Cette thèse a pour but l’étude théorique de métamatériaux métalliques empilés. Ces structures sont actuellement proposées pour améliorer et élargir les fonctionnalités des métamatériaux métalliques. Nous portons un intérêt particulier aux propriétés de polarisation de ces structures métalliques empilées.En premier lieu, nous précisons le type de métamatériaux que nous étudions et nous présentons la méthode modale qui nous permet de décrire les propriétés électromagnétiques de la structure. A l’aide d’un Formalisme de Jones Etendu (FJE), développé récemment dans notre équipe, nous faisons ressortir les principales propriétés de polarisation linéaire de ces métamatériaux métallique.En alliant le FJE à l’algorithme de propagation de la matrice S, nous étudions un empilement de deux métamatériaux vus comme un montage polariseur-analyseur. Nous établissons ensuite une expression de la transmission de la structure: la loi de Malus étendue. Cela nous permet notamment de démontrer les résonances de type Fabry-Perot qui ont lieu entre les métamatériaux.Pour des structures plus conséquentes, nous montrons qu’il est possible de réaliser une rotation de la polarisation, à très faible perte et spectralement agile, grâce aux résonances de type Fabry-Perot.Fondamentalement, nous révélons une nouvelle façon d’exciter des résonances Fano qui sont induites par les propriétés de polarisation des métamatériaux. Ces résonances peuvent être utilisées pour des applications de capteur ou de filtrage. De plus, ces résonances Fano induites par la polarisation ouvrent de nouvelles possibilités d’applications pour les empilement de métamatériaux métalliques. / This PhD thesis deals with the theoretical study of stacked metallic metamaterials. Such structures are currently investigated to extend the functionalities offered by single metallic metamaterials. We especially focus on the specific polarization properties of the stacked metallic metamaterials.We first present the type of metamaterial that we consider, and we describe the modal method that is used to model its electromagnetic properties. We outline the linear polarization properties characterizing the metamaterial thanks to an Extended Jones Formalism (EJF) recently developed by our team.In combination with the EJF, we apply the S-matrix algorithm to the study of a stack of two metallic metamaterials in a polarizer-analyzer configuration. We derive an analytical expression for the transmission response of the stacked structure: the Extended Malus Law. Mainly, it highlights the Fabry-Perot-like resonances located between the metamaterials.Using larger stacked structures, we demonstrate that spectrally tunable and low loss polarization rotation can be achieved owing to these Fabry-Perot-like resonances.In essence, we reveal a new way of realizing Fano resonances which are induced by the specific polarization properties of the metamaterials. We show that such resonances can be engineered for sensing or filtering applications. Moreover, the polarization-induced Fano resonances expand the possibilities of stacked metallic metamaterials.

Ce travail de thèse a été consacré à l’étude expérimentale, théorique et numériquede métamatériaux auto-assemblés constitués de nanoparticules d’or, opérant dans la gammedu visible. Nous nous sommes intéressés à trois types de structures différentes et avons analyséleurs propriétés optiques par ellipsométrie spectroscopique.Nous avons étudié expérimentalement et numériquement l’effet de la proximité d’un substratde haut indice sur la réponse plasmonique d’une nanoparticule, grâce à un système expérimentalconstitué de monocouches de nanoparticules d’or sur une multicouche de polyélectrolytes.Nous avons discuté d’un effet d’exaltation de la section efficace d’absorption des nanoparticulesaux plus faibles distances au substrat. Nous avons montré que des films composites denses depolymère et de nanoparticules d’or ont des réponses contrôlées par la fraction en or et qu’ilsse comportent, à haute fraction en or, soit comme des diélectriques soit comme des métauxselon la gamme de fréquence. Nous avons développé un modèle phénoménologique, adapté àde nombreuses situations, qui décrit bien les propriétés optiques des films. Enfin, nous avonsétudié des nanocomposites lamellaires à base de copolymères à blocs et de nanoparticules d’or.Nous avons montré comment avoir accès, pour certains systèmes, à l’extraction et la modélisationde leur anisotropie de permittivité, qui est affectée par la résonance plasmonique desnanoparticules. / This PhD work was dedicated to the experimental, theoretical and numerical studyof the optical properties of self-assembled metamaterials made of gold nanoparticles, operatingat visible frequencies. We were interested in three different structure types and analyzed theiroptical properties experimentally by spectroscopic ellipsometry.We studied the effect of a high index substrate proximity on the plasmonic response of goldnanoparticles, both experimentally and numerically, on nanoparticle monolayers deposited ontopolyelectrolytes multilayers. We discuss an enhancement effect of the nanoparticle absorptioncross-section for small distances to the substrate. Dense polymer/gold nanoparticles compositefilms were shown to have tunable optical properties depending on their gold filling fractionand to behave, at high filling fraction, like a dielectric or a metal depending on the frequencyrange. We developed a phenomenological model, adapted to a large number of cases, whichsuccessfully describes the films optical properties. Finally, lamellar films made of block copolymersand gold nanoparticles were studied. We have shown how to access, for certain structuralconditions, the extraction and the modelisation of the effective permittivity anisotropy, affectedby the resonance of the nanoparticles.

