Abstract

A new design methodology for constructing optical space-invariant hypercube interconnection networks for connection of a two-dimensional array of inputs to a two-dimensional array of outputs is presented. The methodology permits the construction of larger hypercube networks from smaller networks in a systematic and incremental fashion. It is shown that the proposed methodology greatly improves area utilization as compared with previous methods. An example network is provided that illustrates the proposed design method. Owing to their totally space-invariant nature, the resulting three-dimensional hypercube networks are highly amenable to optical implementations by use of simple optical hardware such as multiple-imaging components and space-invariant holographic techniques. We present a space-invariant optical implementation technique for the realization of such networks. A theoretical analysis of the physical limitations of the implementation method is also presented. The analysis indicates that two-dimensional arrays of 512 × 512 nodes interconnected in a hypercube (18-cube) topology could be implemented.

© 1993 Optical Society of America

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