Optical Analog Solutions Of Partial Differential And Integral Equations

Abstract

Confocal feedback systems exist in a variety of forms and can solve a wide range of partial differential equations (PDEs) and integral equations (lEs). In this paper we describe several of these feedback systems and how they can be applied to provide optical analog solutions to PDEs of constant coefficients (e.g., diffusion, Poisson's, and wave equations), PDEs of variable coefficients (e.g., modified Helmholtz equations), three-dimensional PDEs, four-dimen-sional PDEs, and IEs (e.g., Fredholm and Volterra equations). The important advantage of obtaining the solutions by optical analog methods rather than digital methods is speed. The disadvantage is solution accuracy, although the accuracy obtainable with optical feedback is better than without feedback. To further improve solution accuracy, we suggest the replacement of simple spherical mirrors by Mangin mirrors and the incorporation of coherent image amplification by photorefractive crystals (e.g., BaTiO3 or BSO) in the confocal systems.