Mathematical work on the foundation of Jones-Mueller formalism and its application to nano optics
[eng] Jones matrix and nondepolarizing Mueller matrix are the basic elements of the calculus of polarization optics. In this thesis we discus other forms that can be used to represent optical properties of deterministic systems. We investigate four different forms that we interpret as the states of...
| Autor: | |
|---|---|
| Tipo de recurso: | tesis doctoral |
| Estado: | Versión publicada |
| Fecha de publicación: | 2019 |
| País: | España |
| Institución: | Universidad de Barcelona |
| Repositorio: | Dipòsit Digital de la UB |
| OAI Identifier: | oai:diposit.ub.edu:2445/148625 |
| Acceso en línea: | https://hdl.handle.net/2445/148625 http://hdl.handle.net/10803/668367 |
| Access Level: | acceso abierto |
| Palabra clave: | El·lipsometria Polarització (Llum) Nanotecnologia Òptica Coherència (Òptica) Ellipsometry Polarization (Light) Nanotechnology Optics Coherence (Optics) |
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Mathematical work on the foundation of Jones-Mueller formalism and its application to nano optics |
| title |
Mathematical work on the foundation of Jones-Mueller formalism and its application to nano optics |
| spellingShingle |
Mathematical work on the foundation of Jones-Mueller formalism and its application to nano optics Kuntman, Ertan El·lipsometria Polarització (Llum) Nanotecnologia Òptica Coherència (Òptica) Ellipsometry Polarization (Light) Nanotechnology Optics Coherence (Optics) |
| title_short |
Mathematical work on the foundation of Jones-Mueller formalism and its application to nano optics |
| title_full |
Mathematical work on the foundation of Jones-Mueller formalism and its application to nano optics |
| title_fullStr |
Mathematical work on the foundation of Jones-Mueller formalism and its application to nano optics |
| title_full_unstemmed |
Mathematical work on the foundation of Jones-Mueller formalism and its application to nano optics |
| title_sort |
Mathematical work on the foundation of Jones-Mueller formalism and its application to nano optics |
| dc.creator.none.fl_str_mv |
Kuntman, Ertan |
| author |
Kuntman, Ertan |
| author_facet |
Kuntman, Ertan |
| author_role |
author |
| dc.contributor.none.fl_str_mv |
Arteaga Barriel, Oriol Canillas i Biosca, Adolf Universitat de Barcelona. Departament de Física Aplicada |
| dc.subject.none.fl_str_mv |
El·lipsometria Polarització (Llum) Nanotecnologia Òptica Coherència (Òptica) Ellipsometry Polarization (Light) Nanotechnology Optics Coherence (Optics) |
| topic |
El·lipsometria Polarització (Llum) Nanotecnologia Òptica Coherència (Òptica) Ellipsometry Polarization (Light) Nanotechnology Optics Coherence (Optics) |
| description |
[eng] Jones matrix and nondepolarizing Mueller matrix are the basic elements of the calculus of polarization optics. In this thesis we discus other forms that can be used to represent optical properties of deterministic systems. We investigate four different forms that we interpret as the states of deterministic optical systems. Vector state |h⟩ is the basic element of our formalism. Coherent parallel combination of deterministic optical systems can be most conveniently expressed as a linear combination of vector states. In other words, any nondepolarizing optical system can be considered as a coherent combination of other deterministic systems that serve as basis systems. Vector states are not suitable for representing serial combination of optical systems, because |h⟩ vectors cannot be multiplied as |h1⟩|h2⟩|h2⟩···. We observe that there exists a matrix state Z that mimics all properties of Jones matrices. Z matrices are also akin to the nondepolarizing Mueller matrices by the relation, M=ZZ∗. We show that Z matrices transform the Stokes matrix S into another Stokes matrix S′ according to the relation, S′=ZSZ†, where S corresponds to the Stokes vector |s⟩ and S′ corresponds to the transformed Stokes vector |s′⟩ (|s′⟩=M|s⟩). Z matrices also transform Stokes vectors, |s⟩ into complex vectors| ̃s⟩,| ̃s⟩=Z|s⟩. It can be shown that| ̃s⟩vectors bears the phase introduced by the optical system. We observe that |h⟩vectors and Z matrices are different representations of quatenion states h. Quaternion states can be added or multiplied to yield new quaternion states, therefore they are suitable for representing any coherent combination of deterministic optical