La tesis estudia cinco formulaciones del método de modos acoplados para analizar guías con medios magnéticos en su interior. La formulación indirecta, de tipo general, se ha aplicado al análisis de desfasadores toroidales obteniéndose resultados similares a los obtenidos mediante un método numérico puro como es el de diferencias finitas. La tesis introduce igualmente una formulación del método de adaptación que junto con el método de modos acoplados permite analizar discontinuidades simples. La combinación de los métodos anteriores con la matriz de dispersión generalizada ha permitido analizar discontinuidades en guías de onda con ferritas transversalmente magnetizadas con discontinuidades en las tres direcciones del sistema de coordenadas.

An efficient numerical analysis method for wavelength-scale and sub-wavelength-scale photonic structures is developed. It is applied to metal-clad nano-lasers and photonic crystal-based DBRs to calculate intrinsic losses (from open boundaries), and to photonic crystal-based waveguides to calculate intrinsic and extrinsic losses (due to fabrication errors). Our results show that a metal-clad surface plasmon-based laser in a cylindrical configuration requires more gain to lase than is available from a semiconductor gain region. However, the lowest order TE and HE guided modes exhibit less loss than the other modes, and hold the most promise for lasing. For photonic crystal-based structures, our matrix-free implementation of the planewave expansion method for calculating layer modes combined with mode-matching between layers using a few lower order modes is shown to be a computationally efficient and reliable method. This method is then used to introduce robust design concepts for designing photonic crystal-based structures in the presence of fabrication uncertainties. Accounting for fabrication uncertainties is shown to be particularly important in the regions of the device where the light exhibits very low group velocity (`slow light'). Finally, the modal discrimination properties of photonic crystal-based DBRs (Distributed Bragg Reflectors) are compared with the properties of conventional oxide-DBR combinations to analyze the contribution of out-of-plane diffraction losses to modal discrimination.

[pt] No processo de perfilagem de poços de petróleo e gás, as propriedades entre duas camadas axiais podem apresentar diferenças. Estas descontinuidades das propriedades algumas vezes trazem dificuldades na representação do comportamento dos campos electromagnéticos. Nas análises eletromagnéticas de perfilagem de poço de petróleo, o Método de Casamento de Modos (NMM) vem sendo utilizado a partir da combinação de técnicas numéricas com analíticas e da resolução das equações de Maxwell em meios heterogêneos, cujos campos eletromagnéticos, na direção axial, são representados via decomposição espectral, e, na direção radial, por meio de solução das equações diferenciais ordinárias. Assim, com o objetivo de explorar a representação dos campos eletromagnéticos sobre as interfaces axiais via NMM, este trabalho propõe a utilização de funções B-Splines cúbicas na expansão dos campos, na direção axial, bem como a incorporação da multiplicidade de nós, que permitem uma melhor representação do comportamento dos campos nas interfaces axiais. O algoritmo implementado foi validado nas suas diversas etapas ao comparar os autovalores da representação modal com os obtidos analiticamente em problemas canônicos, e os resultados finais comparados com exemplos apresentados na literatura e calculados com o Método de Diferenças Finitas no Tempo (FDTD). O método NMM, combinado às funções B-Splines cúbicas, foi aplicado a vários perfis de poços de petroléo que serviram de exemplo neste estudo. Um estudo comparativo mostrou que o uso das funções B-Splines cúbicas com multiplicidade dos nós sobre as descontinuidades permitiu uma redução no número total de nós nas expansões dos campos eletromagnéticos. / [en] In the logging process of gas and oil wells, differences in the properties between two axial layers can usually be found. These property discontinuities can bring difficulties for the representation of electromagnetic fields behavior. For electromagnetic analysis of well logging, the Numerical Mode-Matching - NMM method has been used. It combines numerical and analytical techniques, by solving equations Maxwell s in a heterogeneous media. There, the electromagnetic fields in the axial direction are represented by spectral decomposition and in the radial direction are represented by the solution of Ordinary Differential Equations (ODE). With the objective of explorer the representation of the electromagnetic fields on axial interfaces in the Numerical Mode Matched Method, this work explores the use of B-Splines cubic functions to expand the fields in the axial direction, as well as the incorporation of the multiple knots fetching to become the representation of fields behavior most optimized and realistic on axial interfaces. The NMM algorithm was implemented and it was validated by comparing the final results with those obtained by using Finite Difference Time-Domain – FDTD to analyse examples shown in the literature. To validate the results obtained for the eigenvalues, they were compared with the analytical solutions obtained for canonical configurations. The use of NMM Method combined with B-Spline cubic has been applied to several well profiles shown in the literature. The comparative study showed that the use B-Spline cubic with multiple knots near the discontinuities allows a reduction in the overall number of knots employed in the field expansion.