The principle of coordinate invariance states that all physical laws must be formulated in a mathematical form that is independent of the geometrical properties of any particular coordinate system. Embracing this principle is the key to understand how to systematically incorporate curved material interfaces into a numerical solution of Maxwell’s equations. This dissertation describes how to generate a coordinate invariant representation of Maxwell’s equations in differential form, and it demonstrates why employing such representation is crucial to the development of robust finite-difference discretisations with consistent global error properties. As part of this process, two original contributions are presented that address the issue of constructing finite-difference approximations at the locations of material interfaces. The first contribution is a domain-decomposition procedure to enforce the tangential field continuity conditions with a second-order local truncation error that can be applied in 2-D or 3-D. The second contribution is a similar domain-decomposition procedure that enforces the tangential field continuity conditions with a local truncation of order 2L—where L is an integer greater or equal to one—but that can only be applied in 1-D. To conclude, the dissertation also describes the interesting connection that exists between the use of a coordinate invariant representation of Maxwell’s equations to design artificial materials and the use of the same representation to model curved material interfaces in a finite-difference discretisation.

The principle of coordinate invariance states that all physical laws must be formulated in a mathematical form that is independent of the geometrical properties of any particular coordinate system. Embracing this principle is the key to understand how to systematically incorporate curved material interfaces into a numerical solution of Maxwell’s equations. This dissertation describes how to generate a coordinate invariant representation of Maxwell’s equations in differential form, and it demonstrates why employing such representation is crucial to the development of robust finite-difference discretisations with consistent global error properties. As part of this process, two original contributions are presented that address the issue of constructing finite-difference approximations at the locations of material interfaces. The first contribution is a domain-decomposition procedure to enforce the tangential field continuity conditions with a second-order local truncation error that can be applied in 2-D or 3-D. The second contribution is a similar domain-decomposition procedure that enforces the tangential field continuity conditions with a local truncation of order 2L—where L is an integer greater or equal to one—but that can only be applied in 1-D. To conclude, the dissertation also describes the interesting connection that exists between the use of a coordinate invariant representation of Maxwell’s equations to design artificial materials and the use of the same representation to model curved material interfaces in a finite-difference discretisation.

Inspirados por las investigaciones realizadas en los campos de la plasmónica y los metamateriales, en este trabajo hemos estudiado la difusión de la luz por pequeñas partículas (nanopartículas en el rango del visible) con propiedades ópticas arbitraria, tanto convencionales (dieléctricas como metálicas) como no convencionales (con permeabilidad magnética distinta de 1). El trabajo está principalmente enfocado en controlar la propiedades (principalmente la dirección) de la luz difundida por una partícula mediante la manipulación de sus constantes ópticas. Las principales aplicaciones de este estudio se pueden concentrar en los campos de los biosensores y/o de las comunicaciones ópticas. Es por esto que hemos considerado tanto partículas aisladas como sistemas de partículas(dímeros principalmente). / Inspired by the last researches on plasmonics and metamaterials, this work is devoted to the study of light scattering by small particles (nanoparticles in the visible range) with arbitrary optical properties, both conventional and non-conventional. We focused the analysis on the control of the directionality of light scattering by tunning the optical constants of the scatterer. This could be interesting for the design of futuristic optical communications and/or for the generation of improved biosensores. For this reason, isolated particles and also clusters of them (mainly dimers) were considered.

