Este trabalho tem por objetivo a extensão de métodos numéricos baseados em diferenças finitas no domínio do tempo (FDTD) e no domínio da freqüência (FD-BPM) para a simulação da propagação de ondas eletromagnéticas em materiais com propriedades ópticas diversas, por exemplo, isotrópicos, anisotrópicos, lineares, não-lineares, bem como a combinação destes em uma mesma estrutura. Inicialmente foram elaborados formalismos bidimensionais (FDTD e FD-BPM), dos quais foram investigados modos com polarização TM (Magnético Transversal) que se propagam em estruturas planares magnetoópticas/não-lineares/lineares. Esta polarização foi escolhida tendo em vista o campo magnetostático dc adotado, o qual possibilitou a observação do fenômeno não-recíproco associado ao não-linear simultaneamente. Por outro lado, é bem sabido que o método FDTD é computacionalmente muito intensivo. Portanto, um grande esforço foi dedicado aos formalismos no domínio da freqüência, os quais foram implementados em duas e três dimensões. Este último foi estendido para um formalismo totalmente vetorial, capaz de simular modos híbridos ou até mesmo a transferência de energia entre modos de polarizações ortogonais. Isto nos permitiu investigar geometrias ainda mais complexas, tais como um isolador óptico baseado em um guia de onda tip rib utilizando material magnetooptico. Adicionalmente, fenômenos de natureza complexa, tais como a dinâmica dos condensados de luz em materiais com não-lineares do tipo Kerr com saturação, também conhecidos como meios não-lineares cúbico-qüínticos, foram investigados pela primeira vez com um formalismo vetorial. Finalmente, métodos numéricos capazes de considerar qualquer combinação de materiais com propriedades ópticas distintas (linear e/ou não-linear e/ou magnetoóptico) são uma ferramenta extraordinária para a comunidade científica para o projeto de novos dispositivos ópticos, bem como a investigação de novos efeitos físicos com vistas à aplicações em computação óptica, que podem resultar em um menor e mais eficiente número de componentes para sistemas de comunicações ópticos. / This work introduces three improved formalisms for the analysis of electromagnetic wave propagation through materials with distinct optical properties, i.e., isotropic, anisotropic, linear, nonlinear, or any combination of them. Two finite difference approaches were extensively investigated in this work for this purpose, namely the finite difference in time domain (FDTD), and the finite difference beam propagation method (2D and 3D FD-BPM), these in frequency domain. Initially, a TM (transverse magnetic) mode propagating through a planar magnetooptic/nonlinear/linear waveguide was investigated by way of a two-dimensional formalism (FDTD and FD-BPM). This mode polarization was chosen based on the orientation of the external magnetostatic field adopted, which favored the observation of non-reciprocal and nonlinear effects simultaneously. On the other hand, it is well known that FDTD formalisms are computationally intensives. Therefore, a great effort was dedicated to its frequency domain counterpart (FD-BPM), which was implemented in two and three dimensions. The later was further extended to a fully vectorial formalism, which is capable of simulating hybrid modes or even the energy transfer between orthogonal modes. This enabled us to investigate more complex geometries, such as an optical isolator based on magnetooptic rib waveguide. Additionally, complex phenomena, such as the dynamic of light condensates in bulk nonlinear Kerr media with saturation, also known as cubic-quintic nonlinear media, were investigated for the first time with a 3D vectorial formalism. Finally, numerical methods capable of handling any combination of materials with distinct optical properties (linear and/or nonlinear and/or magnetooptic) are an extraordinary tool for the scientific community for the design of new optical devices, as well as the investigation of new physical effects aimed for optical computing, that may result in fewer and more efficient components for optical communication systems.