[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.

Le bruit tonal d’interaction rotor-stator, généré par l’impact des sillages issus des pales d’un rotorsur la grille d’aubes d’un stator redresseur, contribue de manière déterminante au bruit d’origineaérodynamique des turbomachines axiales carénées, qui équipent une large part des systèmes de propulsionaéronautique et de conditionnement d’air. La prédiction du bruit par l’utilisation de simulationsnumériques demeure onéreuse, notamment dans les premières phases de conception lorsque de nombreusesconfigurations doivent être testées. Dans cette optique, l’approche analytique choisie dans cettethèse apporte une alternative tout à fait appropriée. Les modèles analytiques basés sur une fonctionde réponse aéroacoustique de profil isolé ne permettent pas de reproduire l’effet de grille engendrépar le nombre important d’aubes de stator. Inversement, de fortes approximations sont nécessairespour décliner les fonctions de réponse de grilles d’aubes existantes dans des configurations tridimensionnelles.Le formalisme proposé, basé sur la méthode de raccordement modal, permet d’introduiresimplement l’effet de grille dans une géométrie annulaire d’étage rotor-stator. Un modèle de réponse degrille rectilinéaire bidimensionnel est tout d’abord présenté pour la transmission d’ondes acoustiques àtravers le stator ainsi que pour la génération de bruit par l’impact de rafales hydrodynamiques. Dansce cadre, une analyse linéaire et non visqueuse est considérée, pour laquelle les modes acoustique ettourbillonnaire d’un gaz sont couplés par le biais des frontières rigides. Les perturbations de vitessesliées aux sillages sont modélisées comme des rafales convectées. Leur impact sur la grille de statorgénère des ondes acoustiques se propageant en amont, en aval ainsi que dans les espaces inter-aubesdu stator, vu comme un réseau périodique de guides d’ondes. Les sections de bords d’attaque et defuite des aubes sont considérées comme des interfaces sur lesquelles la continuité des fluctuations depression, de vitesse axiale et de vorticité est vérifiée. Un système d’équations est ainsi obtenu, puisrésolu par des projections sur les bases modales du conduit et des inversions matricielles. Le champacoustique rayonné est ainsi déterminé uniformément dans tout le domaine. Les résultats issus de cesmodélisations sont comparés à ceux des fonctions de réponse de grilles d’aubes rectilinéaires issues dela littérature, montrant un très bon accord avec les modèles basés sur la technique de Wiener-Hopf. Leformalisme est par la suite étendu aux grilles annulaires par l’ajout de fonctions de Bessel comme fonctionsde forme radiale exprimant les effets tridimensionnels. Finalement, une procédure est présentéepour rendre compte de l’hétérogénéité des aubes de stator, caractéristique des nouvelles architecturesde turbomachines. Cette méthodologie est basée sur l’emploi conjoint du principe du dipôle de bordd’attaque et de la fonction de réponse aéracoustique de la grille de stator à l’aide de la technique deraccordement modal. Le principe de dipôle de bord identifie le chargement instationnaire des aubesinduit par l’impact de rafales hydrodynamiques, calculé par le formalisme d’Amiet, avec la trace duchamp de pression acoustique produit par un dipôle placé au voisinage du bord de l’aube. Les prédictionsissues de ce modèle, appliqué dans un cadre bidimensionnel, sont ensuite comparées à des mesuresobtenues pendant la campagne d’essais du projet SEMAFOR. / The rotor-stator wake-interaction tonal noise, generated by the impingement of rotor wakes onoutlet guide vanes, plays a crucial role in the aerodynamic noise of axial-flow ducted fan stages. Thelatter are widely used in most aeronautic propulsion and air-conditioning systems. The noise predictionby means of numerical simulations remains expensive, especially at the preliminary design stage whennumerous configurations must be tested. In this respect, the analytical approach chosen in this thesisprovides a well suited alternative. The analytical modeling based on an isolated-airfoil response functioncan not reproduce the cascade effect introduced by the large number of stator vanes. Conversely, drasticapproximations are required to extend the current cascade response functions to three-dimensionalconfigurations. The proposed modeling based on the mode-matching technique simply introduces thecascade effect in an annular rotor-stator stage. A rectilinear cascade response function is firstly presentedto account for the acoustic transmission through the stator along with the wake-interaction noise.In this context, a linearized and non-viscous analysis is carried out, in which the acoustic and vorticalmodes of a gas are coupled at rigid physical boundaries. The velocity perturbations issued from thewakes are written as a sum of convected gusts. Their impingement on the cascade of vanes generatesacoustic waves propagating upstream, downstream of the cascade, as well as inside the inter-vane channelsof the stator, seen as a periodic array of bifurcated waveguides. The duct cross sections at theleading-edge and the trailing-edge of the vanes are seen as interfaces on which the continuity of thefluctuating pressure, axial velocity and vorticity is fulfilled. A system of linear equations is obtained,then solved by means of modal projections and matrix inversions. The acoustic field is then uniformlycalculated in the whole domain. Comparisons with rectilinear cascade response functions show a verygood agreement with predictions based on the Wiener-Hopf technique. The configuration of an annularcascade is addressed by introducing the Bessel functions as radial shape functions, expressing threedimensionaleffects. Finally, a procedure is presented to account for the heterogeneity of the statorvanes, typical of modern fan architectures. This approach is based on the combinaison of the leadingedgedipole principle and the cascade response function derived from the mode-matching technique.The edge-dipole principle identifies Amiet’s solution for the unsteady loading and the radiation of adipole approached very close to the edge of a half plane. The predictions provided by this modeling,applied in a two-dimensional configuration, are finaly compared to measurements performed in the testcampaign of the SEMAFOR project.

