L'objectif principal de cette thèse est l'étude des problèmes et des applications qu'ils se développent dans le domaine de la nanophotonique. Plus précisément, nous considérons les structures de métaux nobles où les modèles de dispersion locaux sont insuffisants et la non-localité doit être incluse dans le modèle. Ici, le système physique sous-jacent est typiquement modélisé comme des équations de Maxwell couplées à des lois de dispersion spatio-temporelles dans le régime des longueurs d'onde optiques. Bien que les solutions analytiques puissent être dérivées pour un petit nombre de problèmes, cela n'est généralement pas possible pour les dispositifs du monde réel, qui présentent souvent des géométries complexes et des compositions de matériaux. Suite à une analyse rigoureuse des propriétés physiques et mathématiques du modèle continu original, nous proposons une méthode de type à éléments finis d'ordre élevé pour discrétiser le modèle continu dans l'espace et le temps. Les méthodes discontinues Galerkin (DG) sont bien établies pour la discrétisation spatiale des équations de Maxwell. Cette thèse prolonge les travaux antérieurs sur les systèmes couplés des équations de Maxwell et les lois de dispersion spatiale. Nous utilisons des méthodes explicites de Runge-Kutta (RK) d'ordre élevé pour la discrétisation temporelle. L'intégration temporelle RK garantit un ordre de convergence espace-temps élevé du schéma entièrement discret, qui repose sur un schéma de preuve de convergence. Parallélisme MPI (Message Passing Interface), éléments curvilignes et PML (Perfectly Matched Layers) autour des aspects d'implémentation et d'évaluation des performances dans le cadre du logiciel développé à Inria Sophia Antipolis-Méditerannée (DIOGENES). La méthode développée est appliquée à de nombreuses simulations nanophotoniques réelles de dispositifs où des observables tels que la réflexion, la section transversale (CS) et la spectroscopie de perte d'énergie électronique (EELS) sont étudiés. Entre autres, nous élaborons une feuille de route pour un étalonnage expérimental robuste du modèle de dispersion non local linéarisé basé sur la solution de problèmes inverses et la quantification d'incertitude (UQ) des paramètres géométriques stochastiques. Nous avons également amélioré les accords de simulations numériques non locales et les résultats expérimentaux pour la résonance des plasmons d'espacement des nano-cubes d'argent. Cela démontre la pertinence de simulations non locales précises. / The main objective of this thesis is the study of problems and applications as they arise in the field of nanophotonics. More speci cally, we consider noble metal structures where local dispersion models are insu cient and nonlocality has to be included in the model. Here, the underlying physical system is typically modeled as Maxwell’s equations coupled to spatio- temporal dispersion laws in the regime of optical wavelengths. While analytical solutions can be derived for a small number of problems, this is typically not possible for real-world devices, which often feature complicated geometries and material compositions. Following a rigorous analysis of the physical and mathematical properties of the original continuous model, we propose a high order finite element type method for discretizing the continuous model in space and time. Discontinuous Galerkin (DG) methods are well established for the spatial discretization of Maxwell’s equations. This thesis extends previous work on the coupled systems of Maxwell’s equations and spatial dispersion laws. We use explicit high-order Runge-Kutta (RK) methods for the subsequent time discretiz- ation. RK time integration guarantees a high space-time convergence order of the fully-discrete scheme, which is underpinned by a sketch of a convergence proof. Message Passing Interface (MPI) parallelization, curvilinear elements and Perfectly Matched Layers (PMLs) round of implementation aspects and performance assessments in the scope of the Software developed at Inria Sophia Antipolis-Méditerannée (DIOGENeS). The developed method is applied to numerous real-world nanophotonics simulations of devices where observables like re ectance, Cross Section (CS) and Electron Energy Loss Spectroscopy (EELS) are studied. Inter alia, we elaborate a roadmap for a robust experimental calibration of the linearized nonlocal disper- sion model based on the solution of inverse problems and Uncertainty Quanti cation (UQ) of stochastic geometric parameters. We also find improved agreements of nonlocal numerical simulations and exper- imental results for the gap-plasmon resonance of silver nano-cubes. This demonstrates the relevance of accurate nonlocal simulations.

