Abstract

The need to solve eigenvector-eigenvalue equations for large size matrices offers optical processors the opportunity to take full advantage of their high speed and high degree of parallelism. A confocal Fabry-Perot processor (CFPP) with optical feedback is employed to solve the eigenvector- eigenvalue equation AX = λX, where A is a large size matrix with eigenvectors X and eigenvalues λ. The feedback loop contains an analog matrix-vector multiplier (AX) and a coherent image amplifier (g). With no input vector provided to the CFPP, the self-starting oscillating mode X dominates when it fulfills the processor equation gAX = X, thus the amplitude distribution associated with the oscillating mode or eigenvector can be obtained in real time. The image amplifier, which consists of a photorefractive crystal operating in a two-wave mixing configuration, provides high gain, large space-bandwidth product, and also exhibits the coherence restoration property necessary for good accuracy. The matrix-vector multiplier works on the inner product principles; real-time operation is achieved by utilizing a microcomputer-controlled display of the matrix on a liquid crystal spatial light modulator. In the presentation we discuss theoretical and experimental evaluation of the system, as well as the introduction of a photorefractive phase conjugator for phase distortion compensation for further improvement in solution accuracy.

© 1986 Optical Society of America