systems. Z matrix and quaternion formulations are especially useful for describing the emergence of depolarization effects. But, density matrix approach is more convenient when we want to find the original constituents of a depolarizing Mueller matrix. Density matrices that associated with deterministic (pure) optical systems are defined in terms of |h⟩vectors as H=|h⟩⟨h|. A depolarizing Muller can be written as a convex sum of nondepolarizing Mueller matrices. The associated H matrix (density matrix of the mixture) can also be written as a convex sum of density matrices corresponding to the pure component systems. It can be shown that if there exists some knowledge about the anisotropy properties of component systems it is possible to find the nondepolarizing Mueller matrices of original constituents uniquely by means of the rank conditions of Hmatrices. Weapply our formalism to several phenomena. We study the interference effects in a Young’s double slit experiment with complete polarimetric methods. We show that our formalism can be useful for the analytic formulation of interacting dipole systems. We apply the vector state decomposition method to analyze plasmon hybridization, Fano resonances and circular effects in chiral and achiral geometries. |
| publishDate |
2019 |
| dc.date.none.fl_str_mv |
2019 |
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info:eu-repo/semantics/doctoralThesis info:eu-repo/semantics/publishedVersion |
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doctoralThesis |
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publishedVersion |
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https://hdl.handle.net/2445/148625 http://hdl.handle.net/10803/668367 |
| url |
https://hdl.handle.net/2445/148625 http://hdl.handle.net/10803/668367 |
| dc.language.none.fl_str_mv |
Inglés |
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Inglés |
| dc.rights.none.fl_str_mv |
(c) Kuntman,, 2019 info:eu-repo/semantics/openAccess |
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(c) Kuntman,, 2019 |
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openAccess |
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application/pdf |
| dc.publisher.none.fl_str_mv |
Universitat de Barcelona |
| publisher.none.fl_str_mv |
Universitat de Barcelona |
| dc.source.none.fl_str_mv |
Tesis Doctorals - Departament - Física Aplicada reponame:Dipòsit Digital de la UB instname:Universidad de Barcelona |
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Universidad de Barcelona |
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Dipòsit Digital de la UB |
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Dipòsit Digital de la UB |
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1869411886456373248 |
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Mathematical work on the foundation of Jones-Mueller formalism and its application to nano opticsKuntman, ErtanEl·lipsometriaPolarització (Llum)NanotecnologiaÒpticaCoherència (Òptica)EllipsometryPolarization (Light)NanotechnologyOpticsCoherence (Optics)[eng] Jones matrix and nondepolarizing Mueller matrix are the basic elements of the calculus of polarization optics. In this thesis we discus other forms that can be used to represent optical properties of deterministic systems. We investigate four different forms that we interpret as the states of deterministic optical systems. Vector state |h⟩ is the basic element of our formalism. Coherent parallel combination of deterministic optical systems can be most conveniently expressed as a linear combination of vector states. In other words, any nondepolarizing optical system can be considered as a coherent combination of other deterministic systems that serve as basis systems. Vector states are not suitable for representing serial combination of optical systems, because |h⟩ vectors cannot be multiplied as |h1⟩|h2⟩|h2⟩···. We observe that there exists a matrix state Z that mimics all properties of Jones matrices. Z matrices are also akin to the nondepolarizing Mueller matrices by the relation, M=ZZ∗. We show that Z matrices transform the Stokes matrix S into another Stokes matrix S′ according to the relation, S′=ZSZ†, where S corresponds to the Stokes vector |s⟩ and S′ corresponds to the transformed Stokes vector |s′⟩ (|s′⟩=M|s⟩). Z matrices also transform Stokes vectors, |s⟩ into complex vectors| ̃s⟩,| ̃s⟩=Z|s⟩. It can be shown