Photorefractive two-beam coupling equations with multiple spatial-temporalfeatures: an SVD approach

We analyze the evolution of multi-feature two-beam coupling, wherein each b eam contains several spatial-temporal features (spatial patterns modulated by different signals), using a one-dimensional plane wave model to describe the evolution of paired components. This general scenario is of interest f or analyzing signal-processing applications of photorefractives, such as so urce-separation by orthogonalization of source-modulated spatial patterns. We use singular-value decomposition (SVD) to express each beam as a simple superposition of modes that are both temporally uncorrelated and spatially orthogonal. We find a solution that is a natural matrix generalization of t he scalar solution for simple two-beam coupling, and a test for its validit y: the two operators that give the spatial overlap associated with the temp oral basis signals in the two beams must commute. Equivalently, this means that the same set of signals must be modulating the SVD modes in the two be ams. Then the SVD modes are preserved in the two-beam coupling evolution, w ith only their amplitudes changing.