L'objet de cette thèse porte sur la conception et la réalisation de deux sources laser non linéaires accordables dans les domaines IR et UV, pour le raccordement de la sensibilité spectrale des détecteurs au moyen du radiomètre cryogénique du laboratoire commun de métrologie (LCM). La source IR est un oscillateur paramétrique optique (OPO) résonant sur les ondes pompe et signal (PRSRO), utilisant un cristal de niobate de lithium à inversion de domaines de polarisation dopé par 5% d'oxyde de magnésium (ppMgCLN). Pompé par un laser Ti:Al2O3 en anneau mono-fréquence et accordable, délivrant 500 mW de puissance utile autour de 795 nm, l'OPO possède un seuil d'oscillation de 110 mW. Une couverture spectrale continue entre 1 µm et 3.5 µm a été obtenue, avec des puissances de l'ordre du mW pour l'onde signal (1 µm à 1.5 µm) et des puissances comprises entre $20$ à $50$ mW pour l'onde complémentaire couvrant un octave de longueur d'onde IR entre 1.7 µm et 3.5 µm. La source UV est obtenue par doublage de fréquence en cavité externe du laser Ti:Al2O3, dans un cristal de triborate de lithium (LiB3O5). Un accord de phase en température à angle d'accord de phase fixé permet l'obtention d'une couverture spectrale comprise entre 390 nm et 405 nm. L'asservissement de la cavité de doublage sur la fréquence du laser Ti:Al2O3 par la méthode de Pound-Drever-Hall, ainsi qu'une adaptation de mode optimale, permet d'obtenir une puissance de 5.64 mW à 400 nm à partir de 480 mW de puissance fondamentale. / The work presented in this PhD dissertation details the strategy adopted to build two non-linear laser sources that are widely in the mid-infrared and blue-UV spectral ranges. These laser sources are needed for the traceability to SI units of coherent light irradiance measurements using a cryogenic radiometer of the using cryogenic radiometer of the Laboratoire commun de métrologie (LCM) .The infrared laser source is an optical parametric oscillator (OPO) resonating on the pump and signal wavelengths (PRSRO) and employing a periodically poled Lithium Niobate non-linear crystal doped with 5% magnesium oxide (ppMgCLN). The PRSRO is pumped by a single-frequency tunable bow-tie ring cavity Titanium-Sapphire laser (Ti:Al2O3) delivering 500 mW output power at 795 nm wavelength, , resulting in a power oscillation threshold of 110 mW. The PRSRO emission could continuously cover the spectral range from 1 µm to 3.5 µm. The level of output power achieved is of the order of 1 mW for the signal wave (1 µm to 1.5 µm) and between 20 mW and 50 mW for idler wave spanning an octave wavelength range (1.7 µm to 3.5 µm).The UV source based on the second harmonic generation on the Titanium-Sapphire tunable laser using an external enhancement cavity containing a critically phase-matched LBO non linear crystal (LiB3O5). Temperature-tuning of the phase-matching condition at a fixed crystal orientation leads to a wide tunability from 390 nm to 405 nm wavelength. The external cavity optical pathlength was actively locked to the laser frequency using a¨Pound-Drever-Hall servo, allowing to extract up to 6 mW power at 400 nm wavelength with a 480 mW pump power. Despite a perfect mode-matching efficiency, the power performance was limited by the poor nonlinear impedance matching of the resonator, due to both the weak nonlinearity of the crystal and the low incoming laser power.