that| ̃s⟩vectors bears the phase introduced by the optical system. We observe that |h⟩vectors and Z matrices are different representations of quatenion states h. Quaternion states can be added or multiplied to yield new quaternion states, therefore they are suitable for representing any coherent combination of deterministic optical systems. Z matrix and quaternion formulations are especially useful for describing the emergence of depolarization effects. But, density matrix approach is more convenient when we want to find the original constituents of a depolarizing Mueller matrix. Density matrices that associated with deterministic (pure) optical systems are defined in terms of |h⟩vectors as H=|h⟩⟨h|. A depolarizing Muller can be written as a convex sum of nondepolarizing Mueller matrices. The associated H matrix (density matrix of the mixture) can also be written as a convex sum of density matrices corresponding to the pure component systems. It can be shown that if there exists some knowledge about the anisotropy properties of component systems it is possible to find the nondepolarizing Mueller matrices of original constituents uniquely by means of the rank conditions of Hmatrices. Weapply our formalism to several phenomena. We study the interference effects in a Young’s double slit experiment with complete polarimetric methods. We show that our formalism can be useful for the analytic formulation of interacting dipole systems. We apply the vector state decomposition method to analyze plasmon hybridization, Fano resonances and circular effects in chiral and achiral geometries.[spa] En esta tesis discutimos otras formas que pueden usarse para representar las propiedades ópticas de los sistemas deterministas. Investigamos cuatro formas diferentes que interpretamos como los estados de los sistemas ópticos deterministas. El estado vectorial es el elemento central de nuestro formalismo. La combinación paralela coherente de sistemas ópticos deterministas puede expresarse más convenientemente como una combinación lineal de estados vectoriales. En otras palabras, cualquier sistema óptico no despolarizante puede considerarse como una combinación coherente de otros sistemas deterministas que sirven como sistemas básicos. Los estados vectoriales no son adecuados para representar una combinación en serie de sistemas ópticos. Observamos que existe un estado de matriz Z que imita todas las propiedades de las matrices de Jones. Las matrices de Z también contienen la misma información que las matrices de Mueller no despolarizantes. Las matrices Z también transforman vectores de Stokes en vectores complejos. Observamos que vectores h y matrices Z son diferentes representaciones de estados de cuaternión. Los estados de cuaternión se pueden agregar o multiplicar para producir nuevos estados de cuaternión, por lo tanto, son adecuados para representar cualquier combinación coherente de sistemas ópticos deterministas. La matriz asociada (matriz de densidad de la mezcla) también se puede escribir como una suma convexa de matrices de densidad correspondientes a los sistemas de componentes puros. Se puede demostrar que si existe algún conocimiento acerca de las propiedades de anisotropía de los sistemas de componentes, es posible encontrar las matrices de Mueller no despolarizantes de los componentes originales únicamente mediante las condiciones de rango de las matrices. Aplicamos nuestro formalismo a varios fenómenos, en particular estudiamos por ejemplo los efectos de interferencia en un experimento de doble rendija de Young con métodos polarimétricos completos. También demostramos que nuestro formalismo puede ser útil para la formulación analítica de sistemas dipolo interactivos. Finalmente, aplicamos el método de descomposición del estado vectorial para analizar la hibridación de plasmones, resonancias de Fano y efectos circulares en geometrías quirales y aquirales.Universitat de BarcelonaArteaga Barriel, OriolCanillas i Biosca, AdolfUniversitat de Barcelona. Departament de Física Aplicada2019info:eu-repo/semantics/doctoralThesisinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://hdl.handle.net/2445/148625http://hdl.handle.net/10803/668367Tesis Doctorals - Departament - Física Aplicadareponame:Dipòsit Digital de la UBinstname:Universidad de BarcelonaInglés(c) Kuntman,, 2019info:eu-repo/semantics/openAccessoai:diposit.ub.edu:2445/1486252026-05-27T06:46:51Z |
| score |
15,300724 |