A Lagrangian Formulation For Optical Backpropagation Training In Kerr-Type Optical Networks

A training method based on a form of continuous spatially distributed optical error back-propagation is presented for an all optical network composed of nondiscrete neurons and weighted interconnections. The all optical network is feed-forward and is composed of thin layers of a Kerrtype self focusing/defocusing nonlinear optical material. The training method is derived from a Lagrangian formulation of the constrained minimization of the network error at the output. This leads to a formulation that describes training as a calculation of the distributed error of the optical signal at the output which is then reflected back through the device to assign a spatially distributed error to the internal layers. This error is then used to modify the internal weighting values. Results from several computer simulations of the training are presented, and a simple optical table demonstration of the network is discussed.