Photorefractive Parallel Matrix-Matrix Multiplier Using a Mutually Incoherent Laser Array

Abstract

Wave mixing and holographic recording in photorefractive media have been used to perform parallel matrix-vector multiplication [1]. Although the technique can be extended to perform parallel matrix-matrix multiplication, the implementation requires critical alignment of the matrix elements. In this paper, we propose to demonstrate a novel technique to perform parallel matrix-matrix multiplication which uses the simultaneous formation of multiple gratings in a photorefractive crystal. The concept is shown in Fig. 1 where a simple example is used. The matrices to be multiplied are given by amn and bkl. While all the light sources shown in the figure are of the same nominal wavelength, each source differs from its neighboring source by some frequency δw which is chosen to satisfy δω ≫ 1/τ where τ is the photorefractive response time.