Optical matrix-vector multiplication using four-wave mixing

Abstract

Optical four-wave mixing in nonlinear media can be employed to perform parallel matrix multiplication. In our approach, two of the input beams, each carrying a matrix information along the transverse dimensions, enter the medium and form an index grating. This grating contains information about the product of the matrix elements of these two matrices. The index grating is then read out by a reference beam. In the appropriate conditions, the diffracted beam consists of the integrated contribution from each part of the volume grating along the beam path and is proportional to the matrix product. In our experiments, transparencies were used to imprint the 5 × 5 matrix information onto the light beams. A photorefractive BaTiO3 crystal is placed at the common image plane of these transparencies. The multiplication of matrices or vectors was carried out via the degenerate four-wave mixing process inside the photorefractive crystal. This paper describes the new method and reports the first experimental demonstration of an all-optical matrix–vector multiplication in a photorefractive BaTiO3 crystal. The same technique can also be utilized to perform optical interconnection and logic operations.