This dissertation investigates the design of a quarter-wave polarization transformer and presents some options for a high-performance polarizer in both normally incident and obliquely incident cases. Then, a novel concept for investigating polarization transformation is presented. Based on this concept, the broad axial ratio bandwidth polarizer, composed by anisotropic and chiral media, is accomplished using genetic algorithm. For the normally incident case, we present some methods to eliminate the reflection for designing novel high-performance polarizer in two situations. The polarizers provide perfect linear-to-circular polarization transformation without insertion loss at the center frequency. Then, two novel designs are presented for a high-performance quarter-wave polarizer in the obliquely incident case. In these designs, the material parameters of uniaxial media can be arbitrary. The polarizer is achieved by using only one layer of the uniaxial anisotropic medium without conventional anti-reflection coatings because of the unique property of the oblique incidence. The polarizer can produce a perfect linear-to-circular polarization transformation without any insertion loss at the center frequency. The equivalent circuit concept is presented to study polarization transformations. This concept is more convenient when dealing with polarization transformation problems in multiple layers. The anisotropic medium and the chiral medium can be regarded as circuit elements. Specifically, we show that anisotropic media can be seen as transformers and chiral media as transmission lines. Once the equivalent circuits are determined, the microwave network theory can be used to investigate the polarization transformation. An example is used to demonstrate the transformation from the horizontally polarized wave to the circularly polarized wave employing the equivalent circuit concept. Based on the equivalents concept, we present broad axial ratio bandwidth quarter-wave polarizer composed of mutilayered uniaxial anisotropic media and chiral media using genetic algorithm. In our design, the constitutive parameters of materials can be arbitrary. This broadband polarizer can be realized through the adjustment of the thickness of materials. The nearly optimal and suitable thickness of each cell is determined by using a genetic algorithm. Two numerical examples with three and five cells are presented to validate the design. The axial ratio bandwidths of about 84.1% and 92.8% can be achieved, more than double the maximum theoretical bandwidth for the case of the single uniaxial anisotropic slab.

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<p>Domain decomposition method provides a solution for the very large electromagnetic</p><p>system which are impossible for single domain methods. Discontinuous Galerkin</p><p>(DG) method can be viewed as an extreme version of the domain decomposition,</p><p>i.e., each element is regarded as one subdomain. The whole system is solved element</p><p>by element, thus the inversion of the large global system matrix is no longer necessary,</p><p>and much larger system can be solved with the DG method compared to the</p><p>continuous Galerkin (CG) method.</p><p>In this work, the DG method is implemented on a subdomain level, that is, each subdomain contains multiple elements. The numerical flux only applies on the</p><p>interfaces between adjacent subdomains. The subodmain level DG method divides</p><p>the original large global system into a few smaller ones, which are easier to solve,</p><p>and it also provides the possibility of parallelization. Compared to the conventional</p><p>element level DG method, the subdomain level DG has the advantage of less total</p><p>DoFs and fexibility in interface choice. In addition, the implicit time stepping is </p><p>relatively much easier for the subdomain level DG, and the total CPU time can be</p><p>much less for the electrically small or multiscale problems.</p><p>The hybrid of elements are employed to reduce the total DoF of the system.</p><p>Low-order tetrahedrons are used to catch the geometry ne parts and high-order</p><p>hexahedrons are used to discretize the homogeneous and/or geometry coarse parts.</p><p>In addition, the non-conformal mesh not only allow dierent kinds of elements but</p><p>also sharp change of the element size, therefore the DoF can be further decreased.</p><p>The DGTD method in this research is based on the EB scheme to replace the</p><p>previous EH scheme. Dierent from the requirement of mixed order basis functions</p><p>for the led variables E and H in the EH scheme, the EB scheme can suppress the</p><p>spurious modes with same order of basis functions for E and B. One order lower in</p><p>the basis functions in B brings great benets because the DoFs can be signicantly</p><p>reduced, especially for the tetrahedrons parts.</p><p>With the basis functions for both E and B, the EB scheme upwind </p><p>ux and</p><p>EB scheme Maxwellian PML, the eigen-analysis and numerical results shows the</p><p>eectiveness of the proposed DGTD method, and multiscale problems are solved</p><p>eciently combined with the implicit-explicit hybrid time stepping scheme and multiple</p><p>kinds of elements.</p><p>The EB scheme DGTD method is further developed to allow arbitrary anisotropic</p><p>media via new anisotropic EB scheme upwind </p><p>ux and anisotropic EB scheme</p><p>Maxwellian PML. The anisotropic M-PML is long time stable and absorb the outgoing</p><p>wave eectively. A new TF/SF boundary condition is brought forward to</p><p>simulate the half space case. The negative refraction in YVO4 bicrystal is simulated</p><p>with the anisotropic DGTD and half space TF/SF condition for the rst time with</p><p>numerical methods.</p> / Dissertation

