Optical design of programmable logic arrays
Alan Huang1988, Applied Optics
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Abstract
Regular free-space interconnects such as the perfect shuffle and banyan provided by beam splitters, lenses, and mirrors connect optical logic gates arranged in 2-D arrays. An algorithmic design technique transforms arbitrary logic equations into a near-optimal depth circuit. Analysis shows that an arbitrary interconnect makes little or no improvement in circuit depth and can even reduce throughput. Gate count is normally higher with a regular interconnect, and we show cost bounds. We conclude that regularly interconnected circuits will have a higher gate count compared with arbitrarily interconnected circuits using the design techniques presented here and that regular free-space interconnects are comparable with arbitrary interconnects in terms of circuit depth and are preferred to arbitrary interconnects for maximizing throughput. 1. Introduction All-optical digital computers have the potential for high speed, cheap communications, and massive parallelism. Logic gates based on nonlinear dielectric constants were investigated theoretically in the early 1960s by von Neumann. 1 In the last few years optical bistable devices, 2 ' 3 nonlinear Fabry-Perots, 4 ' 5 and hybrid electrooptic devices 6 have been studied experimentally. These results encourage development of architectures suitable for optics. Historically, two architectural approaches have dominated the field. One approach uses integrated optics to interconnect optical logic devices. A system designed with this approach is architecturally similar to a conventional computer, with logic gates connected in arbitrary configurations. This similarity means that an optical computer designed with this approach is worth building only if it can be made more cheaply or more powerful. An alternative approach makes use of 2-D arrays of devices interconnected in free space. This approach uses space-variant interconnects (provided by holograms) or space-invariant regular interconnects (provided by beam splitters). We prefer the space-invariant regular interconnect approach for simplicity, extensibility, and high throughput. To take advan
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