Finite difference approximations are methods for solving differential equations by approximating derivatives. This work will begin with how to solve a partial differential equation (PDE) called the advection equation, ut + cux = 0. Both analytically, and approximately with three different finite difference methods for the spatial part of the equation: • Central in space, • First order upwind in space, • Beam-Warming in space, and forward Euler for the temporal part. We then use the theoretical approximations considered for the advection equation and apply it on Maxwell’s equations for electromagnetism in 1D. This is a system of advection equations that describes how electromagnetic waves propagate through a dielectric material. In the end of this work we will model this electromagnetic wave, or wave of light moving through materials with different refraction indexes.

Les travaux effectués durant cette thèse s’inscrivent dans le cadre d’une collaboration entre l’équipe CEM de l’Institut Pascal et l’équipe EDPAN du Laboratoire de Mathématiques de l’Université Blaise Pascal de Clermont-Ferrand. Nous présentons ici une étude qui, partant de l’analyse du processus de Retournement Temporel en électromagnétisme, a débouché sur le développement d’une méthode originale baptisée Linear Combination of Configuration Fields (LCCF) ou, en français, Combinaison Linéaire de Configurations de Champs. Après avoir introduit l’ensemble des outils et méthodes utilisés dans ces travaux, ce mémoire détaille le processus de Retournement Temporel de base ainsi qu’un ajout apporté à celui-ci. Par la suite, la méthode LCCF s’étant révélée applicable à plusieurs problèmes d’identification de sources en électromagnétisme, nous nous consacrons à la présentation détaillée des différentes variantes de celle-ci et nous illustrons son utilisation sur de nombreux exemples numériques. / This Ph.D thesis is the result of a collaboration between the CEM team of Pascal Institute and the EDPAN team of the Laboratory of Mathematics of the Blaise Pascal University in Clermont-Ferrand. We present here a study based on Time Reversal process in Electromagnetics. This work led to the development of a novel method called Linear Combination of Configuration Field (LCCF). This thesis first introduces the tools and the numerical methods used during this work. Then, we describe the Time Reversal process and a possible improvement to the basic technic. Afterwards, several possible applications of the LCCF method to electromagnetic source identification problems are detailed and we illustrate each of it on various numerical examples.

Dans cette thèse, nous nous intéressons à l’amélioration des performances numériques dela méthode Galerkin Discontinu en Domaine Temporel (GDDT), afin de valoriser son emploi industrielpour des problèmes de propagation d’ondes électromagnétiques. Pour ce faire, nous cherchons à réduire lenombre d’éléments des maillages utilisés en appliquant une stratégie de h-déraffinement/p-enrichissement.Dans un premier temps, nous montrons que si ce type de stratégie permet d’améliorer significativementl’efficacité numérique des résolutions dans un cadre conforme, son extension aux maillages non-conformespeut s’accompagner de contre-performances rédhibitoires limitant fortement leur intérêt pratique. Aprèsavoir identifié que ces dernières sont causées par le traitement des termes de flux non-conformes, nousproposons une méthode originale de condensation afin de retrouver des performances avantageuses. Cellecise base sur une redéfinition des flux non-conformes à partir d’un opérateur de reconstruction de traces,permettant de recréer une conformité d’espaces, et d’un produit scalaire condensé, assurant un calculapproché efficace. La stabilité et la consistance du schéma GDDT ainsi défini sont établies sous certainesconditions portant sur ces deux quantités. Dans un deuxième temps, nous détaillons la construction desopérateurs de trace et des produits scalaires associés. Nous proposons alors des flux condensés pourplusieurs configurations non-conformes, et validons numériquement la convergence du schéma GDDT résultant.Puis, nous cherchons à concevoir un algorithme de h-déraffinement/p-enrichissement automatisé,dans le but de générer des maillages hp minimisant les coûts de calcul du schéma. Ce processus est traduitsous la forme d’un problème d’optimisation combinatoire sous plusieurs contraintes de natures trèsdiverses. Nous présentons alors un algorithme de post-maillage basé sur un parcours efficace de l’arbrede recherche des configurations admissibles, associé à un processus de déraffinement hiérarchique. Enfin,nous mettons en œuvre la chaîne de calcul développée sur plusieurs cas-tests d’intérêt industriel, etévaluons son apport en termes de performances numériques. / This thesis is devoted to improving the numerical efficiency of the Discontinuous Galerkinin Time Domain (DGDT) method, in order to enhance its suitability for industrial use. One can noticethat, in an hp-conforming context, increasing correlatively the approximation order and the mesh sizeis a powerful strategy to reduce numerical costs. However, in complex