A continuous-time optical neural network

A description is given of the architecture and functioning of an all-optical, continuous-time recurrent neural network. The network is a ring resonator which contains a saturable, two-beam amplifier, two volume holograms, and a linear, two-beam amplifier. The saturable amplifier permits, through the use of a spatially patterned signal beam, the realization of an optical neuron array; the two volume holograms provide global network interconnectivity; and the linear amplifier supplies sufficient cavity gain to permit resonant, convergent operation of the network. Numerical solutions of the network equations of motion indicate that, for real-valued neural state vectors, the network functions in much the same way as either J.J. Hopfield´s continuous-time model (1984) or a continuous-time version of D.Z. Anderson and M.C. Erie´s BSB model (1987). For complex-valued neural state vectors, the network always converges to the dominant network attractor, thereby suggesting a paradigm for solving optimization problems in which entrapment by local minima is avoided.<>