An optical analog of the neural networks involved in sensory processing consists of a dispersive medium with gain in a narrow band of wave numbers, cubic saturation, and a memory nonlinearity that may imprint multiplexed volume holographic gratings. Coupled-mode equations are derived for the time evolution of a wave scattered off these gratings; eigenmodes of the coupling matrix κ saturate preferentially, implementing stable reconstruction of a stored memory from partial input and associative reconstruction of a set of stored memories. Multiple scattering in the volume reconstructs cycles of associations that compete for saturation. Input of a new pattern switches all the energy into the cycle containing a representative of that pattern; the system thus acts as an abstract categorizer with multiple basins of stability. The advantages that an imprintable medium with gain biased near the critical point has over either the holographic or the adaptive matrix associative paradigms are (1) images may be input as noncoherent distributions which nucleate long-range critical modes within the medium, and (2) the interaction matrix κ of critical modes is full, thus implementing the sort of full connectivity needed for associative reconstruction in a physical medium that is only locally connected, such as a nonlinear crystal.
© 1986 Optical Society of America
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