Submitted by Edisangela Bastos (edisangela@ufpa.br) on 2018-03-21T17:23:02Z No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Tese_MetodoDiferencasFinitas.pdf: 3779369 bytes, checksum: 428516d3d9e3d5e445fa15ec4b27cb81 (MD5) / Approved for entry into archive by Edisangela Bastos (edisangela@ufpa.br) on 2018-03-22T18:23:25Z (GMT) No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Tese_MetodoDiferencasFinitas.pdf: 3779369 bytes, checksum: 428516d3d9e3d5e445fa15ec4b27cb81 (MD5) / Made available in DSpace on 2018-03-22T18:23:25Z (GMT). No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Tese_MetodoDiferencasFinitas.pdf: 3779369 bytes, checksum: 428516d3d9e3d5e445fa15ec4b27cb81 (MD5) Previous issue date: 1996-02-09 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / A formulação para diferenças finitas no domínio do tempo (FDTD), aplicada a plasma magnetizado segundo direção arbitrária, é desenvolvida para aplicação em dispositivos dielétricos em duas (2D-FDTD) e três dimensões (3D-FDTD). A ênfase é dada no processo de cálculo iterativo da convolução entre o campo elétrico e o tensor susceptibilidade elétrica do plasma magnetizado. Também, são propostos diversos tipos de dispositivos para propagação de sinais na banda milimétrica. O método é aplicado a estruturas controladas por plasma. Este plasma pode ser induzido por um feixe áptico sobre uma película semicondutora, depositada sobre o guia. Neste caso, as características de propagação do guia são controladas por um feixe áptico com energia apropriada. Esse plasma também pode ser estabelecido em semicondutor por dopagem. Neste tipo de dispositivo, o núcleo do guia é totalmente preenchido com plasma. Nesta opção, a propagação dos campos de RF é controlada por um campo magnetostático. Alguns dispositivos com guias singelos e acoplados são analisados. Observa-se então a possibilidade de controle efetivo de fase e acoplamento, assim como o controle na faixa de operação de modo único, notadamente nos guias opticamente controlados. Devido à carência de dados na literatura especializada, são estabelecidos critérios para discretização graduada e rigorismo nos testes de convergências propostos. Diversos tipos de dados são utilizados para essa finalidade. Obtém-se, então, uma espécie de perfil de discretização, o qual é aplicado aos demais dispositivos. / A finite-difference in the time domain (FDTD) formulation is developed for plasmas magnetized along an arbitrary direction and applicable to two dimensions (2D-FDTD) and to three dimensions (3D-FDTD) dielectric devices. Emphasis is given to the iterative calculation of the convolution between the electric field vector and the electric susceptibility tensor of the magnetized plasma. Various types of devices are also proposed for the propagation of signals in the millimeter-wave band. The method is applied to structures controlled by plasma. This plasma may be induced by an optical beam applied to a semiconductor layer deposited on the waveguide. In this case, the propagation characteristic of the waveguide is controlled by an optical beam with appropiate energy. This plasma may also also be introduced in the semiconductor by means of doping. For these devices the waveguide core is completely filled with plasma. With this option the propagation of the RF fields is controlled by a static magnetic field. Some devices with single and coupled waveguides are analyzed. The possibility of an effective control of phase and coupling, as well as the operating bandwidth with a single mode was examined, particularly with optically controlled waveguides. Due to the lack of data in the specialized literature, gradual discretization criteria and rigorous tests of convergence are proposed. Various types of data are used to accomplish this objective. As a result, a kind of discretization profile is obtained and is applied to the remaining devices.

