Abstract

Conventional multistage interconnection networks (MINs), such as omega networks, have space-variant interconnections. In this paper, we describe the designs of optical three-dimensional MINs based on different dilation structures of interconnection. The dilation interconnection preserves the spatial-invariant property. Such space-invariant interconnections are easy to implement in optics because they can he realized by simple space-invariant optical systems. Two basic parameters, degree and distance, can be used to precisely define a dilation structure. Degree represents the number of destinations to be connected, while distances indicate which neighboring nodes, in terms of physical distances, are to be linked. Optical three-dimensional MINs use three-dimensional free-space interconnections between nodes in a two-dimensional array. It is convenient to organize the two-dimensional array of nodes into rectangular (or square) mesh such that it can easily match a conventional rectangular coordinate system. A rectangular-dilation MIN for N nodes requires degree-9 dilation interconnections to maintain the log N routing stages, ranging from 0 to (log N - 1). The dilation distance in the kth stage is k. The destination-address bits are used for the routing in the corresponding stage as in the two-dimensional environment.

© 1990 Optical Society of America