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Journal of the Optical Society of America B

Photorefractive two-beam coupling with light of partial spatiotemporal coherence

Mark Cronin‐Golomb, Hongzhi Kong, Wieslaw Z. Krolikowski

Published Sep 1, 1992• 16 citations
Publisher

Abstract

The effect of partial spatiotemporal coherence in photorefractive two-beam coupling is studied theoretically and experimentally. Coupled-wave equations and a beam-propagation method are used to study the influence of coupling on the statistical properties of the beams. The spatial coherence is found to improve for amplified and to deteriorate for deamplified beams. A two-beam coupling experiment with light of reduced spatial coherence was performed with photorefractive barium titanate. Qualitative agreement between theory and experiment was obtained.

DOI
10.1364/josab.9.001698

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Journal of the Optical Society of America B•Dec 1, 1993•17 citations
The effect of partial spatiotemporal coherence in photorefractive two-beam coupling is studied theoretically and experimentally. Coupled-wave equations and a beam-propagation method are used to study the influence of coupling on the statistical properties of the beams. The spatial coherence is found to improve for amplified and to deteriorate for deamplified beams. A two-beam coupling experiment with light of reduced spatial coherence was performed with photorefractive barium titanate. Qualitative agreement between theory and experiment was obtained.
The slowing down of light pulses with backward-wave four-wave mixing is analyzed for photorefractive crystals with different coupling strengths. The conditions are found for which the delay of a phase-conjugate pulse decreases when the coupling strength increases and can even become negative, switching the pulse deceleration to acceleration. It is shown that for relatively low coupling strength the backward-wave four-wave mixing ensures a longer delay as compared to the two-beam-coupling technique. For coupling strengths tending to zero, the delay of long pulses approaches the response time of the medium. The conclusions of the theoretical analysis are confirmed experimentally with backward-wave four-wave mixing in barium titanate.
We show theoretically that the group velocity of light can be slowed down by means of phase coupling in the photorefractive two-wave mixing process. It is shown that the group velocity of light propagating in a photorefractive material could be significantly reduced because of a steep variation of the phase-coupling coefficient with respect to the angular frequency difference between two coupling beams in a two-wave mixing process. The results for the case of a photorefractive Bi12SiO20 crystal are presented and discussed in detail.
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.
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.