Optical Matrix-Vector Multiplication Using a Spatial Light Modulator and a Phase Conjugator

Abstract

A variety of optical matrix processing schemes [1, 2] use two-dimensional spatial modulation of optical intensity to represent a matrix to exploit the inherent parallel nature of optics. Such an approach typically requires the projection of a spatial pattern to match another pattern to perform the element-by-element multiplication. The basic incoherent matrix-vector multiplication scheme [3], for example, requires the use of anamorphic optics to project a linear array of sources (or a one dimensional spatial light modulator) to precisely match a two dimensional matrix masks. In the matrix-vector multiplication scheme using four-wave mixing in nonlinear media [4], simultaneous alignment of all the pixels of the matrix and vector is a major task, particularly for a large number of pixels. Misalignment of the pixels may lead to severe errors. For a given size of matrix mask, the density of elements increases as the dimension (N) of the matrix increases. As a result, the requirement on alignment becomes more and more stringent. In practice, the critical alignment required is likely to impose a practical limit on the optimum dimension of the matrix (N) to be of the order of one hundred or less depending on the specific architecture.