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Ce travail de thèse consiste en l’étude de la mise en forme topologique de la lumière et de la matière et s’articule autour de deux axes de recherche. Le premier concerne la mise en forme topologique de la lumière à partir d’interfaces spin-orbite à base de cristaux liquides. En l’occurrence, nous montrons dans ce manuscrit que différents systèmes de défauts topologiques naturels permettent de générer des vortex optiques par interaction spin-orbite de la lumière, de manière efficace, accordable en longueur d’onde et reconfigurable en temps réel et donnant accès à des charges topologiques diverses. Tout ceci nous a permis de travailler à des échelles microscopiques et de manière spatialement contrôlée. Ces avancées ouvrent la voie au contrôle de l’état orbital de la lumière sur une large bande spectrale.Le second axe concerne la mise en forme topologique d’un film de cristal liquide cholestérique dans le cadre du stockage de l’information de nature topologique. Nous avons démontré la possibilité de générer une grande diversité de défauts topologiques métastables, de manière contrôlée et reconfigurable, à la fois dans le temps et dans l’espace. Nous avons développé une approche permettant de réduire drastiquement le coût énergétique d’écriture de ces défauts. Nous avons également montré qu’il était possible d’obtenir un nouveau type de mémoire réinscriptible contrôlé par le degré de liberté «spin» du photon. / The enclosed work deals with the study of the topological shaping of light and matter and will bedivided into two categories of research. The first focuses on the topological shaping of light from liquid-crystal based spin-orbit interfaces. In particular, we show in this manuscript, that different systems based on the use of natural topological defects behave as highly efficient natural optical spin-orbit encoders, for distinct topological charges, at the micron scale and with spatial control.The operating wave length and operation mode of such interfaces can be tuned in real-time using low voltage electric fields. This breakthrough opens the path to the ultra-broadband control of the light’sorbital state. The second category concerns the topological shaping of a cholesteric liquid crystal film in context of mass data storage. We show the potential to generate metastable topological mi-crostructures in a controlled and reconfigurable way, both in time and space and with a low energy cost. We also demonstrated a new, unique type of rewritable memory, controlled by the«spin»ofthe laser-generated incident photon

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[pt] Células de medição (MCs) são amplamente utilizadas na engenharia de micro-ondas para a caracterização eletromagnética dos materiais. Neste trabalho, apresentamos uma formulação baseada na técnica de casamento de modos (MMT) para a caracterização eletromagnética de MCs para materiais anisotrópicos uniaxiais. Apresentamos e validamos uma técnica para modelagem de MCs com uma e duas portas por meio da de matrizes de espalhamento generalizadas (GSMs) extraídas do MMT. Uma vez que as soluções fechadas (isto é, não numéricas) são usadas para calcular as integrais de acoplamento das GSMs, a presente abordagem é uma alternativa computacionalmente eficiente para modelar MCs quando comparada às técnicas usuais de força bruta numérica (tais como soluções baseadas em elementos, volumes, ou diferenças finitas). Um algoritmo de inversão também é apresentado para recuperar os parâmetros constitutivos de meios complexos (materiais com perdas e anisotrópicos). Diferentemente da maioria dos trabalhos que utilizam métodos semi-analíticos, a novidade do presente método consiste em considerar MCs com seção transversal grande frente ao comprimento de onda, em vários modos podem ser progagantes. Apresentamos uma série de resultados numéricos que mostram que a técnica de inversão apresentada neste estudo pode recuperar adequadamente os parâmetros constitutivos de um material de amostra, uma vez que os parâmetros de espalhamento da MC são conhecidos. / [en] Measurement cells (MCs) are widely used in microwave engineering for the electromagnetic characterization of materials. In this work, we present a mode-matching technique (MMT) formulation for the electromagnetic characterization of MCs for uniaxial anisotropic materials. We present and validate a technique for modeling MCs with one- and two-ports via generalized scattering matrices (GSMs) extracted from the MMT. Since closed-form solutions are used for computing the coupling integrals of the GSMs, the present approach is a computationally-efficient alternative to modeling MCs when compared to usual brutal-force techniques (such as finite-elements, finitevolumes, and finite-difference solutions). An inverse algorithm is also presented to retrieve the constitutive parameters of complex media (lossy and anisotropic materials). Differently from the majority of the works using semi-analytical methods, the novelty of the present method rely on considering overmoded MCs. We present a series of numerical results that show that the inversion technique presented herein can properly retrieve the constitutive parameters of a sample material once the MC scattering parameters are known.