Dans ce mémoire, nous étudions l’exposition aux ondes électromagnétiques l’échelle d’une population. Cette étude est réalisée pour une exposition à une onde plane orientée frontalement sur des modèles anatomiques du corps humains (fantômes) avec une puissance incidente de 1W/m2 et une fréquence de 2.1 GHz. Pour ce faire, l’idée est de construire un modèle du WBSAR (Whole Body averaged Specific Absorption Rate) en fonction de lamorphologie. Les facteurs morphologiques influençant le WBSAR ont été identifiés à l’aide des fantômes existant dont le nombre se limite à 18 et des modèles de régressions. Cette analyse préliminaire montre que les facteurs morphologiques externes (taille, poids ...) seuls ne suffisent pas pour construire un tel modèle, mais l’introduction des facteurs morphologiques internes (muscles, graisse ...) est nécessaire. L’absence de données statistiques sur les facteurs morphologiques internes de populations nous a conduits à intégrer des connaissances apriori sur ces facteursafin d’étudier l’exposition d’une population donnée. Des lois paramétriques usuelles et des mélanges de gaussiennes sont utilisés pour modéliser ces facteurs internes afin d’étudier leur influence sur le quantile du WBSAR à 95 %.L’utilisation des fantômes homogènes où le fantôme homogène est obtenu en remplaçant tous les tissus internes par un unique tissu équivalent. Ces fantômes homogènes permettent de s’affranchir de l’influence de la morphologie interne dans un modèle du WBSAR et facilitent également leur déformation par une technique de morphing. Ainsi nous avons pu enrichir la base de fantômes existant. Pour donner une estimation du quantile du WBSAR à 95 %, nous avons mis en place un plan d’expériences séquentiel qui repose sur un modèle paramétrique du WBSAR et l’inférence bayésienne et qui permet de raffiner la région à 95 %. Cette approche nous a permis de trouver le quantile à 95 % pour une population et un exemple de fantôme correspondant. Cependant, cette approche ne permet pas d’obtenir une estimation de toute la distribution du WBSAR. Afin d’obtenir une estimation de toute cette distribution, nous avons construit une surface de réponse en utilisant les polynômes de chaos. Dans l’objectif d’obtenirdes résultats cohérents nous avons effectué un changement de variables permettant de traduire les connaissances physiques dans cette surface de réponse. / In this report, a study of the exposure to electromagnetic waves at the level of population is proposed. This study is conducted in the case of a plane wave oriented frontally on anatomical models (phantoms) with an incident power of 1W/m2 and at the frequency of 2.1 GHz. For this purpose, the idea is to build a surrogate model of the WBSAR (Whole Body averaged Specific Absorption Rate) as a function of morphology. An identificationof morphological factor is performed using the limited number of phantoms (18phantoms)and different regressions. This analysis shows that to use only external morphological factors (height, weight ...) is not sufficient to build such surrogate model and that internal morphological factors (muscles, fat ...) are also important. The absence of statistical data on internal morphology conducts us to introduce some prior knowledge on these internal factors to study the exposure for a given population. Some parametric laws and Gaussian mixture are used to study their influence on the quantile of the WBSAR at 95 The lack of data on internal morphology led us to consider homogeneous phantoms instead of the heterogeneous one. In homogeneous phantoms, all the internal tissues are substituted by an equivalent tissue. These homogeneous phantoms allow us to overcome the influence of internal morphology for a WBSAR model and to use a morphing technique to increase the database of phantoms. To give an estimation of the WBSAR quantile at 95 %, a sequential experiment design is used. This approach is based on a parametric model and Bayesian inference. This experiment design allows us to estimate the quantile at 95 for a given population and an example of one corresponding phantom. Nevertheless, this approach does not allow one to estimate the whole distribution of the WBSAR for a given population. To give an estimate of this distribution a surface of response is established using polynomial chaos. This approach gives incoherent results with the physical phenomenon. To obtain coherent results, physical knowledge is introduced by variables changing in this responsesurface.

