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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Amplification of amplitude modulated signals in a self-pumped photorefractive phase conjugator

Paul Michael Petersen, Preben Buchhave

Published Feb 1, 1991• 0 citations
Publisher

Abstract

The properties of a self-pumped photorefractive phase conjugator as an amplifier of amplitude modulated signal beams are investigated. In principle the crystal acts as a self-adjusting beam combiner which allows homodyne detection of the weaksignalbeam superimposed on a stronger reference beam. In our experiments the mixing takes placevia a four wave interaction process in the crystal. In this paperwe investigate the salient characteristics ofthe self-pumped phase conjugate amplifier and explain details of the beam interaction inside the ciystal.

DOI
10.1117/12.24566

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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)•Jan 1, 1996•0 citations
The properties of a self-pumped photorefractive phase conjugator as an amplifier of amplitude modulated signal beams are investigated. In principle the crystal acts as a self-adjusting beam combiner which allows homodyne detection of the weaksignalbeam superimposed on a stronger reference beam. In our experiments the mixing takes placevia a four wave interaction process in the crystal. In this paperwe investigate the salient characteristics ofthe self-pumped phase conjugate amplifier and explain details of the beam interaction inside the ciystal.
Two-wave mixing in photorefractive crystals has been shown to combine coherently a modulated optical signal beam with a strong pump optical field.’ For a phase-modulated signal beam, the induced index of refraction phase grating inside the crystal yields a coupling of the optical fields of the pump and signal so that subsequent intensity detection results in apparent intensity modulation of the transmitted signal or pump beams. This provides an easy way to detect phase differences between two optical beams. Some of the advantages the above scheme offers over commonly used coherent optical phase detection schemes are: no loss of 3 dB in the signal beam intensity at the 50/50 beam splitter (used to combine signal and local oscillator fields); automatic alignment of the index of refraction grating with the two incident optical wavefronts; insensitivity to slow random changes in the phases of both beams. Experimental results are given, and a new definition for the resulting mixing gain for the phase-modulated beam is introduced, through which optimal conditions for input beam intensity ratios can be found. Applications to coherent homodyne detection are discussed.
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.
While the interaction of optical beams in photorefractive crystals can often be accurately described in terms of 1-D plane-wave approximation, 2-D models are sometimes more suitable, as suggested by recent work.1 Here we discuss some aspects of photorefractive interaction of finite size optical beams. We have solved the system of partial differential equations governing two- and four-wave mixing numerically by using iterative procedures. Simulations of beam amplification in two-beam coupling show strong beam deformation even without any spatial information imposed on them. Spatially nonuniform energy transfer is responsible for this effect. The pump beam loses energy during propagation and at the end of its passage through the beam intersection region (which was completely inside the crystal) it is strongly depleted and cannot contribute significantly to beam amplification. As the pump beam crosses through the probe, it amplifies most strongly that side of the probe that it meets first. By the time the pump has reached the far side of the probe, it is strongly depleted and less effective at probe amplification. In the case of phase conjugation through four-wave mixing, we found that the conjugate beam is strongly deformed only when the coupling constant is negative (corresponding to deamplification of the probe input beam). For positive coupling constants the output conjugate beam is a good replica of the input probe beam.
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.
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.
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.