This dissertation includes the study of effective medium theories (EMTs) and their applications in describing wave propagation in anisotropic metamaterials, which can guide the design of metamaterials. An EMT based on field averaging is proposed to describe a peculiar anisotropic dispersion relation that is linear along the symmetry line but quadratic in the perpendicular direction. This dispersion relation is associated with the topological transition of the iso-frequency contours (IFCs), suggesting interesting wave propagation behaviors from beam shaping to beam splitting. In the framework of coherent potential approximation, an analytical EMT is further developed, with the ability to build a direct connection between the microscopic structure and the macroscopic material properties, which overcomes the requirement of prior knowledge of the field distributions. The derived EMT is valid beyond the long-wavelength limit. Using the EMT, an anisotropic zero-index metamaterial is designed. Moreover, the derived EMT imposes a condition that no scattered wave is generated in the ambient medium, which suggests the input signal cannot detect any object that might exist, making it invisible. Such correspondence between the EMT and the invisibilityinspires us to explore the wave cloaking in the same framework of coherent potential approximation. To further broaden the application realm of EMT, an EMT using the parameter retrieval method is studied in the regimes where the previously-developed EMTs are no longer accurate. Based on this study, in conjunction with the EMT mentioned above, a general scheme to realize coherent perfect absorption (CPA) in anisotropic metamaterials is proposed. As an exciting area in metamaterials, the field of metasurfaces has drawn great attention recently. As an easily attainable device, a grating may be the simplest version of metasurfaces. Here, an analytical EMT for gratings made of cylinders is developed by using the multiple scattering theory (MST) method and the lattice sum. Validation of the theory is verified by the agreement between the EMT predictions and the numerical calculations. It is found the EMT is capable of accurately predicting the wave transport behaviors, even for frequencies where the Mie resonances happen.

No description available.

Carbon nanotube forests are vertically grown tubular formations of graphene. Samples were grown with an injection chemical vapor deposition method on substrates of silicon with various deposited layers and bare fused silica. The morphology of the forest is characterized by the height, density, and presence of defects. Total diffuse reflectance and transmittance measurements were taken in the 2-16 �m spectral range and correlated to the forest’s specific morphology. From these correlations, the conditions necessary to maximize the absorption of the forest were found and exploited to cater sample growth for specific substrates to make ideal absorbers. From the transmittance data, the absorption coefficient is found via Beer-Lambert’s Law and also correlated to sample morphology, giving us an indication of the height of the forest needed for ideal absorption. Two models were used to attempt to reproduce the experimental absorption coefficient: an effective medium theory using a Maxwell Garnett approximation and by treating the carbon nanotube forest as an effective cylindrical waveguide with walls of graphite. Each model leads to a set of fitting parameters providing a better physical understanding of the forests. It was found that the effective medium theory gave results loosely corroborated with electron microscopy, but had trouble fitting the experimental data, and the index of refraction it provides does not behave like a unified medium. The waveguide model fits the data well, but it requires more experimental evidence to be more conclusive. The theoretical models need more work, but fabrication of ideal absorbers has been achieved on various substrates providing framework for their usage in radiometry and spectroscopy.

Composite metamaterials are periodic metal-dielectric structures operating at wavelengths larger than the structure period. If properly designed these structures behave as homogeneous media described by effective permittivity and permeability parameters. These effective parameters can be designed to take values in domains that are not available in naturally occurring media; notably it is possible to design composite metamaterials with simultaneously negative permittivity and permeability, or, in other words, with a negative refractive index. However, in many experimental or numerical studies it is far from obvious that the use of a homogeneous model is justified for a given structure at a given wavelength. This issue is often glossed over in the literature. <br />In this work I take a detailed look at the fundamental assumptions on which effective medium models rely and put forward a method for determining frequency domains where a given structure may or may not be accurately described by homogeneous effective medium parameters. This work opens the door to a more detailed understanding of the transition between homogeneous and inhomogeneous behavior in composite metamaterials, in particular by introducing the novel notions of custom made effective medium model, and of meta-photonic crystal.