Descargas atmosféricas representam uma das principais causas de interrupção no fornecimento de energia para os consumidores, e embora tenham efeitos mais intensos quando incidem diretamente nas redes elétricas, é o caso das descargas indiretas que chama mais atenção, já que elas ocorrem com maior frequência. Tanto as primeiras descargas que geralmente ocorrem com maior intensidade de corrente, quanto as descargas subsequentes que têm menor tempo de frente associado, irradiam campos eletromagnéticos que ao se acoplarem com as redes elétricas geram surtos que podem causar tanto a interrupção do fornecimento de energia quanto danos a equipamentos. A presença de edifícios na região de incidência da descarga atmosférica afeta a propagação das ondas irradiadas, criando diferentes padrões de campos resultantes, os quais são responsáveis por sobretensões induzidas. Embora tanto a descarga atmosférica em si quanto a caracterização do ambiente ao seu redor sejam de natureza complexa para sua representação, ferramentas computacionais bem estruturadas podem representar o fenômeno de forma satisfatória, como é o caso da ferramenta computacional desenvolvida neste trabalho utilizando o método das diferenças finitas no domínio do tempo. O presente trabalho apresenta dois estudos para verificação da influência de edificações na propagação de campo irradiado por descargas atmosféricas. O primeiro estudo avaliou o comportamento das componentes do campo elétrico e do campo magnético irradiados, comparando resultados obtidos com e sem a presença de edificações numa pequena região. Tanto os parâmetros geométricos dos três edifícios considerados neste estudo, como a permissividade e a condutividade elétrica do solo e dos edifícios, foram variados para identificar a sua influência nos campos irradiados. Os resultados mostraram diferentes comportamentos das componentes dos campos resultantes em função da variação desses parâmetros, observando-se inversão de polaridade, oscilações na forma de onda e tanto redução quanto aumento do valor de campo. O segundo estudo avaliou um caso mais geral em que a componente vertical de campo elétrico foi tomada em nove pontos diferentes de uma região tipicamente urbana, com a presença de 102 edifícios. Os valores de campo avaliados em cada ponto, dez metros acima do solo, consideraram a incidência aleatória de 28 descargas atmosféricas distintas, cada uma atingindo o topo de um dado edifício. Os resultados desse segundo estudo mostraram que exceto nos casos em que a descarga atmosférica ocorre próximo do ponto analisado, há reduções significativas do campo elétrico vertical. Desta forma é possível perceber que não apenas a existência de edifícios, mas a sua concentração com diferentes características elétricas e geométricas, podem influenciar significativamente a propagação de campo irradiado. Os valores calculados a partir da ferramenta desenvolvida podem ser usados em conjunto com modelos de acoplamento, para o cálculo de sobretensões induzidas em redes elétricas, em situações realistas com configurações mais complexas. / Atmospheric discharges represent one of the main causes of interruption in power supply to consumers, and although they have more intense effects when direct impact on energy lines, are the case of indirect discharges that draws more attention, since they occur more frequently. Both the first discharges, occurring generally with greater intensity of current, as subsequent discharges that have shorter front time associated, radiate electromagnetic fields which engage with the electrical networks generating surges that can cause so much disruption of power supply as damage to the equipment. The presence of buildings in the lightning incident area affects the propagation of the radiated waves, creating different patterns of resultant fields, which are responsible for induced overvoltages. Although both the lightning itself and characterization of the surrounding environment are of a complex nature for its representation, structured computational tools can represent satisfactorily the phenomenon, such as the software tool developed here using the finite difference time domain method. This work presents two studies to verify the influence of buildings in the propagation of lightning irradiated field. The first study assessed the behavior of the components of the electric field and magnetic field irradiated, by comparing results obtained with and without the presence of buildings in a small region. Both the geometric parameters of the three buildings considered in this study, as the permittivity and electrical conductivity of the soil and buildings, were changed to identify their influence on radiated fields. The results showed different behaviors of the components of the resulting field due to the variation of these parameters, observing polarity inversion, oscillations in the waveform and either a reduction or increase of the field value. The second study evaluated a more general case where the vertical component of the electric field was taken at nine different points of a typical urban area, in the presence of 102 buildings. The field values evaluated at each point, ten meters above the ground, considered the effect of 28 different random lightning, which hit the top of a given building. The results of this second study showed that except in cases where atmospheric discharge occurs near the analyzed point, there are significant reductions of the vertical electric field. Thus it can be seen that not only the existence of buildings, but its concentration with different electrical and geometrical characteristics, can significantly influence the propagation of irradiated field. The values calculated from the developed tool can be used in conjunction with coupling models for calculating induced overvoltages on power lines, in realistic situations with complex configurations.