Split ring resonator (SRR) is a metamaterial structure which displays negative permeability values over a relatively small bandwidth around its magnetic resonance frequency. Unit SRR cells and arrays have been used in various novel applications including the design of miniaturized microwave devices and antennas. When the SRR arrays are combined with the arrays of conducting wires, left handed materials can be constructed with the unusual property of having negative valued effective refractive indices. In this thesis, unit cells and arrays of single-ring multiple-split type SRR structures are numerically analyzed by using Ansoft&rsquo / s HFSS software that is based on the finite elements method (FEM). Some of these structures are constructed over low-loss dielectric substrates and their complex scattering parameters are measured to verify the numerical simulation results. The major purpose of this study has been to establish equivalent circuit models to estimate the behavior of SRR structures in a simple and computationally efficient manner. For this purpose, individual single ring SRR cells with multiple splits are modeled by appropriate two-port RLC resonant circuits paying special attention to conductor and dielectric loss effects. Results obtained from these models are compared with the results of HFSS simulations which use either PEC/PMC (perfect electric conductor/perfect magnetic conductor) type or perfectly matched layer (PML) type boundary conditions. Interactions between the elements of SRR arrays such as the mutual inductance and capacitance effects as well as additional dielectric losses are also modeled by proper two-port equivalent circuits to describe the overall array behavior and to compute the associated transmission spectrum by simple MATLAB codes. Results of numerical HFSS simulations, equivalent circuit model computations and measurements are shown to be in good agreement.

A persistent challenge in the design of composite materials is the ability to fabricate materials that simultaneously display high stiffness and high loss factors for the creation of structural elements capable of passively suppressing vibro-acoustic energy. Relevant recent research has shown that it is possible to produce composite materials whose macroscopic mechanical stiffness and loss properties surpass those of conventional composites through the addition of trace amounts of materials displaying negative stiffness (NS) induced by phase transformation [R. S. Lakes, et al., Nature, 410, pp. 565-567, (2001)]. The present work investigates the ability to elicit NS behavior without employing physical phenomena such as inherent nonlinear material behavior (e.g., phase change or plastic deformation) or dynamic effects, but rather the controlled buckling of small-scale structural elements, metamaterials, embedded in a continuous viscoelastic matrix. To illustrate the effect of these buckled elements, a nonlinear hierarchical multiscale material model is derived which estimates the macroscopic stiffness and loss of a composite material containing pre-strained microscale structured inclusions. The nonlinear multiscale model is then utilized in a set-based hierarchical design approach to explore the design space over a wide range of inclusion geometries. Finally, prototype NS inclusions are fabricated using an additive manufacturing technique and tested to determine quasi-static inclusion stiffness which is compared with analytical predictions. / text

