Shuffle-equivalent interconnection topologies based on computer-generated binary-phase gratings

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Abstract
Several different shuffle-equivalent interconnection topologies that can be used within the optical link stages of photonic-switching networks are studied. These schemes include the two shuffle, the two banyan, and the segmented two shuffle, which can be used to interconnect two-input, two-output switching nodes. The schemes also include the four shuffle and the four banyan, which can be used to interconnect four-input, four-output switching nodes. (Note: The segmented two shuffle and the four banyan are novel interconnection topologies that were developed to satisfy some of the constraints of free-space digital optics). It is shown that each of these interconnection topologies can be implemented by the use of relatively simple imaging optics that contain space-invariant computer-generated binary-phase gratings. The effects of node type and interconnection topology on the laser power requirements and the optical component complexity within the resulting systems are also studied. The general class of networks known as extended generalized shuffle networks is used as a baseline for the analysis. It is shown that (2, 1, 1) nodes and (2, 2, 2) nodes connected by two-banyan interconnections can produce power-efficient and cost-effective systems. The results should help identify the architectural trade-offs that exist when a node type and an interconnection topology are selected for implementation within a switching system based on free-space digital optics.