Optical operations on wave functions as the Abelian subgroups of the special affine Fourier transformation

Title: Optical operations on wave functions as the Abelian subgroups of the special affine Fourier transformation
Authors: Abe, Sumiyoshi
Sheridan, John T.
Permanent link: http://hdl.handle.net/10197/3330
Date: 15-Nov-1994
Online since: 2011-11-22T16:49:56Z
Abstract: The special affine Fourier transformation (SAFT) is a generalization of the fractional Fourier transformation (FRT) and represents the most general lossless inhomogeneous linear mapping, in phase space, as the integral transformation of a wave function. Here we first summarize the most well-known optical operations on lightwave functions (i.e., the FRT, lens transformation, free-space propagation, and magnification), in a unified way, from the viewpoint of the one-parameter Abelian subgroups of the SAFT. Then we present a new operation, which is the Lorentz-type hyperbolic transformation in phase space and exhibits squeezing. We also show that the SAFT including these five operations can be generated from any two independent operations.
Funding Details: Other funder
Type of material: Journal Article
Publisher: Optical Society of America
Journal: Optics Letters
Volume: 19
Issue: 22
Start page: 1801
End page: 1803
Copyright (published version): 1994 Optical Society of America
Subject LCSH: Fourier transformations
Abelian groups
DOI: 10.1364/OL.19.001801
Other versions: http://dx.doi.org/10.1364/OL.19.001801
Language: en
Status of Item: Not peer reviewed
Appears in Collections:Electrical and Electronic Engineering Research Collection

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