geometries, the mesh can beconstrainted by the presence of small-scale inner elements, leading to hp-nonconforming configurationswith hanging nodes. The first issue we are dealing with is related to the nonconforming fluxes involvedin these configurations, whose high computational costs can deter the use of hp-coarsening strategies.In order to recover a satisfactory performance level, an original flux-lumping technique is set up. Thistechnique relies on recasting hybrid fluxes into conforming ones, and is performed by introducing twoingredients : a reconstruction operator designed to map traces from each side of a nonconforming interfaceinto the same functional space, and a lumped scalar product granting efficient integral computations.The resulting DGTD scheme is then proved to be stable and consistent, under some assumptions on thelatter two elements. Subsequently, we develop a lumped flux construction routine, and show numericalconvergence results on basic hybrid configurations. In a second part, we implement an automated strategyaiming at generating efficient hp-nonconforming meshes, well-suited to the previous DGDT scheme. To doso, a post-meshing process is formalized into a constrained optimization problem. We then put forward aheuristic hp-coarsening algorithm, based on a hierarchical coarsening approach coupled with an efficientsearch over the feasible configuration tree. Lastly, we present several numerical examples related toelectromagnetic wave propagation problems, and evaluate computational cost improvements.

Transformation optics, a recently booming area, provides people a new approach to design optical devices for manipulating light. With transformation optics, a lot of novel optical devices are proposed, such as invisibility cloaks, optical wormholes, optical black holes, illusion devices. The present thesis is devoted to investigate transformation optics for manipulating light. Firstly, an introduction to transformation optics is given. This part includes: (1) introducing differential geometry as the mathematical preparation; (2) expressing Maxwell’s equations in an arbitrary coordinate system and introducing the concept of transformation media as the foundation stone of transformation optics; (3) discussing light from the geometry perspective as the essence of transformation optics; (4) showing how to use transformation optics to design optical devices. For our works on invisibility cloaks, we analyze the properties of arbitrary shaped invisibility cloaks, and confirm their invisibility abilities. The geometrical perturbations to cylindrical and spherical shaped cloaks are analyzed in detail. We show that the cylindrical cloak is more sensitive to the perturbation than a spherical cloak. By imposing a PEC (PMC) layer at the interior boundary of the cylindrical cloak shell for TM (TE) wave, the sensitivity can be reduced dramatically. A simplified non-magnetic cylindrical cloak is also designed. We show that the dominant zeroth order scattering term can be eliminated by employing an air gap between the cloak and the cloaked region. We propose a compensated bilayer by a folding coordinate transformation based on transformation optics. It is pointed out that complementary media, perfect negative index lens and perfect bilayer lens made of indefinite media are well unified under the scope of the transformed compensated bilayer. We demonstrate the applications of the compensated bilayer, such as perfect imaging and optical illusion. Arbitrary shaped compensated bilayers are also analyzed. Nihility media known as the media with ε =μ= 0, are generalized from transformation optics as transformation media derived from volumeless geometrical elements. The practical constructions of nihility media by metamaterials are discussed. The eigen fields in the nihility media are derived. The interactions between an external incident wave and a slab of nihility media in the free space background are analyzed. A new type of transformation media called α media is proposed for manipulating light. Light rays in the α media have a simple displacement or rotation relationship with those in another media (seed media). Such relationship is named α relationship. The α media can be designed and simplified to a certain class of diagonal anisotropic media, which are related to certain isotropic media by the α relationship. Several optical devices based on the α transformation media are designed. Invisibility cloaks obtained from the coordinate transformation approach are revisited from a different perspective. / QC 20101102

