Theory of light scattering on a paraboloid of revolution

Detalhes bibliográficos
Ano de defesa: 2022
Autor(a) principal: Echeverry Naranjo, Camilo Eduardo
Orientador(a): Cesar, Carlos Lenz
Banca de defesa: Não Informado pela instituição
Tipo de documento: Dissertação
Tipo de acesso: Acesso aberto
Idioma: eng
Instituição de defesa: Não Informado pela instituição
Programa de Pós-Graduação: Não Informado pela instituição
Departamento: Não Informado pela instituição
País: Não Informado pela instituição
Palavras-chave em Português:
Luz - Espalhamento
Coordenadas parabólicas
Helmholtz, Equação de
Laguerre, Polinômios de
Link de acesso: http://www.repositorio.ufc.br/handle/riufc/68487
Resumo: A theory for light scattering on a paraboloid of revolution is developed by the use of Hertz vectors. The expansion of a scalar plane wave traveling on any direction was found in terms of separable functions which are solutions of the scalar Helmholtz equation. This result was used to find the expansion of plane waves and a focused field. The solution of the parabolic Helmholtz equation is expressed in terms of Laguerre functions similar to the solution of the hydrogen atom in parabolic coordinates. Many identities related to those functions are demonstrated including a multiplication theorem. A method for solving the boundary conditions is also presented in which the corresponding coefficients of the scattered and incident fields are calculated.
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spelling Echeverry Naranjo, Camilo EduardoCesar, Carlos Lenz2022-09-23T15:44:13Z2022-09-23T15:44:13Z2022ECHEVERRY NARANJO, C. E. Theory of light scattering on a paraboloid of revolution. 2022. 157 f. Dissertação (Mestrado em Física) - Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2022.http://www.repositorio.ufc.br/handle/riufc/68487A theory for light scattering on a paraboloid of revolution is developed by the use of Hertz vectors. The expansion of a scalar plane wave traveling on any direction was found in terms of separable functions which are solutions of the scalar Helmholtz equation. This result was used to find the expansion of plane waves and a focused field. The solution of the parabolic Helmholtz equation is expressed in terms of Laguerre functions similar to the solution of the hydrogen atom in parabolic coordinates. Many identities related to those functions are demonstrated including a multiplication theorem. A method for solving the boundary conditions is also presented in which the corresponding coefficients of the scattered and incident fields are calculated.Uma teoria para espalhamento de luz em um parabolóide de revolução é desenvolvida pelo uso de vetores Hertz. A expansão de uma onda plana escalar viajando em qualquer direção foi encontrada em termos de funções separáveis que são soluções da equação escalar de Helmholtz. Este resultado foi usado para encontrar a expansão de ondas planas e um campo focalizado. A solução da equação parabólica de Helmholtz é expressa em termos de funções de Laguerre semelhantes à solução do átomo de hidrogênio em coordenadas parabólicas. Muitas identidades relacionadas a essas funções são demonstradas incluindo um teorema de multiplicação. Um método para resolver as condições de contorno também é apresentado no qual os coeficientes correspondentes dos campos espalhado e incidente são calculados.Luz - EspalhamentoCoordenadas parabólicasHelmholtz, Equação deLaguerre, Polinômios deTheory of light scattering on a paraboloid of revolutioninfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisengreponame:Repositório Institucional da Universidade Federal do Ceará (UFC)instname:Universidade Federal do Ceará (UFC)instacron:UFCinfo:eu-repo/semantics/openAccessORIGINAL2022_dis_ceecheverrynaranjo.pdf2022_dis_ceecheverrynaranjo.pdfapplication/pdf2018223http://repositorio.ufc.br/bitstream/riufc/68487/7/2022_dis_ceecheverrynaranjo.pdfafa48c7d4be9d12e194b4d8fde15d90dMD57LICENSElicense.txtlicense.txttext/plain; charset=utf-82152http://repositorio.ufc.br/bitstream/riufc/68487/6/license.txtfb3ad2d23d9790966439580114baefafMD56riufc/684872022-09-23 12:45:14.51oai:repositorio.ufc.br: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Repositório InstitucionalPUBhttp://www.repositorio.ufc.br/ri-oai/requestbu@ufc.br || repositorio@ufc.bropendoar:2022-09-23T15:45:14Repositório Institucional da Universidade Federal do Ceará (UFC) - Universidade Federal do Ceará (UFC)false
dc.title.pt_BR.fl_str_mv Theory of light scattering on a paraboloid of revolution
title Theory of light scattering on a paraboloid of revolution
spellingShingle Theory of light scattering on a paraboloid of revolution
Echeverry Naranjo, Camilo Eduardo
Luz - Espalhamento
Coordenadas parabólicas
Helmholtz, Equação de
Laguerre, Polinômios de
title_short Theory of light scattering on a paraboloid of revolution
title_full Theory of light scattering on a paraboloid of revolution
title_fullStr Theory of light scattering on a paraboloid of revolution
title_full_unstemmed Theory of light scattering on a paraboloid of revolution
title_sort Theory of light scattering on a paraboloid of revolution
author Echeverry Naranjo, Camilo Eduardo
author_facet Echeverry Naranjo, Camilo Eduardo
author_role author
dc.contributor.author.fl_str_mv Echeverry Naranjo, Camilo Eduardo
dc.contributor.advisor1.fl_str_mv Cesar, Carlos Lenz
contributor_str_mv Cesar, Carlos Lenz
dc.subject.por.fl_str_mv Luz - Espalhamento
Coordenadas parabólicas
Helmholtz, Equação de
Laguerre, Polinômios de
topic Luz - Espalhamento
Coordenadas parabólicas
Helmholtz, Equação de
Laguerre, Polinômios de
description A theory for light scattering on a paraboloid of revolution is developed by the use of Hertz vectors. The expansion of a scalar plane wave traveling on any direction was found in terms of separable functions which are solutions of the scalar Helmholtz equation. This result was used to find the expansion of plane waves and a focused field. The solution of the parabolic Helmholtz equation is expressed in terms of Laguerre functions similar to the solution of the hydrogen atom in parabolic coordinates. Many identities related to those functions are demonstrated including a multiplication theorem. A method for solving the boundary conditions is also presented in which the corresponding coefficients of the scattered and incident fields are calculated.
publishDate 2022
dc.date.accessioned.fl_str_mv 2022-09-23T15:44:13Z
dc.date.available.fl_str_mv 2022-09-23T15:44:13Z
dc.date.issued.fl_str_mv 2022
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/masterThesis
format masterThesis
status_str publishedVersion
dc.identifier.citation.fl_str_mv ECHEVERRY NARANJO, C. E. Theory of light scattering on a paraboloid of revolution. 2022. 157 f. Dissertação (Mestrado em Física) - Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2022.
dc.identifier.uri.fl_str_mv http://www.repositorio.ufc.br/handle/riufc/68487
identifier_str_mv ECHEVERRY NARANJO, C. E. Theory of light scattering on a paraboloid of revolution. 2022. 157 f. Dissertação (Mestrado em Física) - Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2022.
url http://www.repositorio.ufc.br/handle/riufc/68487
dc.language.iso.fl_str_mv eng
language eng
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.source.none.fl_str_mv reponame:Repositório Institucional da Universidade Federal do Ceará (UFC)
instname:Universidade Federal do Ceará (UFC)
instacron:UFC
instname_str Universidade Federal do Ceará (UFC)
instacron_str UFC
institution UFC
reponame_str Repositório Institucional da Universidade Federal do Ceará (UFC)
collection Repositório Institucional da Universidade Federal do Ceará (UFC)
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