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

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dc.contributor.author Abe, Sumiyoshi
dc.contributor.author Sheridan, John T.
dc.date.accessioned 2011-11-22T16:49:56Z
dc.date.available 2011-11-22T16:49:56Z
dc.date.copyright 1994 Optical Society of America en
dc.date.issued 1994-11-15
dc.identifier.citation Optics Letters en
dc.identifier.issn 0146-9592 (print)
dc.identifier.issn 1539-4794 (online)
dc.identifier.uri http://hdl.handle.net/10197/3330
dc.description.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. en
dc.description.sponsorship Other funder en
dc.format.extent 327117 bytes
dc.format.extent 1072 bytes
dc.format.mimetype application/pdf
dc.format.mimetype text/plain
dc.language.iso en en
dc.publisher Optical Society of America en
dc.rights This paper was published in Optical Letters and is made available as an electronic reprint with the permission of OSA. The paper can be found at the following URL on the OSA website: http://www.opticsinfobase.org/abstract.cfm?URI=ol-19-22-1801. Systematic or multiple reproduction or distribution to multiple locations via electronic or other means is prohibited and is subject to penalties under law. en
dc.subject.lcsh Fourier transformations en
dc.subject.lcsh Abelian groups en
dc.title Optical operations on wave functions as the Abelian subgroups of the special affine Fourier transformation en
dc.type Journal Article en
dc.internal.availability Full text available en
dc.internal.webversions http://dx.doi.org/10.1364/OL.19.001801 en
dc.status Not peer reviewed en
dc.identifier.volume 19 en
dc.identifier.issue 22 en
dc.identifier.startpage 1801 en
dc.identifier.endpage 1803 en
dc.identifier.doi 10.1364/OL.19.001801
dc.neeo.contributor Abe|Sumiyoshi|aut| en
dc.neeo.contributor Sheridan|John T.|aut| en
dc.description.othersponsorship Futaba Electronics Memorial Foundation en
dc.description.othersponsorship European Commission en
dc.description.admin pe, la, sp, ke, is, en - TS 22.11.11 en

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