[pt] Plasma é um dos quatro estados fundamentais da matéria, presente em forma natural na Terra na ionosfera, em relâmpagos e nas chamas resultantes de combustão, assim como em forma artificial em lâmpadas de neônio, lâmpadas fluorescentes e processos industriais. O comportamento de plasmas é extraordinariamente complexo e variado, como por exemplo a formação espontânea de características espaciais interessantes em variadas escalas diferentes de comprimento. Uma antena de plasma, por sua vez, é uma estrutura radiante baseada em um elemento de plasma em vez de um condutor metálico, o que gera diversas vantagens e características úteis de um ponto de vista tecnológico. Nesse presente trabalho, uma investigação da propagação eletromagnética dentro de estruturas de plasma é realizada através de métodos teóricos e numéricos como um primeiro passo em direção ao desenvolvimento de modelos apropriados para o estudo de antenas de plasma. / [en] Plasma is one of the four fundamental states of matter, present on Earth in natural form at the ionosphere, in lightning strikes and in the flames resulting from combustion, as well as in artificial form in neon signs, fluorescent light bulbs and industrial processes. Plasma behaviour is extraordinarily complex and varied, e.g. the spontaneous formation of interesting spatial features over a wide range of length scales. A plasma antenna, on the other hand, is a radiating structure based in a plasma element instead of a metallic conductor, which creates several technological advantages and useful characteristics. In this present work, an investigation of electromagnetic propagation inside of plasma structures is performed through both theoretical and numerical means as a first step towards constructing appropriate models for the study of plasma antennas.

[pt] Neste presente trabalho, o Método do Casamento de Modos é aplicado na análise e no projeto de estruturas coaxiais. A estrutura de excitação é um dos pontos críticos do projeto de antenas do tipo discone quando se pretende explorar suas características de banda larga. Seções não uniformes de guias de ondas coaxiais são usualmente utilizadas como elementos dessa estrutura de excitação sendo, eventualmente, necessária a inclusão de anéis dielétricos para garantir a rigidez mecânica da antena. Devido a essas não uniformidades encontradas nas dimensões e no meio dielétrico desse dispositivo de microondas, métodos numéricos serão utilizados na predição do seu comportamento eletromagnético. O correto dimensionamento desses anéis e das descontinuidades de guias de onda coaxiais que compõe a estrutura de alimentação, permite estabelecer um compromisso entre minimização das perdas, alargamento da banda passante e rigidez mecânica. Associados ao Método do Casamento de Modos serão utilizados algoritmos de otimização que farão o ajuste das dimensões dessas seções de guias de onda coaxiais não uniformes, visando à minimização da perda de retorno e o aumento da banda de operação da antena. Finalmente, será feito o estudo de algumas estruturas de excitação, onde serão otimizados seus desempenhos para a perda de retorno. / [en] In this present work, the Mode Matching technique is applied in the analysis and project of coaxial structures. The feed junction is one of the critical points of the project of discone antennas when broadband performance is expected. Usually, these junctions are composed of nonuniform sections of coaxial waveguide and, to guarantee the necessary mechanical rigidity of the structure, some sections are filled with dielectric material. The project of these feed junctions requires a compromise between frequency band, compact structure, minimal losses, and mechanical rigidity. Due to the discontinuities, numerical methods are used to predict the electromagnetic behavior. Here, Mode Matching technique associated with an optimization algorithm is employed in the adjustment of the dimensions of the coaxial waveguide sections, seeking the minimization of the return loss and the enlargement of the antenna bandwidth. Several types of junctions are explored and their performance is compared.