In this thesis, we had studied the transmissivity of electromagnetic waves in onedimensional photonic structures composed by metamaterials in many ways. Applying the formalism of transfer matrix, comparing the transmission spectra between two systems: defective photonic superlattices composed of subwavelength slab widths and a simple photonic structures formed by three layers. Through the effective medium theory, with good accuracy, we had shown the equivalence of the above systems in the spectral region in which there are modes of resonant tunneling for both structures. Furthermore, we had derived a general condition which should be satisfied to observe the resonant modes. Our analytical results may be useful from a technological point of view to propitiate, in the design and development of photonic devices, adjustment or selection of resonant frequencies. Finally, we investigated the electromagnetic wave transmission properties through a multilayer system consisting of alternated layers of air and uniaxially anisotropic metamaterials. The optical axis of each heterostructure coincides with the direction of stacking of the layers. The components of the electric permittivity and magnetic permeability tensors that characterize the metamaterial are modeled by a Drude-type response and split-ring resonator metamaterial response, respectively. Different plasmon frequencies are considered for directions perpendicular and parallel to the optical axis. For oblique incidence, longitudinal plasmon polariton modes are found in the neighborhood of the plasmon frequency along the optical axis. The anisotropy leads to unfolding of nearly dispersionless plasmon-polariton bands either above or below the plasmon frequency. Moreover, it is shown that, even in the presence of loss /absorption, these plasmon polariton modes do survive and, therefore, should be experimentally detected. / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Nessa tese, estudamos a transmissividade de ondas eletromagnéticas em estruturas fotônicas unidimensionais formadas por metamateriais, sob vários aspectos. Aplicando o formalismo de matriz de transferência, comparamos os espectros de transmissão entre dois sistemas: redes defeituosas com camadas no regime de sub-comprimento de onda e simples estruturas fotônicas formadas por três camadas. Através da teoria do meio efetivo, com boa acurácia, mostramos a equivalência dos supracitados sistemas na região espectral em que há modos de tunelamento ressonante para ambas estruturas. Além disso, derivamos uma condição geral que deve ser satisfeita para observarmos os modos ressonantes. Nossos resultados analíticos podem ser úteis do ponto de vista tecnológico por propiciarem, na concepção e no desenvolvimento de dispositivos fotônicos, o ajuste ou seleção das frequências de ressonância. Por fim, investigamos as propriedades de transmissão de ondas eletromagnéticas através de sistemas multicamadas consistindo de camadas alternadas de ar e metamateriais uniaxialmente anisotrópicos. O eixo óptico de cada heteroestrutura coincide com a direção de empilhamento das camadas. As componentes dos tensores de permissividade elétrica e permeabilidade magnética que caracterizam os metamateriais são modeladas por respostas do tipo Drude e split-ring resonator, respectivamente. Diferentes frequências de plasmon são consideradas para as direções perpendiculares e paralela ao eixo óptico. Para incidência oblíqua, modos de plasmon polariton longitudinais são encontrados nas vizinhanças da frequência de plasmon ao longo do eixo óptico. A anisotropia leva ao desdobramento de bandas de plasmon polariton quase sem dispersão acima ou abaixo da frequência de plasmon. Além disso, mostramos que mesmo na presença de perdas/absorções, esses modos de plasmon polariton sobrevivem e, portanto, devem ser detectados experimentalmente.

Ce travail de thèse porte sur l'étude de l'intégration des fonctions d'amortissement vibroacoustique dans des plaques en matériau composite. Dans un premier temps, pour une méta-plaque non composite, les caractéristiques d'atténuation des vibrations ont été étudiées avec un réseau périodique de résonateurs (poutre-masse) attachés à une plaque.L'effet de périodicité et des résonances locales permet de bloquer la propagation d'ondes sur des plages de fréquences données, appelée bandes interdites. Des simulations numériques basées sur la MEF ont permis de calculer les diagrammes de bandes des plaques périodiques et d'analyser la sensibilité de ces bandes interdites aux différents paramètres de conception de méta-plaque. Les calculs de coefficient de transmission d'une onde plane selon la direction perpendiculaire à la zone traitée, mettent en évidence la présence des bandes interdites prédites par le diagramme de bande. Les réponses fréquentielles de plusieurs modèles sont comparées, pour mettre en évidence les écarts entre une structure infinie et une structure finie. Une méthode automatique originale est mise au point pour détecter les gammes de fréquences des bandes interdites pour une méta-plaque finie.Ces méthodes théorique et expérimentale sont alors appliquées à des plaques composites SMC avec des perforations périodiques. Des essais avec une excitation unidirectionnelle et une excitation ponctuelle sont réalisés. L'influence de chaque type de sollicitation sur la réponse vibratoire des plaques est analysée pour mettre en évidence la détectabilité des bandes interdites. Enfin, la robustesse des bandes interdites aux variations du réseau périodique est validée. / The vibration attenuation characteristics of a metamaterial plate were investigated theoretically and experimentally with a 2-dimensional periodic array of resonators (mass-beam) attached to a thin homogeneous plate.The sensitivity analysis of the band gap frequency range took into account the uncertainties of all the design parameters of the metamaterial plate. The theoretical approach used the finite element method (FEM) to compare the predicted band gaps with those derived from infinite and finite models of the metamaterial.An original automatic method is proposed to detect the frequency ranges of band gaps in finite metamaterial based on the behavior of the corresponding bare plate. Directional plane wave excitation and point force excitation were applied to evaluate the efficiency of the detection method. The results of these analyses were compared with experimental measurements. Frequency ranges of experimental vibration attenuation are in good agreement with the theoretically predicted complete and directional band gaps.These theoretical and experimental methods are then applied to SMC (Sheet Molding Compound) composite plates with periodic perforations. Tests with unidirectional excitation and point force excitation are performed. The influence of each type of excitation on the vibratory response of the plates is analyzed in order to demonstrate the detectability of the bands gaps.Finally, the robustness of the band gap to the variations of the periodic lattice is validated following an integration of perturbations: addition of local mass on half of the unit cells according to a periodic or random positions.

