Reinforcement and backpropagation training for an optical neural network using self-lensing effects

The optical bench training of an optical feedforward neural network, developed by the authors, is presented. The network uses an optical nonlinear material for neuron processing and a trainable applied optical pattern as the network weights. The nonlinear material, with the applied weight pattern, modulates the phase front of a forward propagating information beam by dynamically altering the index of refraction profile of the material. To verify that the network can be trained in real time, six logic gates were trained using a reinforcement training paradigm. More importantly, to demonstrate optical backpropagation, three gates were trained via optical error backpropagation. The output error is optically backpropagated, detected with a CCD camera, and the weight pattern is updated and stored on a computer. The obtained results lay the ground work for the implementation of multilayer neural networks that are trained using optical error backpropagation and are able to solve more complex problems.