[pt] Este trabalho apresenta um estudo abrangente sobre novas técnicas para modelagem de sensores eletromagnéticos usados na prospecção de petróleo. Estes sensores normalmente ficam imersos em formações geofísicas complexas (não homogêneas, dissipativas e anisotrópicas) com dimensões e parâmetros constitutivos do meio envolvendo múltiplas escalas, e isso representa um problema desafiador para as técnicas tradicionais de eletromagnetismo computacional. Nossa proposta supera esses problemas e contribui para uma melhor compreensão dos fenômenos eletromagnéticos físicos que ocorrem nessas estruturas. Analisamos o problema de propagação usando: a) uma técnica de onda completa baseada no método de casamento de modos, b) soluções perturbacionais para a equação integral de Fredholm vetorial baseadas na aproximação de Born, e c) métodos variacionais para o cálculo da impedância dos sensores eletromagnéticos de interesse para a exploração geofísica. Nós apresentamos resultados que demostram a capacidade das técnicas introduzidas nesta tese para modelar de forma acurada e eficiente sensores eletromagnéticos de forma mais realista do que as alternativas disponiveis na literatura. O custo computacional dos algoritmos desenvolvidos é relativamente baixo comparado com técnicas puramente numéricas tradicionais (tais como os métodos de elementos e diferenças finitas ou o método dos momentos). / [en] This work presents a comprehensive study on some techniques for modeling electromagnetic sensors used in well prospecting. These sensors are usually immersed in complex geophysical formations (inhomogeneous, dissipative, and anisotropic) with multiscale dimensions and constitutive parameters of the medium abruptly varying, resulting in a challenging problem for conventional computational electromagnetic techniques. Our proposal overcomes these problems and contributes to a better understanding of the physical electromagnetic phenomena that occur in these structures. We analyzed the propagation problem by using: a) a fullwave method based on the mode-matching technique, b) perturbational solutions for solving a Fredholm integral equation on the grounds of the Born approximation, and c) variational methods for calculating the sensor impedance. We present results that demonstrate the ability of the techniques introduced in this dissertation to accurately and efficiently modeling electromagnetic sensors in a more realistic fashion when compared with other methods available in the literature.The computational cost of the numerical algorithms developed in this work is relatively low if compared to that required in traditional techniques (such as finite elements, finite differences, and method of moments).

In this thesis, we analyze the electromagnetic wave propagation in waveguidestructuresexhibiting periodical geometry, including glide symmetry. The analysisis performed using a mode matching technique which correlates the different modecoefficients from separate but, connected regions in the structure. This technique isused to obtain the dispersion diagrams for two one-dimensional periodic structures:a glide-symmetric corrugated metasurface and a coaxial line loaded with periodicholes. The mode matching formulation is presented in Cartesian and cylindricalcoordinate system for the former and the later, respectively. The mode matchingresults are compared to simulated results obtained from the Eigenmode Solver inCST Microwave Studio and are found to agree very well. / I detta examensarbete, analyseras elektromagnetisk v°agutbredning i periodiskav°agledarstrukturer som uppvisar glid symmetri. Analysen genomf¨ordes genom enmod matchnings-teknik som korrelerar de olika mod-koefficienterna fr°an separeraderegioner i strukturen med varandra. Denna teknik anv¨ands f¨or att ta framdispersionsrelationen f¨or tv°a endimensionella periodiska strukturer: en glid symmetriskkorrugerad meta-yta och en koaxial ledare belagd med periodiskt urgr¨opdah°aligheter. Mod matchnings-formuleringen presenteras i Kartesiska och cylindriskakoordinatsystem respektive f¨or de ovan n¨amnda fallen. Mod matchnings-resultatenj¨amf¨ors med data-simulerade resultat erh°allna fr°an CST Microwave Studio och de¨overenst¨ammer v¨al med varandra.