Multistage optical interconnection architecture with the least possible growth of system size

Cataloged from PDF version of article.Multistage interconnection architectures can provide an arbitrary pattern of one-to-one connections between N input and N output channels. We show that bitonic multistage architectures, such as the Banyan architecture, result in the fundamentally least possible growth of system size with increasing N

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

Fractional Fourier transform as a tool for analyzing beam propagation and spherical mirror resonators

Cataloged from PDF version of article.The complex amplitude distributions on two spherical reference surfaces of given curvature and spacing are simply related by a fractional Fourier transform. The order of the fractional Fourier transform is proportional to the Gouy phase shift between the two surfaces. This result provides new insight into wave propagation and spherical mirror resonators as well as the possibility of exploiting the fractional Fourier transform as a mathematical tool in analyzing such systems

Fractional Fourier transforms and their optical implementation: I

Cataloged from PDF version of article.Fourier transforms of fractional order a are defined in a manner such that the common Fourier transform is a special case with order a = 1. An optical interpretation is provided in terms of quadratic graded index media and discussed from both wave and ray viewpoints. Several mathematical properties are derived

Fractional Fourier Transforms and their optical implementation II

Cataloged from PDF version of article.The linear transform kernel for fractional Fourier transforms is derived. The spatial resolution and the space-bandwidth product for propagation in graded-index media are discussed in direct relation to fractional Fourier transforms, and numerical examples are presented. It is shown how fractional Fourier transforms can be made the basis of generalized spatial filtering systems: Several filters are interleaved between several fractional transform stages, thereby increasing the number of degrees of freedom available in filter synthesis

Every Fourier optical system is equivalent to consecutive fractional-Fourier-domain filtering

Cataloged from PDF version of article.We consider optical systems composed of an arbitrary number of lenses and filters, separated by arbitrary distances, under the standard approximations of Fourier optics. We show that every such system is equivalent to 1i2 consecutive filtering operations in several fractional Fourier domains and 1ii2 consecutive filtering operations alternately in the space and the frequency domains

Optical implementations of two-dimensional fractional Fourier transforms and linear canonical transforms with arbitrary parameters

Cataloged from PDF version of article.We provide a general treatment of optical two-dimensional fractional Fourier transforming systems. We not only allow the fractional Fourier transform orders to be specified independently for the two dimensions but also allow the input and output scale parameters and the residual spherical phase factors to be controlled. We further discuss systems that do not allow all these parameters to be controlled at the same time but are simpler and employ a fewer number of lenses. The variety of systems discussed and the design equations provided should be useful in practical applications for which an optical fractional Fourier transforming stage is to be employed. © 1998 Optical Society of Americ

Compact Optical Temporal Processors

Cataloged from PDF version of article.Optical signal processing can be done with time-lens devices. A temporal processor based on chirp-z transformers is suggested. This configuration is more compact than a conventional 4-f temporal processor. On the basis of implementation aspects of such a temporal processor, we did a performance analysis. This analysis leads to the conclusion that an ultrafast optical temporal processor can be implemented

Synthesis of mutual intensity distributions using the fractional Fourier transform

Cataloged from PDF version of article.Our aim in this paper is to obtain the best synthesis of a desired mutual intensity dis~but~on, by filtering in fractional Fourier domains. More specifically, we find the optimal fractional-domain filter that transforms a given (source) mutual intensity distribution into the desired one as closely as possible (in the minimum mean-square error sense). It is observed that, in some cases, closer approximations to the desired profile can be obtained by filtering in fractional Fourier domains, in comparison to filtering in the ordinary space or frequency domains

Convolution, filtering, and multiplexing in fractional Fourier domains and their relation to chirp and wavelet transforms

Cataloged from PDF version of article.A concise introduction to the concept of fractional Fourier transforms is followed by a discussion of their relation to chirp and wavelet transforms. The notion of fractional Fourier domains is developed in conjunction with the Wigner distribution of a signal. Convolution, filtering, and multiplexing of signals in fractional domains are discussed, revealing that under certain conditions one can improve on the special cases of these operations in the conventional space and frequency domains. Because of the ease of performing the fractional Fourier transform optically, these operations are relevant for optical information processing