Ce travail de thèse a été consacré à l'étude théorique et numérique de métamatériaux pour la gamme submillimétrique (domaine térahertz), formés de sphères diélectriques présentant des résonances dipolaires de Mie électrique et magnétique, dispersées dans un milieu-hôte. Tout d'abord, les matériaux à utiliser ainsi que les tailles et fraction volumique des sphères permettant l'obtention d'effets de perméabilité ont été précisées. Ensuite, nous avons mené une étude de la polydispersité en taille, mettant en évidence qu'une polydispersité contrôlée pouvait engendrer un élargissement des zones de perméabilité négative ou une zone de perméabilité nulle. Enfin, nous avons étudié le comportement électromagnétique d'assemblages bidisperses de sphères par simulations numériques, et avons procédé à une analyse des modes de Bloch, semblant indiquer l'existence d'une bande d'indice négatif pour des fractions volumiques élevées. / This PhD work was dedicated to the theoretical and numerical study of metamaterials in the terahertz range made of dielectric spheres embedded in a host medium and exhibiting dipolar electric and magnetic Mie resonances. The materials as well as the sizes and the filling fractions of the spheres to use to achieve magnetism in this range of frequency were precised. As a second step, we interested in the size distribution effects on the effective permeability, and showed that a controlled polydispersity can generate a widening of the negative permeability zone with a magnitude close to zero. Finally, we studied the electromagnetic behaviour of bidisperse array of TiO2 spheres with numerical simulations, and a Bloch mode analysis seems to proove the existence of a negative index band for high filling fractions.

Os metamateriais acústicos/elásticos são materiais que apresentam características elásticas diferentes dos materiais comuns encontrados na natureza, sendo o índice de refração negativo a principal característica destes novos materiais. A literatura reporta que esta propriedade é atingida para uma faixa muito estreita de frequências, sendo um efeito muito localizado, e, adicionalmente, as estruturas propostas são ideais em extremo, o que dificulta sua aplicação prática em dispositivos acústicos. O objetivo do presente trabalho foi projetar metamateriais acústicos e elásticos tridimensionais com índice de refração negativo numa faixa de frequência mais longa em relação ao reportado na literatura, e utilizando geometrias e materiais que tornem viável sua implementação prática para a fabricação de dispositivos. Com este propósito foi desenvolvido um formalismo da teoria de meio efetivo (TME), no limite de comprimento de onda longa e baixas frações de preenchimento. Com a TME desenvolvida foi estudado o espalhamento de inclusões esféricas simples, revestidas e duplamente revestidas em diferentes matrizes hospedeiras. Os resultados mostraram a existência de bandas ressonantes nos coeficientes da matriz T relacionadas aos modos monopolares, dipolares e quadrupolares. Materiais compósitos constituídos por esferas simples, revestidas ou duplamente revestidas foram analisados utilizando o formalismo TME. Os resultados mostraram que os valores negativos dos parâmetros elásticos nestes materiais estão completamente relacionados aos efeitos ressonantes das inclusões esféricas. Metamateriais elásticos e acústicos foram projetados sobrepondo dois ou mais compósitos diferentes, cada um com diferentes propriedades, de tal forma que o efeito total no metamaterial apresente as características definidas no projeto inicial. O metamaterial elástico foi projetado utilizando a sobreposição de três compósitos de inclusões esféricas diferentes. Este metamaterial apresentou índice de refração negativa na região de 2 kHz, numa faixa de largura igual a 80 Hz. O metamaterial acústico foi projetado sobrepondo dois compósitos de inclusões esféricas diferentes. Este material apresentou índice de refração negativa na região de 7 kHz, numa faixa de 500 Hz. As geometrias e materiais utilizados no projeto destes metamateriais são acessíveis e de fácil manipulação, o que facilitará sua futura fabricação em laboratório. Os resultados obtidos neste trabalho sugerem a possibilidade de fabricar estes metamateriais no laboratório e empregá-los no controle de ondas acústicas, elásticas e sísmicas, assim como também no projeto de um manto de invisibilidade acústica/elástica. / The acoustic/elastic metamaterials are materials that show different elastic features from common materials found in nature and their main characteristics are their negative refractive index. The literature reports that this property is reached for a very narrow range of frequencies, as a very localized phenomenon, and additionally, the proposed structures are extremely ideals, which makes its practical application difficult on acoustic devices. The objective of this work was to design acoustic/elastic three-dimensional Metamaterials with negative refractive index in a wider frequency band than that reported in the literature, and using geometries and materials that make it possible their practical implementation for manufacturing acoustic/elastic devices. With this purpose a formalism of the effective medium theory (EMT) was developed, in the limit of wavelength and low fill fractions. With the developed EMT, the scattering of simple spherical inclusions, coated and doubly coated in different host substrates were studied. The results showed the existence of resonant bands in the coefficients of the T matrix related to monopolar, dipolar and quadrupolar modes. Composite materials consisting of simple, coated or double coated spheres were analyzed using the EMT formalism. The results showed that the negative values of elastic parameters in these materials are completely related to resonant effects of the spheres of inclusion. Elastic and acoustic Metamaterials were designed by overlaying two or more different composites, each with different properties, such that the overall effect on the metamaterial shows the desired features defined in the initial project. The elastic metamaterial was designed by overlapping three different composites of different spherical inclusions. This metamaterial shows negative refractive index in the region of 2 kHz, in a band of width of 80 Hz. The acoustic metamaterial was designed by overlapping two composites of different spherical inclusions. This material shows negative refractive index in the region of 7 kHz, in a band of width of 500 Hz. The geometries and materials used in the design of these Metamaterials are affordable and easy to handle, which will facilitate their future fabrication in the laboratory. The results obtained in this study suggest the possibility to manufacture these metamaterials in the laboratory and use them in the control of acoustic, elastic and seismic waves, as well as in the design of invisible cloak.