In high frequency computational electromagnetics, rigorous numerical methods be come unrealistic tools due to computational demand increasing with the frequency. Instead approximations to the solutions of the Maxwell equations can be employed to evaluate th electromagnetic fields. In this thesis, we present the implementations of three high frequency approximat methods. The first two, namely the Geometrical Theory of Diffraction (GTD) and th Physical Optics (PO), are commonly used approximations. The third is a new invention that will be referred to as the Surface Current Extraction-Extrapolation (SCEE). Specifically, the GTD solver is a flexible and modular software package which use Non-Uniform Rational B-spline (NURBS) surfaces to model complex geometries. The PO solver is based on a triangular description of the surfaces and includes fas shadowing by ray tracing as well as contribution from edges to the scattered fields. GTD ray tracing was combined with the PO solver by a well thought-out software architecture Both implementations are now part of the GEMS software suite, the General ElectroMag netic Solvers, which incorporates state-of-the-art numerical methods. During validations both GTD and PO techniques turned out not to be accurate enough to meet the indus trial standards, thus creating the need for a new fast approximate method providing bette control of the approximations. In the SCEE approach, we construct high frequency approximate surface currents ex trapolated from rigourous Method of Moments (MoM) models at lower frequency. T do so, the low frequency currents are projected onto special basis vectors defined on th surface relative to the direction of the incident magnetic field. In such configuration, w observe that each component displays systematic spatial patterns evolving over frequenc in close correlation with the incident magnetic field, thus allowing us to formulate a fre quency model for each component. This new approach is fast, provides good control of th error and represents a platform for future development of high frequency approximations. As an application, we have used these tools to analyse the radar detectability of a new marine distress signaling device. The device, called "Rescue-Wing", works as an inflatabl radar reflector designed to provide a strong radar echo useful for detection and positionin during rescue operations of persons missing at sea. / QC 20101004

Research on metamaterials has been growing ever since the first experimental realization of double negative media. The theory of transformation optics provides people with a perfect tool to make use of vast possibilities of the constitutive parameters for metamaterials. A lot of fascinating designs have been brought to us by transformation optics, with invisibility cloaks being the most intensely studied. The present thesis aims to develop the basic theory of transformation optics, and utilize it to design invisibility cloaks for various applications. After the background description of this field, the theory of transformation optics is first introduced. Formulas of transformation medium parameters and transformed fields are derived with every detail explained, so that the working knowledge of transformation optics can be grasped with minimal prerequisite mathematics. Proof of form invariance of full Maxwell’s equations with sources is presented. Design procedure of transformation optics is then demonstrated by creating perfect invisibility cloaks. The introduction to basic theory is followed by discussions on our works included in our published papers. As our first application, a method of designing two-dimensional reduced cloaks of complex shapes is proposed to relieve the difficulty of singularity occurring in perfect cloaks. The simple and intuitive method is the first way to design two-dimensional reduced cloaks of shapes other than cylindrical. Elliptical and bowtie shaped reduced cloaks are presented to verify the effectiveness of the method. Prominent scattering reduction is observed for both examples. Considering the practical realization, transformations continuous in the whole space must be the identity operation outside certain volume, and thus they can only manipulate fields locally. Discontinuous transformations are naturally considered to break the limitation. We study the possible reflections from such a transformation medium due to a discontinuous transformation by a new concept of inverse transformation. This way, the reflection falls into the framework of transformation optics as well. A necessary and sufficient condition for no reflection is derived as a special case. Unlike the invisibility realized by perfect cloaks, cloaking an object over a dielectric half-space has advantages in some particular applications. Starting from a perfect cloak, a half-space cloak is designed to achieve this. In our design, two matching strips embedded in the dielectric ground are used to induce proper reflection in the upper air space, so that the reflected field is the same as that from the bare dielectric ground. Cloaks obtained from singular transformations and even reduced models all have null principal value in their material parameters, making invisibility inherently very narrowband. In contrast, a carpet cloak designed by only coordinate deformation does not have the narrowband issue, and can perform well in a broad spectrum. The invisibility accomplished by the carpet cloak is also for the half-space case as our previous design. In this part, we extend the original version of a carpet cloak above a PEC sheet to a general dielectric ground. / QC 20110415