Les travaux de cette thèse concernent l'étude d'une méthode d'évaluation des constantes diélectriques du béton d'ouvrage à risque par une approche problème inverse. Pour cela des mesures radar de type GPR et un modèle électromagnétique de ces mêmes mesures seront utilisés. Les deux premiers chapitres de la thèse présentent les concepts clés, le contexte et un historique des travaux déjà réalisés dans le domaine. Le chapitre 2 propose en outre une adaptation des travaux déjà réalisés à la recherche de gradients de propriétés diélectriques dans le béton en profondeur. Cette recherche préliminaire nous a permis de redéfinir le processus de mesures pour le rendre plus adapté à nos besoins. Ainsi le chapitre 3 présente une campagne de mesure réalisée à l'aide d'un nouveau dispositif radar sur des corps d'épreuve conditionnés de telle sorte que la répartition de la teneur en eau soit maîtrisée. Dans ce chapitre, nous détaillons également un nouveau modèle numérique 3D du dispositif qui nous permet de simuler nos mesures de façon réaliste Ces simulations sont nécessaires à l'expression du problème inverse. à partir de ces mesures, dans le quatrième chapitre, nous définissons tout d'abord le problème inverse, puis en utilisant des mesures sur les corps d'épreuves saturés, pouvant être considérés comme homogènes d'un point de vue diélectrique, nous résolvons ce problème inverse par un algorithme d'optimisation basé sur celui de Levenberg-Marquardt. Les résultats obtenus par notre processus d'inversion sont cohérents avec les valeurs physiques que l'on pouvait attendre et sont indépendants des valeurs données à nos inconnues lors de l'initialisation. Ces résultats correspondent effectivement à un minimum de la fonction coût qui mesure la distance entre mesures et simulations. Nous avons ensuite étudié des stratégies pour diminuer le temps de calcul de notre processus d'inversion. Une première approche consiste à utiliser un modèle simplifié en 2D du dispositif, qui permet d'initialiser l'inversion 3D avec un point plus proche de la solution. Une autre idée consiste à utiliser au mieux les performances d'une machine multiprocesseurs en parallélisant le code 3D. Dans le chapitre 5 nous nous intéressons à des mesures sur des corps d'épreuve en béton dont la teneur en eau est une fonction affine de la profondeur. Dans ces conditions nous avons fait l'hypothèse, en première approche, que les constantes diélectriques suivent aussi ce type de loi. Après avoir redéfini les inconnues de notre problème inverse et adapté l'algorithme, nous montrons que le processus d'inversion fourni des résultats cohérents en ce qui concerne la permittivité diélectrique, mais insatisfaisant pour la conductivité. Après analyse de ces résultats nous avons proposé diverses pistes pour améliorer et valider la méthode d'inversion. Finalement en comparant l'ensemble des résultats, il apparaît que notre méthode d'inversion permet de caractériser des gradients de permittivité, mais pas de conductivité. Cela représente néanmoins une avancée significative pour la mesure de la teneur en eau dans les bétons, facteur principal influençant la constante diélectrique de ce matériau, dans le contexte du contrôle non destructif des ouvrages du génie civil. / That thesis aims to propose an assessment method of the concrete electromagnetic properties by using radar measurements in a context of building sustainability, by inverse problem. For that purpose Ground Penetrating Radar (GPR) measurements are used as well as a numerical model of the radar device. The first two chapters of the thesis present the key concepts, the context of the study, as well as the history of the research on that topic in particular in our laboratory. Chapter 2 also expands those early works on the search of electromagnetic properties of concrete in depth. That preliminary work helped us to develop a measurement device that is more fitted to our needs. Chapter 3 presents a measurement campaign that was carried out by using a new measurement device on specially made reinforced concrete slabs whose water content is monitored. In that chapter a 3D model of the device is also described. That model allows us to simulate the measurements very precisely. Those simulations are a critical link on the inverse process. Chapter 4 details the formulation of the inverse problem for the case of concrete slabs saturated with water, which can be therefore considered to have homogeneous electromagnetic properties. The problem is solved by using an optimization algorithm based on Levenberg-Marquardt method. The values obtained by the inverse process are physically acceptable and independent of the values given to the unknowns when initializing the algorithm. Those values are the minimum of the cost function that computes the distance between measured and simulated electromagnetic fields. We then studied some strategies to reduce the computing time of the inverse process. A first approach consists in the use of a 2D simplified model of our device to initialize the 3D inversion with values closer to the searched solution. Another idea is to better take advantage of all the resources of a multiprocessor computer by implementing a parallel version of the 3D code. In chapter 5 we focus on the concrete slab with water content being an affine function of depth. We define the new parameters that represent the unknowns of our problem and we adapt the previous algorithm. Then we show that the inverse process gives satisfying results with regard to the dielectric permittivity only. We suggest some ways to improve the method. Finally we conclude that our method allows to retrieve the permittivity of the concrete, but not its conductivity. Nevertheless that result represents a significant step for the measuring of water content in reinforced concrete in particular when a gradient is present, by using radar measurements.