Os metamateriais acústicos/elásticos são materiais que apresentam características elásticas diferentes dos materiais comuns encontrados na natureza, sendo o índice de refração negativo a principal característica destes novos materiais. A literatura reporta que esta propriedade é atingida para uma faixa muito estreita de frequências, sendo um efeito muito localizado, e, adicionalmente, as estruturas propostas são ideais em extremo, o que dificulta sua aplicação prática em dispositivos acústicos. O objetivo do presente trabalho foi projetar metamateriais acústicos e elásticos tridimensionais com índice de refração negativo numa faixa de frequência mais longa em relação ao reportado na literatura, e utilizando geometrias e materiais que tornem viável sua implementação prática para a fabricação de dispositivos. Com este propósito foi desenvolvido um formalismo da teoria de meio efetivo (TME), no limite de comprimento de onda longa e baixas frações de preenchimento. Com a TME desenvolvida foi estudado o espalhamento de inclusões esféricas simples, revestidas e duplamente revestidas em diferentes matrizes hospedeiras. Os resultados mostraram a existência de bandas ressonantes nos coeficientes da matriz T relacionadas aos modos monopolares, dipolares e quadrupolares. Materiais compósitos constituídos por esferas simples, revestidas ou duplamente revestidas foram analisados utilizando o formalismo TME. Os resultados mostraram que os valores negativos dos parâmetros elásticos nestes materiais estão completamente relacionados aos efeitos ressonantes das inclusões esféricas. Metamateriais elásticos e acústicos foram projetados sobrepondo dois ou mais compósitos diferentes, cada um com diferentes propriedades, de tal forma que o efeito total no metamaterial apresente as características definidas no projeto inicial. O metamaterial elástico foi projetado utilizando a sobreposição de três compósitos de inclusões esféricas diferentes. Este metamaterial apresentou índice de refração negativa na região de 2 kHz, numa faixa de largura igual a 80 Hz. O metamaterial acústico foi projetado sobrepondo dois compósitos de inclusões esféricas diferentes. Este material apresentou índice de refração negativa na região de 7 kHz, numa faixa de 500 Hz. As geometrias e materiais utilizados no projeto destes metamateriais são acessíveis e de fácil manipulação, o que facilitará sua futura fabricação em laboratório. Os resultados obtidos neste trabalho sugerem a possibilidade de fabricar estes metamateriais no laboratório e empregá-los no controle de ondas acústicas, elásticas e sísmicas, assim como também no projeto de um manto de invisibilidade acústica/elástica. / The acoustic/elastic metamaterials are materials that show different elastic features from common materials found in nature and their main characteristics are their negative refractive index. The literature reports that this property is reached for a very narrow range of frequencies, as a very localized phenomenon, and additionally, the proposed structures are extremely ideals, which makes its practical application difficult on acoustic devices. The objective of this work was to design acoustic/elastic three-dimensional Metamaterials with negative refractive index in a wider frequency band than that reported in the literature, and using geometries and materials that make it possible their practical implementation for manufacturing acoustic/elastic devices. With this purpose a formalism of the effective medium theory (EMT) was developed, in the limit of wavelength and low fill fractions. With the developed EMT, the scattering of simple spherical inclusions, coated and doubly coated in different host substrates were studied. The results showed the existence of resonant bands in the coefficients of the T matrix related to monopolar, dipolar and quadrupolar modes. Composite materials consisting of simple, coated or double coated spheres were analyzed using the EMT formalism. The results showed that the negative values of elastic parameters in these materials are completely related to resonant effects of the spheres of inclusion. Elastic and acoustic Metamaterials were designed by overlaying two or more different composites, each with different properties, such that the overall effect on the metamaterial shows the desired features defined in the initial project. The elastic metamaterial was designed by overlapping three different composites of different spherical inclusions. This metamaterial shows negative refractive index in the region of 2 kHz, in a band of width of 80 Hz. The acoustic metamaterial was designed by overlapping two composites of different spherical inclusions. This material shows negative refractive index in the region of 7 kHz, in a band of width of 500 Hz. The geometries and materials used in the design of these Metamaterials are affordable and easy to handle, which will facilitate their future fabrication in the laboratory. The results obtained in this study suggest the possibility to manufacture these metamaterials in the laboratory and use them in the control of acoustic, elastic and seismic waves, as well as in the design of invisible cloak.

