Exception to Causality of the Effective Refractive Index Function in Heterogeneous Media

[EN] Optical constants are generally assumed to be causal functions. Mathematically, causality manifest itself in the Kramers-Kronig (KK) relations that relate the real and imaginary part of physical parameters in stable systems. These relations are also widely used to retrieve optical constants. He...

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Autores: Báez-Chorro, Miguel Ángel|||0000-0003-3138-2147, Vidal, Borja|||0000-0002-0942-3259
Tipo de recurso: artículo
Fecha de publicación:2025
País:España
Institución:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/221402
Acceso en línea:https://riunet.upv.es/handle/10251/221402
Access Level:acceso abierto
Palabra clave:Scattering
Optical constants
Causality
Terahertz spectroscopy
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spelling Exception to Causality of the Effective Refractive Index Function in Heterogeneous MediaBáez-Chorro, Miguel Ángel|||0000-0003-3138-2147Vidal, Borja|||0000-0002-0942-3259ScatteringOptical constantsCausalityTerahertz spectroscopy[EN] Optical constants are generally assumed to be causal functions. Mathematically, causality manifest itself in the Kramers-Kronig (KK) relations that relate the real and imaginary part of physical parameters in stable systems. These relations are also widely used to retrieve optical constants. Here, we present a stable physical heterogeneous system that is macroscopically described by a noncausal effective refractive index. We find that elastic scattering in heterogeneous media where particles have a lower refractive index than the surrounding matrix, results in optical constants that are not connected through KK relations. A modification of KK relations for anticausal media is presented and simulations with established scattering theories, numerical full-field electromagnetic analysis and experimental evidence support the agreement of these relations. Therefore, this physical system, although having a causal impulse response, has noncausal optical constants. These results offer a new insight into causality and restrict its range of applications, showing that some stable physical media can be described by noncausal functions. It also opens new paths to shape the electromagnetic response of artificial materials.This work was supported in part by the Spanish Ministeriode Cienciae Innovacion-Agencia Estatal de Investigacion under Project PID2019-111339GBI00American Chemical SocietyEscuela Técnica Superior de Ingeniería de TelecomunicaciónDepartamento de ComunicacionesInstituto Universitario de Tecnología NanofotónicaAgencia Estatal de InvestigaciónUniversitat Politècnica de ValènciaRepositorio Institucional de la Universitat Politècnica de València Riunet20252025-05-13journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://riunet.upv.es/handle/10251/221402reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengAgencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PID2019-111339GB-I00 ENSANCHANDO LOS LIMITES DEL CONTROL DE CALIDAD CON THZopen accesshttp://purl.org/coar/access_right/c_abf2Reconocimiento (by)http://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/2214022026-06-13T07:49:27Z
dc.title.none.fl_str_mv Exception to Causality of the Effective Refractive Index Function in Heterogeneous Media
title Exception to Causality of the Effective Refractive Index Function in Heterogeneous Media
spellingShingle Exception to Causality of the Effective Refractive Index Function in Heterogeneous Media
Báez-Chorro, Miguel Ángel|||0000-0003-3138-2147
Scattering
Optical constants
Causality
Terahertz spectroscopy
title_short Exception to Causality of the Effective Refractive Index Function in Heterogeneous Media
title_full Exception to Causality of the Effective Refractive Index Function in Heterogeneous Media
title_fullStr Exception to Causality of the Effective Refractive Index Function in Heterogeneous Media
title_full_unstemmed Exception to Causality of the Effective Refractive Index Function in Heterogeneous Media
title_sort Exception to Causality of the Effective Refractive Index Function in Heterogeneous Media
dc.creator.none.fl_str_mv Báez-Chorro, Miguel Ángel|||0000-0003-3138-2147
Vidal, Borja|||0000-0002-0942-3259
author Báez-Chorro, Miguel Ángel|||0000-0003-3138-2147
author_facet Báez-Chorro, Miguel Ángel|||0000-0003-3138-2147
Vidal, Borja|||0000-0002-0942-3259
author_role author
author2 Vidal, Borja|||0000-0002-0942-3259
author2_role author
dc.contributor.none.fl_str_mv Escuela Técnica Superior de Ingeniería de Telecomunicación
Departamento de Comunicaciones
Instituto Universitario de Tecnología Nanofotónica
Agencia Estatal de Investigación
Universitat Politècnica de València
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Scattering
Optical constants
Causality
Terahertz spectroscopy
topic Scattering
Optical constants
Causality
Terahertz spectroscopy
description [EN] Optical constants are generally assumed to be causal functions. Mathematically, causality manifest itself in the Kramers-Kronig (KK) relations that relate the real and imaginary part of physical parameters in stable systems. These relations are also widely used to retrieve optical constants. Here, we present a stable physical heterogeneous system that is macroscopically described by a noncausal effective refractive index. We find that elastic scattering in heterogeneous media where particles have a lower refractive index than the surrounding matrix, results in optical constants that are not connected through KK relations. A modification of KK relations for anticausal media is presented and simulations with established scattering theories, numerical full-field electromagnetic analysis and experimental evidence support the agreement of these relations. Therefore, this physical system, although having a causal impulse response, has noncausal optical constants. These results offer a new insight into causality and restrict its range of applications, showing that some stable physical media can be described by noncausal functions. It also opens new paths to shape the electromagnetic response of artificial materials.
publishDate 2025
dc.date.none.fl_str_mv 2025
2025-05-13
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://riunet.upv.es/handle/10251/221402
url https://riunet.upv.es/handle/10251/221402
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Agencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PID2019-111339GB-I00 ENSANCHANDO LOS LIMITES DEL CONTROL DE CALIDAD CON THZ
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reconocimiento (by)
http://creativecommons.org/licenses/by/4.0/
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
Reconocimiento (by)
http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv American Chemical Society
publisher.none.fl_str_mv American Chemical Society
dc.source.none.fl_str_mv reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
instname:Universitat Politècnica de València (UPV)
instname_str Universitat Politècnica de València (UPV)
reponame_str RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
collection RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
repository.name.fl_str_mv
repository.mail.fl_str_mv
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