Ce travail vise à utiliser des surfaces d'alumine nanostructurées pour guider la croissance et l'organisation de particules métalliques (Ag, Au et AgxAu1-x), et à les tester en tant que substrats SERS-actifs robustes et réutilisables. Nous avons utilisé la spectrophotométrie pour la caractérisation des propriétés optiques résultantes, l'ellipsométrie spectroscopique pour l'extraction des indices optiques et la microscopie électronique en transmission pour les caractérisations structurales. La diffusion Raman exaltée de surface (SERS) a été utilisée pour la détection de molécules de bipyridine adsorbées sur la surface des échantillons, en collaboration avec l’Institut des Matériaux Jean Rouxel de Nantes. Nous étudions d'abord des systèmes de nanoparticules monométalliques et bimétalliques afin de comprendre les modes de croissance de telles assemblées. Nous montrons que des arrangements différents de nanoparticules bimétalliques sont obtenus selon la séquence de dépôt utilisée et qu'un alliage est obtenu à l'issue de recuits ex situ sous vide. Les propriétés optiques en champ proche et lointain de nanoparticules d'alliage AgxAu1-x noyées dans une matrice d'Al2O3 sont comparées numériquement à celles des métaux purs, par la méthode de calcul des différences finies dans le domaine temporel. Les résultats indiquent que l’amplification du champ pour les nanoparticules de métal pur est plus élevée que pour les nanoparticules d’alliage. Enfin, les expériences SERS menées sur un système dichroïque de nanoparticules d’Ag plus ou moins couplées montrent que l'on peut obtenir un signal SERS intense avec des nanoparticules recouvertes. / The aim of this work is to use nanostructured alumina surfaces to guide the growth and to optimize the organization of metallic particles (Ag, Au and AgxAu1-x), and to test those systems as reusable SERS-active substrates. We used spectrophotometry to characterize the resulting optical properties, spectroscopic ellipsometry for the determination of the optical index and transmission electron microscopy for the structural characterizations. Surfaced-enhanced Raman spectroscopy (SERS) was used for the detection of adsorbed bipyridine molecules on the sample surface, in collaboration with the Institut des Matériaux Jean Rouxel at Nantes. We first study systems consisting of monometallic and bimetallic nanoparticles in order to understand the growth modes of such particle assemblies. A particular attention is paid to the influence of the sequential deposition of Au and Ag on the structural and optical properties. We show that different arrangements of bimetallic nanoparticles are obtained according to the deposition sequence used and that an alloy is obtained after ex situ annealing under vacuum. The near-field and far-field optical properties of AgxAu1-x nanoparticle alloys embedded in an alumina matrix are compared numerically by the finite difference time domain method, with those of pure metal nanoparticles. Our results indicate that pure metal nanoparticles exhibit a greater field enhancement than alloy nanoparticles. Finally, SERS experiments conducted with a dichroic system made of coupled Ag nanoparticles show that an intense SERS signal can be obtained with coated nanoparticles.

