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Photorefractive Effects, Materials, and Devices

Why Light Beams Follow Curved Paths in Photorefractive Phase Conjugators

V. V. Eliseev, A. A. Zozulya, G. D. Bacher, Jack Feinberg

Published Jan 1, 1991• 0 citations
Publisher

Abstract

In recent years a variety of photorefractive phase conjugators have been demonstrated that rely on stimulated light beams.1-6 These self-pumped and mutually-pumped phase conjugators are all closely related7 and differ only in the number and angle of their input beams. Here we propose a detailed though necessarily simplistic description of how light beams spring up inside a photorefractive crystal, and why under some conditions these stimulated light beams appear to follow curved paths inside the crystal. We show that these curves are composed of a number of straight line segments which spring up by stimulated scattering in the photorefractive crystal.

DOI
10.1364/pmed.1991.mc12

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Stimulated photorefractive phase conjugators often exhibit well-defined curved beam paths that cannot be explained by simple beam fanning. We propose a model of these apparently curved paths as a series of straight-line segments, with beams propagating in both directions along these segments. These line segments spring from the amplification of scattered light between regions of the crystal already containing counterpropagating pump beams. As these line segments form, they create new interaction regions that generate new segments, thereby making the final beam path appear to be curved. Application of our model to a single-interaction-region mutually pumped phase conjugator shows that the threshold coupling strength required for the appearance of these new segments is only slightly higher than the threshold for the phase conjugator itself.

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Annual Meeting Optical Society of America•Jan 1, 1991•1 citation
In recent years a variety of photorefractive phase conjugators have been demonstrated that rely on stimulated light beams.1-6 These self-pumped and mutually-pumped phase conjugators are all closely related7 and differ only in the number and angle of their input beams. Here we propose a detailed though necessarily simplistic description of how light beams spring up inside a photorefractive crystal, and why under some conditions these stimulated light beams appear to follow curved paths inside the crystal. We show that these curves are composed of a number of straight line segments which spring up by stimulated scattering in the photorefractive crystal.
Stimulated photorefractive phase conjugators often exhibit well-defined curved beam paths that cannot be explained by simple beam fanning. We propose a model of these apparently curved paths as a series of straight-line segments, with beams propagating in both directions along these segments. These line segments spring from the amplification of scattered light between regions of the crystal already containing counterpropagating pump beams. As these line segments form, they create new interaction regions that generate new segments, thereby making the final beam path appear to be curved. Application of our model to a single-interaction-region mutually pumped phase conjugator shows that the threshold coupling strength required for the appearance of these new segments is only slightly higher than the threshold for the phase conjugator itself.
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.
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.
We identify three separate regimes in the evolution of self-pumped phase conjugation in photorefractive media. These are evident from the time evolution of transmission, omnidirectional scatter, and phase-conjugate reflection intensities measured experimentally. Initially, beam fanning occurs, manifested by depletion of the transmitted light to one-third of its initial value. This is followed by a gradual increase in the omnidirectional scatter intensity caused by spreading of the light paths in the crystal, until almost all the crystal is flooded. Only much later does the phase-conjugate beam appear and grow to half of the input intensity at the expense of both the transmitted and scattered light. The three processes persist for different durations: fanning is appreciably faster than the other two processes. Each regime is characterized by different beam spread within the crystal, which is observed in top-view images. We postulate physical mechanisms to describe the observed phenomena.
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.