Abstract

Outer product is an important operation in many signal processing systems. The optical implementation of the outer product has been investigated by many authors. A new optical implementation of outer product based on the phase mismatches of forward four-wave mixing is described. This new system is compact and can be used to perform the outer product of 2-D input vectors with a large number of resolution points. Amplitudes of optical waves can be multiplied if nonlinear optics is utilized. Degenerate forward four-wave mixing is due to the third-order nonlinear effect, and the synchronism condition for the above nonlinear mixing is given by k₄ = k₁ + k₂ – k₃, where k₁, k₂, and k₃ are, respectively, the wave vectors of the three incident plane waves, and k₄ is the wave vector of the generated optical wave. In our device, one element in the first input vector and another element in the second input vector are represented by two plane waves having wave vectors k₁, and k₂. By controlling the wave vector k₃, and thus utilizing the phase mismatches arising from the syschtonism condition, the optical outer product for any two input vectors is achieved.

© 1988 Optical Society of America