This thesis introduces spatial filtering, which is a technique to extend the time step size beyond the conventional stability limit for the Finite-Difference Time-Domain (FDTD) method, at the expense of transforming field nodes between the spatial domain and the discrete spatial-frequency domain and removing undesired spatial-frequency components at every FDTD update cycle. The spatially-filtered FDTD method is demonstrated to be almost as accurate as and more efficient than the conventional FDTD method via theories and numerical examples. Then, this thesis combines spatial filtering and an existing subgridding scheme to form the spatially-filtered subgridding scheme. The spatially-filtered subgridding scheme is more efficient than existing subgridding schemes because the former allows the time step size used in the dense mesh to be larger than the dense mesh CFL limit. However, trade-offs between accuracy and efficiency are required in complicated structures.

This thesis introduces spatial filtering, which is a technique to extend the time step size beyond the conventional stability limit for the Finite-Difference Time-Domain (FDTD) method, at the expense of transforming field nodes between the spatial domain and the discrete spatial-frequency domain and removing undesired spatial-frequency components at every FDTD update cycle. The spatially-filtered FDTD method is demonstrated to be almost as accurate as and more efficient than the conventional FDTD method via theories and numerical examples. Then, this thesis combines spatial filtering and an existing subgridding scheme to form the spatially-filtered subgridding scheme. The spatially-filtered subgridding scheme is more efficient than existing subgridding schemes because the former allows the time step size used in the dense mesh to be larger than the dense mesh CFL limit. However, trade-offs between accuracy and efficiency are required in complicated structures.

Ce travail porte sur la conception, la fabrication et la caractérisation de lentilles planaires nano-structurées dédiées aux capteurs d’images CMOS dans le proche-infrarouge. L’étude des applications et des systèmes d’imagerie optronique mis en jeu ont mis en évidence l’intérêt de l’utilisation des capteurs d’images CMOS dans la bande 800-1100 nm. Les inconvénients liés au silicium et à la structure du pixel justifient l’intégration de lentilles planaires nano-structurées compatibles avec le procédé de fabrication CMOS : une lentille plasmonique, une lentille diffractive métallique dite de Huygens, une lentille diélectrique dite de phase de Fresnel et une lentille à gradient d’indice effectif. Les simulationsélectromagnétiques 2D d’un pixel CMOS complet avec chaque lentille planaire ont démontré l’intérêt de la lentille métallique dans un pixel à faible facteur de remplissage et de la lentille de phase de Fresnel pour un pixel standard. Les simulations électromagnétiques 3D ont permis la conception de ces deux dernières lentilles pour leur fabrication tandis que la lentille à gradient d’indice effectif, susceptible d’approcher le profil de phase idéal, a montré son potentiel pour les pixels CMOS. La caractérisation électro-optique a mis en évidence la performance expérimentale de la lentille de phase de Fresnel fabriquée en "post-process" au LPN-CNRS et de la lentille de Huygens fabriquée "in-process" en fonderie CMOS. Les nombreuses perspectives de ce travail liés à la fabrication et à la marge de progression des lentilles ont été explorées. / This work deals with the design, fabrication and characterization of nanostructuredplanar lenses dedicated to near infrared detection for CMOS image sensors.Applications and optronic systems involved in near infrared imaging have been investigatedin order to highlight the strong interest of CMOS images sensors for the 800-1100 nmspectral band. Limitations of silicon and pixel structure explain the integration of nanostructuredplanar lenses compatible with CMOS fabrication process : a plasmonic lens, a dielectricphase-Fresnel lens, a metallic Huygens lens and a gradient-index lens. 2D electromagneticsimulations of a CMOS pixel with each planar lens have demonstrated the good performanceof the Huygens lens for low fill factor pixels and the phase-Fresnel lens for standard pixels.3D simulations of these lenses have been performed for their integration and fabrication inCMOS image sensors. The 3D design by numerical simulations of a gradient-index lens hasshown its potential interest for CMOS pixels. The experimental performance of a dielectriclens "post-process" integrated/fabricated at LPN-CNRS and a metallic lens "in-process" by aCMOS foundy have been evaluated by electro-optical characterization. Several perspectivesof this work about lens fabrication and potential for improvement have been explored.

