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Journal of the Optical Society of America B

Parametric oscillation in photorefractive media

Henrik C. Pedersen, Per Michael Johansen

Published Jun 1, 1995• 24 citations
Publisher

Abstract

We present an analysis of what is called parametric oscillation in photorefractive media. It is shown theoretically that when a running grating and a constant electric field are applied to a photorefractive medium it is possible for two secondary gratings to grow spontaneously. These theoretical predictions are subsequently verified experimentally in the crystal Bi12SiO20, and excellent qualitative agreement is obtained. In previous subharmonic experiments, only grating vectors K/2, K/3, and K /4 were observed. Now, however, a whole continuum of grating vectors has been observed. Thus subharmonic generation in photorefractive materials is simply a special case of parametric oscillation in which the two secondary gratings are identical.

DOI
10.1364/josab.12.001065

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Optics Letters•Mar 1, 1985•123 citations
We present an analysis of what is called parametric oscillation in photorefractive media. It is shown theoretically that when a running grating and a constant electric field are applied to a photorefractive medium it is possible for two secondary gratings to grow spontaneously. These theoretical predictions are subsequently verified experimentally in the crystal Bi12SiO20, and excellent qualitative agreement is obtained. In previous subharmonic experiments, only grating vectors K/2, K/3, and K /4 were observed. Now, however, a whole continuum of grating vectors has been observed. Thus subharmonic generation in photorefractive materials is simply a special case of parametric oscillation in which the two secondary gratings are identical.
We present for the first time, to our knowledge, a theoretical analysis of the nonlinear dynamic space-charge field buildup when a photorefractive medium is exposed simultaneously to two running gratings. It is shown that the two gratings are nonlinearly coupled, hence, for an appropriate choice of parameters, the two gratings interact, causing one grating to be amplified at the expense of the other. This process is referred to as degenerate parametric amplification. In principle an infinite amplification is possible because, even in cases for which no signal grating (i.e., the one to be amplified) is externally seeded into the crystal, a finite signal-grating amplitude is obtained after relaxation of the amplification process.
We present a theoretical model of photorefractive parametric oscillation that covers, for the first time, to our knowledge, the occurrence of the whole spectrum of parametric processes from transversal over degenerate to longitudinal parametric oscillation. It is shown that inclusion of so-called noneigenwaves is essential for completing the model. We report on the first experiment that shows the transition from transversal over degenerate to longitudinal parametric oscillation. The experimental observations agree well with the theoretical predictions.
We demonstrate for the first time, to our knowledge, second harmonic optical phase conjugation, using the second spatial harmonics of a nonsinusoidal grating formed in a photorefractive material. The possibility of harmonic phase conjugation has been considered previously for artificial Kerr media.1 We have applied the same idea to barium titanate, since the existence of the higher-order gratings in this material has been known to us for some time. In our experiment, two 1.06-µm cw Nd:YAG laser beams wrote a grating in a poled photorefractive barium titanate crystal. Then a second harmonic of the YAG at 0.532 µm read out the grating in a counterpropagating direction to one of the writing beams. In this geometry, the usual Bragg condition is not satisfied. The reflectivity of the 0.532-µm signal was rather weak, ~0.01%, with ~0.1-mW reading beam power. The buildup time was around 3 s, with loosely focused writing beams with 50-mW power in each beam. The same experiment with a SBN crystal showed no significant harmonic phase conjugation. Finally, we stress that this effect is different from the previously published result.2
It has been shown experimentally1 that a subharmonic beam may appear spontaneously between two pump beams without detuning either of the beams when a field varying sinusoidally or in the form of a square wave is applied across the crystal. That work has now been extended to cover the rise of the subharmonics as a function of time and their dependence under stationary conditions on the ratio between the pump intensities. The experiments were done on photorefractive bismuth silicate crystals. A simple theory is found to describe well the repetition frequency at which the subharmonics appear.