Abstract

Quadratic polynomial equations of the form x^TAx arise in many applications ranging from optical interconnects for a quadratic neural network to the solution of least-squares fits and minimization problems. We have developed and demonstrated an optical processor for performing this quadratic equation using four-wave mixing in BaTiO₃. Since four-wave mixing provides a coherent multiplication of wavefronts, the processor can evaluate an N-dimensional vector-matrix-vector multiplication for both complex and real valued input data. Both the theory of operation plus experimental results of the processor (using an angular multiplexing of gratings) performing the tensor multiplication in a single crystal are also presented. This angular multiplexing architecture evaluates a complete layer of interconnects for a quadratic neural network in a single crystal. Experimental results obtained with this tensor processor are presented and discussed.

© 1989 Optical Society of America