state (R=0) or to an on state (R>0). The initial condition for the converging off state is that the forward pump beam is turned off throughout. The condition for the converging on state is that the forward pump beam is turned on in advance, and after enough time passes, it is turned off. In both conditions, the backward pump beam and the probe beam continue to illuminate throughout. Whereas both optical arrangements are equivalent after setting up these initial conditions, each phase-conjugate reflectivity converges to different stationary values, R=0 and R>0. Besides, an experiment is performed and we actually control the bistability by this method. Furthermore, the temporal and the spatial variation of the refractive-index grating in the photorefractive crystal is investigated, and the process of the bistability is explained.
When the nonlinear effect of the crystal is strong in four-wave mixing using a photorefractive crystal, the generated phase conjugate light takes multiple values. In this paper, a new method of controlling the bistable values of the phase conjugate reflectivity, that is, the ratio of the phase conjugate beam to the probe beam, via the erase beam is proposed for use in four-wave mixing using the fanning beam generated in the crystal in place of the forward pump beam. It is extremely difficult to solve analytically the problem of four-wave mixing including the fanning beam. By means of a model in which a part of the probe beam is used for fanning and acts as the forward pump beam in the interaction region, the previous method of analysis for four-wave mixing can be used. First, a steady-state analysis of the phase conjugate reflectivity is carried out. It is shown that the phase conjugate reflectivity has bistable values as function of the intensity of the erase beam. Next, by time response analysis, the intensity of the erase beam is varied and the bistable values of the phase conjugate reflectivity are controlled. Finally, the theory is compared with experiments. © 2000 Scripta Technica, Electron Comm Jpn Pt 2, 83(6): 8–14, 2000
Phase-sensitive detection can be realized optically by using degenerate four-wave mixing in photorefractive materials. Phase-sensitive detectors or lock-in amplifiers use a reference-triggered phase-sensitive mixer followed by a time-integrating low-pass filter. Mixing the two signals gives sum- and difference-frequency outputs, and a low-pass filter extracts the difference frequency. The phase encoded in the photorefractive hologram relative to the reference beam provides the mixing, and the response time of photorefractive material provides the time integration. Correctly modulating only the phase of the reference beam at a period much shorter than the photorefractive response time eliminates the phase-conjugate beam. Then modulating the phase of the signal input beam in the same waveform, but at a slightly different frequency from the reference, produces an oscillating phase-conjugate intensity. When the modulation frequencies of the two beams are phase-locked, a stable phase-conjugate signal is obtained with an intensity determined by the relative phase shift. These optical phase-sensitive detection experiments agree with calculations from dynamic photorefractive theory for the phase-conjugate intensity.
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.