First-order optical systems with unimodular eigenvalues

It is shown that a lossless first-order optical system whose real symplectic ray transformation matrix can be diagonalized and has only unimodular eigenvalues is similar to a separable fractional Fourier transformer in the sense that the ray transformation matrices of the unimodular system and the s...

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Detalles Bibliográficos
Autores: Bastiaans, Martin J., Alieva Krasheninnikova, Tatiana
Tipo de recurso: artículo
Fecha de publicación:2006
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/51272
Acceso en línea:https://hdl.handle.net/20.500.14352/51272
Access Level:acceso abierto
Palabra clave:535
Fractional fourier-transforms
Integral transform
Implementation
Óptica (Física)
2209.19 Óptica Física
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repository_id_str
spelling First-order optical systems with unimodular eigenvaluesBastiaans, Martin J.Alieva Krasheninnikova, Tatiana535Fractional fourier-transformsIntegral transformImplementationÓptica (Física)2209.19 Óptica FísicaIt is shown that a lossless first-order optical system whose real symplectic ray transformation matrix can be diagonalized and has only unimodular eigenvalues is similar to a separable fractional Fourier transformer in the sense that the ray transformation matrices of the unimodular system and the separable fractional Fourier transformer are related by means of a similarity transformation. Moreover, it is shown that the system that performs this similarity transformation is itself a lossless first-order optical system. Based on the fact that Hermite-Gauss functions are the eigenfunctions of a fractional Fourier transformer, the eigenfunctions of a unimodular first-order optical system can be formulated and belong to the recently, introduced class of orthonormal Hermite-Gaussian-type modes. Two decompositions of a unimodular first-order optical system are considered, and one of them is used to derive an easy optical realization in more detail.Optical Society of AmericaUniversidad Complutense de Madrid20062006-08-0120062006-08-01journal articlehttp://purl.org/coar/resource_type/c_6501info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.14352/51272reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/512722026-06-02T12:44:21Z
dc.title.none.fl_str_mv First-order optical systems with unimodular eigenvalues
title First-order optical systems with unimodular eigenvalues
spellingShingle First-order optical systems with unimodular eigenvalues
Bastiaans, Martin J.
535
Fractional fourier-transforms
Integral transform
Implementation
Óptica (Física)
2209.19 Óptica Física
title_short First-order optical systems with unimodular eigenvalues
title_full First-order optical systems with unimodular eigenvalues
title_fullStr First-order optical systems with unimodular eigenvalues
title_full_unstemmed First-order optical systems with unimodular eigenvalues
title_sort First-order optical systems with unimodular eigenvalues
dc.creator.none.fl_str_mv Bastiaans, Martin J.
Alieva Krasheninnikova, Tatiana
author Bastiaans, Martin J.
author_facet Bastiaans, Martin J.
Alieva Krasheninnikova, Tatiana
author_role author
author2 Alieva Krasheninnikova, Tatiana
author2_role author
dc.contributor.none.fl_str_mv Universidad Complutense de Madrid
dc.subject.none.fl_str_mv 535
Fractional fourier-transforms
Integral transform
Implementation
Óptica (Física)
2209.19 Óptica Física
topic 535
Fractional fourier-transforms
Integral transform
Implementation
Óptica (Física)
2209.19 Óptica Física
description It is shown that a lossless first-order optical system whose real symplectic ray transformation matrix can be diagonalized and has only unimodular eigenvalues is similar to a separable fractional Fourier transformer in the sense that the ray transformation matrices of the unimodular system and the separable fractional Fourier transformer are related by means of a similarity transformation. Moreover, it is shown that the system that performs this similarity transformation is itself a lossless first-order optical system. Based on the fact that Hermite-Gauss functions are the eigenfunctions of a fractional Fourier transformer, the eigenfunctions of a unimodular first-order optical system can be formulated and belong to the recently, introduced class of orthonormal Hermite-Gaussian-type modes. Two decompositions of a unimodular first-order optical system are considered, and one of them is used to derive an easy optical realization in more detail.
publishDate 2006
dc.date.none.fl_str_mv 2006
2006-08-01
2006
2006-08-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/20.500.14352/51272
url https://hdl.handle.net/20.500.14352/51272
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Optical Society of America
publisher.none.fl_str_mv Optical Society of America
dc.source.none.fl_str_mv reponame:Docta Complutense
instname:Universidad Complutense de Madrid (UCM)
instname_str Universidad Complutense de Madrid (UCM)
reponame_str Docta Complutense
collection Docta Complutense
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.300724

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