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...
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| Formato: | tesis doctoral |
| Estado: | Versión publicada |
| Fecha de publicación: | 2019 |
| País: | España |
| Recursos: | Universidad de Barcelona |
| Repositorio: | Dipòsit Digital de la UB |
| OAI Identifier: | oai:diposit.ub.edu:2445/148625 |
| Acesso em linha: | https://hdl.handle.net/2445/148625 http://hdl.handle.net/10803/668367 |
| Access Level: | acceso abierto |
| Palavra-chave: | El·lipsometria Polarització (Llum) Nanotecnologia Òptica Coherència (Òptica) Ellipsometry Polarization (Light) Nanotechnology Optics Coherence (Optics) |
| Resumo: | [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. |
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