Holographic implementation of crossover networks

A crossover network is a variation of a multistage interconnection network. Its regular interconnection scheme is appropriate for optical implementation by space invariant systems. A crossover network requires two kinds of permutation called pass-through and crossover connections. One implementation of the crossover network uses different prism arrays in each path of a two-path imaging system.1 We propose here a holographic architecture, which can perform pass-through and crossover connections in a single path. The architecture is based on a Gabor-typo hologram. When the input illuminated by a collimated beam is imaged at a Gabor hologram plane (or the input is placed directly at the hologram plane) that has a focus F, it will propagate in two directions. The zero-order image array of the hologram arrives at the input plane of next stage without distortion after propagating a 2F distance. This performs the pass-through connection. At the same time, a first-order image array is diffracted by the hologram and focused at point F. After crossing over each other at F, the crossover connection can be performed at the input plane of next stage.