Convergence properties of a neural optical resonator model for logic operations

The convergence of a neural network model based on optical resonator designs is examined for Boolean logic operations. Computer simulations are performed to investigate convergence performance and to assess possible optical implementations. The model is a simple and general mathematical formulation obtained using standard methods in which plane wave amplitudes and phases are specified at discrete times separated by the resonator period. The model is trained and tested as an associative memory neural network using an input state vector and a hologram matrix that evolves in time according to a set of coupled nonlinear difference equations. In general, these equations represent a high-order threshold logic, and the hologram matrix is a function of the outer product matrix of the evolving complex-element state vector. Model parameters are explored to provide insight on convergence mechanisms, robustness to input perturbations, and optimization of convergence times for both training and testing. The model is of interest for optical resonator designs that incorporate (1) dynamic holograms for massively parallel interconnection and storage functions and (2) nonlinear components such as phase conjugate mirrors (with thresholding and gain) for decision operations.2 These components are often incorporated into resonator loops to provide feedback and adaptation interactions. The neural