Made available in DSpace on 2014-12-17T14:55:54Z (GMT). No. of bitstreams: 1 VitorFB_DISSERT.pdf: 3545980 bytes, checksum: 2759df31b3e705a93ae644db95f0c01f (MD5) Previous issue date: 2012-02-03 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior / Microstrip antennas are subject matter in several research fields due to its numerous advantages. The discovery, at 1999, of a new class of materials called metamaterials - usually composed of metallic elements immersed in a dielectric medium, have attracted the attention of the scientific community, due to its electromagnetic properties, especially the ability to use in planar structures, such as microstrip, without interfering with their traditional geometry. The aim of this paper is to analyze the effects of one and bidimensional metamaterial substrates in microstrip antennas, with different configurations of resonance rings, SRR, in the dielectric layer. Fractal geometry is applied to these rings, in seeking to verify a multiband behavior and to reduce the resonance frequency of the antennas. The results are then given by commercial software Ansoft HFSS, used for precise analysis of the electromagnetic behavior of antennas by Finite Element Method (FEM). To reach it, this essay will first perform a literature study on fractal geometry and its generative process. This paper also presents an analysis of microstrip antennas, with emphasis on addressing different types of substrates as part of its electric and magnetic anisotropic behavior. It s performed too an approach on metamaterials and their unique properties / As antenas de microfita s?o objeto de estudo em diversos campos de pesquisa devido a suas in?meras vantagens. A obten??o, em 1999, de uma nova classe de materiais, chamados metamateriais - normalmente compostos por elementos met?licos imersos em um meio diel?trico, tem atra?do a aten??o da comunidade cient?fica, gra?as ?s suas propriedades eletromagn?ticas e, principalmente, pela capacidade de utiliza??o em estruturas planares, tais como a microfita, sem interferir em sua geometria tradicional. O objetivo desse trabalho ? analisar os efeitos do uso de substratos metamateriais uni e bidimensionais em antenas de microfita, com diferentes configura??es de an?is de resson?ncia - SRR - na camada diel?trica. A geometria fractal ? aplicada a esses an?is, na busca de se verificar um comportamento multibanda e de se reduzir a frequ?ncia de resson?ncia das antenas. Os resultados s?o, ent?o, obtidos com o software comercial Ansoft HFSS, usado para a an?lise do comportamento eletromagn?tico das antenas, por meio do M?todo dos Elementos Finitos (FEM). Para tanto, nessa disserta??o, ? previamente realizado um estudo bibliogr?fico sobre a geometria fractal e seu processo gerador. Este trabalho apresenta tamb?m uma an?lise sobre as antenas de microfita, com ?nfase ? abordagem de diferentes tipos de substratos, evidenciando seu comportamento anisotr?pico el?trico e magn?tico. ? realizada, ainda, uma abordagem sobre os metamateriais e suas propriedades singulares