V této teoretické práci se zabýváme kvantově mechanickými jevy, jež jsou spjaté s vodi- vostními elektrony uzavřenými v kvantových tečkách. Nejprve je odvozen model nanokrys- talu jakožto potenciálové jámy. Při tom se ukazuje, že pouze objem, ne tvar, je významným parametrem modelu pro účely terahertzové spektroskopie. Studované geometrie jsou tak vzájemně zaměnitelné a výběr mezi nimi m·že zjednodušit dané úlohy. Pro zkoumání depo- larizačních efekt·, které jsou zahrnuty v depolarizačním faktoru v Maxwell Garnettově teorii efektivního prostředí, je zvolena sférická symetrie. V rámci poruchy prvního řádu je vyřešena Poissonova rovnice pro elektrony rozmístěné uvnitř koule podle vlnové funkce a je určen depo- larizační faktor. Zatímco v klasické limitě tento nabývá p·vodní hodnoty, pro nanokrystaly se zvyšuje a maxima je dosaženo v ne-degenerovaném režimu, kdy je obsazen pouze základní stav. Navýšení depolarizačního faktoru posouvá plasmonovou rezonanci směrem k vyšším frekvencím. 1

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.

<p>In this thesis we report on the metal-mediated-thermally induced changes of the structural and optical properties of hydrogenated amorphous silicon deposited by hot-wire CVD, where aluminium and nickel were used to induce crystallization. The metal-coated amorphous silicon was subjected to a thermal annealing regime of between 150 and 520&deg / C. The structural measurements, obtained by Raman spectroscopy, show partial crystallization occurring at 350 &deg / C. At the higher annealing temperatures of 450&deg / C and 520&deg / C complete crystallization occurs. Reflection and transmission measurements in the UV-visible range were then used to extract the optical properties. By adopting the effective medium approximation a single optical model could be constructed that could successfully model material that was in different structural phases, irrespective of metal contamination. Changes in the absorption of the material in various stages of transition were confirmed with a directly measured absorption technique, and the modelled absorption closely followed the same trends This study forms part of the larger overall solar cell research project, of which the primary aim is to eventually develop a silicon solar panel that optimises the characteristics for best performance.</p>