Toward an optimal foundation architecture for optoelectronic computing. Part II. Physical construction and application platforms

Cataloged from PDF version of article.Various issues pertaining to the physical construction of systems that are based on regularly interconnected device planes, such as heat removal and extensibility of the optical interconnections for larger systems, are discussed. Regularly interconnected device planes constitute a foundation architecture that is reasonably close to the best possible as defined by physical limitations. Three application platforms based on the foundation architecture described are offered. © 1997 Optical Society of Americ

Repeated fractional Fourier domain filtering is equivalent to repeated time and frequency domain filtering

Cataloged from PDF version of article.Any system consisting of a sequence of multiplicative filters inserted between several fractional Fourier transform stages, is equivalent to a system composed of an appropriately chosen sequence of multiplicative filters inserted between appropriately scaled ordinary Fourier transform stages. Thus every operation that can be accomplished by repeated filtering in fractional Fourier domains can also be accomplished by repeated filtering alternately in the ordinary time and frequency domains

Toward an optimal foundation architecture for optoelectronic computing .1. Regularly interconnected device planes

Cataloged from PDF version of article.By systematically examining the tree of possibilities for optoelectronic computing architectures and offering arguments that allow one to prune suboptimal branches of this tree, I come to the conclusion that electronic circuit planes interconnected optically according to regular connection patterns represent an alternative that is reasonably close to the best possible, as defined by physical limitations. Thus I propose that this foundation architecture should provide a basis for future research and development in this area. © 1997 Optical Society of Americ

The fractional Fourier domain decomposition

Cataloged from PDF version of article.We introduce the fractional Fourier domain decomposition. A procedure called pruning, analogous to truncation of the singular-value decomposition, underlies a number of potential applications, among which we discuss fast implementation of space-variant linear systems. (c) 1999 Published by Elsevier Science B.V. All rights reserved

Space bandwidth product of conventional Fourier Transforming Systems

Cataloged from PDF version of article.It is shown that the space-bandwidth product of conventional "2f" Fourier transforming configurations can be increased without bound by increasing the diameter D and focal length fof the lens simultaneously to Docf 3/4. This results in spacebandwidth product growth ocf ~/2 and accompanying system linear extent growth ocf ~/4. These are derived by considering the validity of the Fresnel approximation, the thin lens approximation, and the effects of aberrations

Scaling of diffractive and refractive lenses for optical computing and interconnections

Cataloged from PDF version of article.We discuss both numerically and analytically how the space-bandwidth product and the information density of lenses scale as functions of their diameter and f-number over many orders of magnitude. This information may be useful for the design of optical computing and interconnection systems. For diffractive lenses, cost is defined as the number of resolution elements the lithographic production system must have; the relationship of this quantity to the space-bandwidth product and information density is also given

Optical-coordinate transformation methods and optical-interconnection architectures

Cataloged from PDF version of article.The analogy between optical one-to-one point transformations and optical one-to-one interconnections is discussed. Methods for performing both operations are reviewed and compared. The multifacet and multistage architectures have the flexibility to implement any arbitrary one-to-one transformation or interconnection pattern. The former would be preferred for low-cost and low-resolution applications, whereas the latter would be preferred for high-cost and high-performance applications

Interpolating between periodicity and discreteness through the fractional Fourier transform

Cataloged from PDF version of article.Periodicity and discreteness are Fourier duals in the same sense as operators such as coordinate multiplication and differentiation, and translation and phase shift. The fractional Fourier transform allows interpolation between such operators which gradually evolve from one member of the dual pair to the other as the fractional order goes from zero to one. Here, we similarly discuss the interpolation between the dual properties of periodicity and discreteness, showing how one evolves into the other as the order goes from zero to one. We also discuss the concepts of partial discreteness and partial periodicity and relate them to fractional discreteness and periodicity

Comparison of fully three-dimensional optical, normally conducting, and superconducting interconnections

Cataloged from PDF version of article.Several approaches to three-dimensional integration of conventional electronic circuits have been pursued recently. To determine whether the advantages of optical interconnections are negated by these advances, we compare the limitations of fully three-dimensional systems interconnected with optical, normally conducting, repeatered normally conducting, and superconducting interconnections by showing how system-level parameters such as signal delay, bandwidth, and number of computing elements are related. In particular, we show that the duty ratio of pulses transmitted on terminated transmission lines is an important optimization parameter that can be used to trade off signal delay and bandwidth so as to optimize applicable measures of performance or cost, such as minimum message delay in parallel computation. © 1999 Optical Society of Americ

Sampling and series expansion theorems for fractional Fourier and other transforms

Cataloged from PDF version of article.We present muchbriefer and more direct and transparent derivations of some sampling and series expansion relations for fractional Fourier and other transforms. In addition to the fractional Fourier transform, the method can also be applied to the Fresnel, Hartley, and scale transform and other relatives of the Fourier transform. (C) 2003 Published by Elsevier B.