Abstract

Applications of photorefractive holography often entail optical beams that are modulated in both space and time. We present a matrix approach applicable to photorefractive problems for which the grating(s) attain a stationary state. A stationary state can arise, for example, when the beams are rapidly modulated in time compared with the photorefractive response time. The matrix approach treats a variety of apparently different problems in a uniform way, thus often effectively simplifying a problem. We present an analytical solution for complex-valued coupling coefficient for beams that vary temporally but not spatially. We believe that this solution has not previously appeared in the literature. The general case of temporally and spatially modulated beams has no analytical solution; nevertheless we show the spatial evolution of the beams within the medium is always such to maximize a single quantity. We also show that the evolution performs a binary sorting function. Numerical integration of the matrix equations is always straightforward so a numerical solution to any given problem can be had. Contrary to what one might expect from an abstract treatment, the matrix approach offers a great deal of physical insight into the nature of two-beam coupling, which we cast in geometrical terms.

© 2001 Optical Society of America