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
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
Copyright (published version): 1994 Optical Society of America
Subject LCSH: Fourier transformations
Abelian groups
DOI: 10.1364/OL.19.001801
Language: en
Status of Item: Not peer reviewed
Appears in Collections:Electrical and Electronic Engineering Research Collection

Show full item record

SCOPUSTM   
Citations 1

142
Last Week
1
Last month
checked on Jun 22, 2018

Google ScholarTM

Check

Altmetric


This item is available under the Attribution-NonCommercial-NoDerivs 3.0 Ireland. No item may be reproduced for commercial purposes. For other possible restrictions on use please refer to the publisher's URL where this is made available, or to notes contained in the item itself. Other terms may apply.