Multistability, chains, and cycles in optical multiwave mixing processes

We exhibit the information processing capabilities of the first few terms that arise in the amplitude expansion for resonant scattering in a medium with a delay nonlinearity (generalized volume hologram). We begin by showing how the physics of intensity dependent charge transport near a two-photon resonance gives both delayed quadratic and quartic nonlinearities. After reviewing the utility for matrix associative memories exhibited by the delayed quadratic nonlinearity (the ordinary Gabor hologram), we examine the role of the quartic nonlinearity, which is a fourth rank tensor. The symmetries of this tensor determine the information processing capabilities (via multilinear correlations) of the medium in an optical computing paradigm. We find multiple basins of stability, Jordan strings, and cycles as possible dynamic behaviors for the medium. We indicate how each corresponds to an information processing task: multiple basins to multiassociative memory, Jordan strings and cycles to chain and sequence memory and to group-invariant pattern recognition. We briefly indicate how branching processes may be implemented by the fourth rank mode-coupling tensor.