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Optics Letters

Critical slowing down of space-charge field relaxation in photorefractive sillenites

Boris I. Sturman, Evgeniy V. Podivilov, Henrik Chresten Pedersen, Per Michael Johansen

Published Aug 15, 1999• 2 citations
Publisher

Abstract

We propose a theoretical model for the recently reported anomalously long decay of a space-charge field that was resonantly excited in a photorefractive sillenite crystal [Phys. Rev. Lett. 79, 67 (1997)]. The model is based on the conventional concept of charge transfer and does not require excessively large values of the quality factor for space-charge waves. The effect in question is qualified as a critical slowing of the relaxation process as the threshold of optical oscillation is approached.

DOI
10.1364/ol.24.001163

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We propose a theoretical model for the recently reported anomalously long decay of a space-charge field that was resonantly excited in a photorefractive sillenite crystal [Phys. Rev. Lett. 79, 67 (1997)]. The model is based on the conventional concept of charge transfer and does not require excessively large values of the quality factor for space-charge waves. The effect in question is qualified as a critical slowing of the relaxation process as the threshold of optical oscillation is approached.
It is shown that when approaching the spatial subharmonics generation threshold in fast photorefractive crystals (the sillenites, CdTe), a practically unlimited (singular) amplification of the nonlinear photorefractive response is possible, which results in a drastic increase in the spatial amplification of weak signals. A theory of critical spatial amplification is developed. This theory takes into account real attributes of fast photorefractive crystals such as the vectorial nature of wave coupling and nonuniform broadening of resonances owing to light absorption. The theory is applied to the analysis of the observable characteristics of critical enhancement and to optimization of the conditions of experiments aimed at the detection and investigation of this phenomenon.
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.
It has been shown recently (see, e.g., Nature, 397, 594, 1999; 409, 490, 2001) that light pulses can be remarkably slowed down in resonant gases under very low temperatures. We show theoretically and experimentally that a similar in nature (and stronger in value) phenomenon occurs in photorefractive nonlinear media. The pulse-maximum velocity can be reduced here to the value of thickness/response time because of the two wave coupling effect. Specific properties of pulse propagation depend on the type of the photorefractive response and also duration and shape of the input pulse. Our theoretical results for the nonlocal nonlinear response are in a good agreement with experimental data obtained with BaTiO3 and Sn2P2S6 crystals.