[pt] Esta tese apresenta um estudo sobre técnicas de modelagem numérica utilizadas na análise da propagação eletromagnética em formações geofísicas comumente encontradas na perfuração de poços de petróleo. O emprego de sensores eletromagnéticos adjacentes à broca de perfuração permite a inferência dos parâmetros constitutivos do solo ao redor do poço. Nos últimos anos, os avanços da tecnologia de perfilagem eletromagnética permitiram a modelagem em tempo real do problema, possibilitando direcionar a perfuração do poço a fim de maximizar a exploração de petróleo, gás, e outros hidrocarbonetos fósseis. Formações geofísicas complexas são predominantes neste tipo de problema, e geralmente são modeladas usando técnicas numéricas de força bruta como os métodos de diferenças finitas, dos elementos finitos ou dos volumes finitos. No entanto, estas técnicas têm um custo computacional relativamente alto em termos de memória e tempo de processamento. O avanço da tecnologia de perfilagem em tempo real requer abordagens mais eficientes. Neste trabalho nós empregamos o método do casamento de modos combinado com uma série de características positivas dos métodos pseudoanalíticos conhecidos na literatura para obter uma técnica inédita que permite analisar poços direcionais com estratificações radiais e longitudinais em formações geofísicas anisotrópicas. A técnica proposta permite modelar problemas ainda não explorados, mas com motivação tecnológica iminente, como a propagação eletromagnética ao longo de poços curvados e a perfuração em camadas inclinadas em relação ao eixo axial do poço. Nós apresentamos uma série de resultados de validação que demonstram que a técnica introduzida neste trabalho pode modelar de forma acurada e eficiente sensores de perfilagem eletromagnética usados na exploração de petróleo e gás. / [en] This research presents a study on numerical techniques to model the electromagnetic propagation in geophysical formations commonly encountered in oil well drilling. The employment of electromagnetic sensors surrounding the drill bit allows inferring the constitutive parameters of the soil around the well. In recent years, advances in electromagnetic logging technology have enabled the real-time modeling of this problem. In this way, the drilling direction can be guided in order to maximize the exploitation of oil, gas, and other fossil hydrocarbons. The complex geophysical formations that are prevalent in this type of problem can be effectively handled using brute-force numerical techniques such as finite-differences, finite-elements and finite-volumes. However, these techniques suffer from relatively high cost in terms of both computer memory and CPU time. The advancement of real-time logging technology demands approaches that are more efficient than purely numerical methods. In this work, we employ the mode-matching technique combining attractive features of the well-known pseudo-analytical approaches to obtain a new technique for analyzing directional well-logging tools in anisotropic formations with both radial and axial stratifications. The proposed technique allows to model problems not yet explored, but with a strong technological motivation, such as electromagnetic propagation along curved wells and drilling along inclined layers. We present a series of validation results showing that the novel technique introduced in this study can model accurately and efficiently electromagnetic logging sensors used in oil and gas exploration.

[pt] Muitos dispositivos e estruturas empregados para guiar ondas eletromagnéticas apresentam conformidade cilíndrica. Aplicações sensíveis de engenharia de micro-ondas e de dispositivos ópticos integrados empregam, muitas vezes, materiais não homogêneos, anisotrópicos e dissipativos, de modo que a pesquisa por modelos computacionais robustos e acurados é um tópico de notável interesse para a Engenharia Elétrica. Este trabalho apresenta uma técnica semianalítica para resolver problemas de valor de contorno associados a guias de onda cilíndricos, anisotrópicos e não homogêneos. Nossa metodologia permite modelar estruturas com camadas radiais, com anisotropia uniaxial, e com perdas. A solução proposta parte das equações de Maxwell para campos harmônicos no tempo, e emprega uma expansão modal em termos da série de Bessel-Fourier. Os autovalores associados ao problema são obtidos por meio do método do winding number, em que diversas abordagens para o cálculo das integrais de caminho no plano complexo são exploradas. Para analisar junções entre guias de ondas estratificados, empregamos a técnica de casamento de modos baseada na conservação da Reação dos campos. Nossa formulação é capaz de avaliar os efeitos da excitação e do acoplamento entre modos puros (TM, TE, e TEM) em guias de ondas homogêneos, bem como dos modos híbridos em estruturas complexas. Uma série de resultados numéricos são apresentados e mostram a capacidade da metodologia desenvolvida nesta pesquisa para caracterizar corretamente estruturas cilíndricas compostas por meios complexos (não homogêneos, anisotrópicos e dissipativos) de forma robusta e computacionalmente eficiente se comparado com outras técnicas convencionais de eletromagnetismo computacional. / [en] Many devices and structures used to guide electromagnetic waves are conformal with the cylindrical coordinates. Sensitive applications of microwave engineering and integrated optical devices often use non-homogeneous, anisotropic and dissipative materials, so that the research for robust and accurate computational models is a topic of remarkable interest for Electrical Engineering. This work presents a semi-analytical technique for solving boundary-value problems associated with cylindrical, anisotropic, and non-homogeneous waveguides. Our methodology allows us to model structures with radial layers, with uniaxial anisotropy, and with losses. The proposed solution starts from Maxwell s equations for time-harmonic electromagnetic fields and employs a modal expansion in terms of the Bessel-Fourier series. The eigenvalues associated with the problem are obtained using the winding number method, in which several approaches for calculating complex-plane contour integrals are explored in detail. In order to properly analyze the junctions between sections of stratified waveguides, we employ a mode-matching technique based on the conservation of the Reaction of the fields. Our formulation can handle the effects of excitation and coupling between pure modes (TM, TE, and TEM) in homogeneous waveguides, as well as hybrid modes in complex structures. A series of numerical results are presented and show the capacity of the methodology developed here to correctly characterize cylindrical structures composed of complex media (inhomogeneous, anisotropic, and dissipative) in a robust and computationally-efficient fashion if compared to other conventional computational electromagnetic techniques.