Este trabalho tem por objetivo a extensão de métodos numéricos baseados em diferenças finitas no domínio do tempo (FDTD) e no domínio da freqüência (FD-BPM) para a simulação da propagação de ondas eletromagnéticas em materiais com propriedades ópticas diversas, por exemplo, isotrópicos, anisotrópicos, lineares, não-lineares, bem como a combinação destes em uma mesma estrutura. Inicialmente foram elaborados formalismos bidimensionais (FDTD e FD-BPM), dos quais foram investigados modos com polarização TM (Magnético Transversal) que se propagam em estruturas planares magnetoópticas/não-lineares/lineares. Esta polarização foi escolhida tendo em vista o campo magnetostático dc adotado, o qual possibilitou a observação do fenômeno não-recíproco associado ao não-linear simultaneamente. Por outro lado, é bem sabido que o método FDTD é computacionalmente muito intensivo. Portanto, um grande esforço foi dedicado aos formalismos no domínio da freqüência, os quais foram implementados em duas e três dimensões. Este último foi estendido para um formalismo totalmente vetorial, capaz de simular modos híbridos ou até mesmo a transferência de energia entre modos de polarizações ortogonais. Isto nos permitiu investigar geometrias ainda mais complexas, tais como um isolador óptico baseado em um guia de onda tip rib utilizando material magnetooptico. Adicionalmente, fenômenos de natureza complexa, tais como a dinâmica dos condensados de luz em materiais com não-lineares do tipo Kerr com saturação, também conhecidos como meios não-lineares cúbico-qüínticos, foram investigados pela primeira vez com um formalismo vetorial. Finalmente, métodos numéricos capazes de considerar qualquer combinação de materiais com propriedades ópticas distintas (linear e/ou não-linear e/ou magnetoóptico) são uma ferramenta extraordinária para a comunidade científica para o projeto de novos dispositivos ópticos, bem como a investigação de novos efeitos físicos com vistas à aplicações em computação óptica, que podem resultar em um menor e mais eficiente número de componentes para sistemas de comunicações ópticos. / This work introduces three improved formalisms for the analysis of electromagnetic wave propagation through materials with distinct optical properties, i.e., isotropic, anisotropic, linear, nonlinear, or any combination of them. Two finite difference approaches were extensively investigated in this work for this purpose, namely the finite difference in time domain (FDTD), and the finite difference beam propagation method (2D and 3D FD-BPM), these in frequency domain. Initially, a TM (transverse magnetic) mode propagating through a planar magnetooptic/nonlinear/linear waveguide was investigated by way of a two-dimensional formalism (FDTD and FD-BPM). This mode polarization was chosen based on the orientation of the external magnetostatic field adopted, which favored the observation of non-reciprocal and nonlinear effects simultaneously. On the other hand, it is well known that FDTD formalisms are computationally intensives. Therefore, a great effort was dedicated to its frequency domain counterpart (FD-BPM), which was implemented in two and three dimensions. The later was further extended to a fully vectorial formalism, which is capable of simulating hybrid modes or even the energy transfer between orthogonal modes. This enabled us to investigate more complex geometries, such as an optical isolator based on magnetooptic rib waveguide. Additionally, complex phenomena, such as the dynamic of light condensates in bulk nonlinear Kerr media with saturation, also known as cubic-quintic nonlinear media, were investigated for the first time with a 3D vectorial formalism. Finally, numerical methods capable of handling any combination of materials with distinct optical properties (linear and/or nonlinear and/or magnetooptic) are an extraordinary tool for the scientific community for the design of new optical devices, as well as the investigation of new physical effects aimed for optical computing, that may result in fewer and more efficient components for optical communication systems.