Submitted by Erika Demachki (erikademachki@gmail.com) on 2017-06-08T17:36:27Z No. of bitstreams: 2 Dissertação - Paulo Roberto Ferreira - 2017.pdf: 14996898 bytes, checksum: cdb17170fa3d2d81ae6bea7a5743f3a9 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2017-06-09T10:59:26Z (GMT) No. of bitstreams: 2 Dissertação - Paulo Roberto Ferreira - 2017.pdf: 14996898 bytes, checksum: cdb17170fa3d2d81ae6bea7a5743f3a9 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2017-06-09T10:59:26Z (GMT). No. of bitstreams: 2 Dissertação - Paulo Roberto Ferreira - 2017.pdf: 14996898 bytes, checksum: cdb17170fa3d2d81ae6bea7a5743f3a9 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2017-03-17 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / The proposal of this dissertation is the development of an extracurricular project that meets the demand of students that are about to conclude high school, of notable knowing in mathematics and physics, specifically in basic electromagnetics. Using the theory of meaningful learning of David Ausubel, the proposal of this project is to incorporate through expositive classes concepts of differential and integral calculus, dot product and vector product of higher education exact sciences courses to the high school environment in order to help high school students that present resourcefulness in exact sciences and yearn for new knowledge. Such mathematical tools presented are going to serve as prior organizers, according to the meaningful learning theory, to the understanding of the pool of the four most influential equations of electromagnetism as a whole: Maxwell's equations. The immediate solutions of Maxwell's equations allow students to link new concept with subsumers already acquired in their regular classes, providing a more detailed view of formulas and concepts only quoted before without any previous reference. In this sense, the goal of this dissertation is not to teach the whole concepts pertinent to higher education, but sharpen the interest for the study area, which is already shown by most students interested in joining exact sciences, engineering courses and similars. Hence, the project improves the performances of apprentices in higher education entrance exams and foments interest in subjects which are classified as boring and difficult both to teach and to learn for most students, although fascinating. / A proposta desta dissertação é o desenvolvimento de um projeto extracurricular que atende à demanda de alunos concluintes do Ensino Médio, de saber notório em matemática, em física, especificamente em eletromagnetismo básico. Utilizando a teoria da aprendizagem significativa de David Ausubel, o objetivo deste projeto é trazer, por meio de aulas expositivas, noções de Cálculo diferencial e integral, produto escalar e produto vetorial, do domínio de cursos superiores de exatas para o ambiente do Ensino Médio de modo a auxiliar estudantes secundaristas que apresentam desenvoltura em exatas e anseiam por um novo saber. Tais ferramentas matemáticas apresentadas servirão como organizadores prévios, de acordo com a teoria da aprendizagem significativa, para o entendimento do conjunto das quatro equações mais influentes do eletromagnetismo na sua forma integral: as equações de Maxwell. As soluções imediatas das equações de Maxwell permitem que os alunos relacionem o novo conceito a subsunçores adquiridos em suas aulas regulares, proporcionando uma visão mais detalhada de fórmulas e de conceitos antes apenas citados e sem qualquer referência anterior. Nesse sentido, a função do presente trabalho não é de ensinar, na sua totalidade, conceitos pertinentes ao ensino superior, mas aguçar o interesse pela área de estudo, que já é demonstrado pela maioria dos estudantes interessados em ingressar em cursos de exatas, engenharias e afins. Dessa forma, o projeto aperfeiçoa as performances dos aprendizes em exames de ingresso ao ensino superior e fomenta o interesse por assuntos que, na maioria das vezes, são classificados como entediantes e difíceis tanto para ensinar quanto para aprender, embora sejam fascinantes.

Dans cette thèse, nous nous intéressons à l’amélioration du schéma de Yee pour traiter demanière plus efficace et pertinente les problèmes industriels auxquels nous sommes confrontés à l’heureactuelle. Pour cela, nous cherchons avant tout à diminuer les erreurs numériques de dispersion et àaméliorer les modélisations des géométries courbes ainsi que des réseaux de câbles. Pour répondre àces besoins, une solution basée sur un schéma Galerkin discontinu pourrait être envisagée. Toutefois,l’utilisation d’une telle technique sur la totalité du volume de calcul est relativement coûteuse. De plus,la prise en compte de structures filaires sur un tel schéma n’est pas encore opérationnelle. C’est pourquoi,dans l’optique d’avoir un outil industriel, et après une étude bibliographique, nous nous sommes plutôtorientés sur l’étude d’un schéma éléments finis (FEM) sur maillage cartésien qui possède toutes lesbonnes propriétés du schéma de Yee. Notamment, à l’ordre d’approximation spatiale égal à 0 ce schémaFEM est exactement le schéma de Yee, et, pour des ordres supérieurs, il permet de réduire fortementl’erreur de dispersion numérique de ce dernier. Dans le travail de cette thèse, pour ce schéma, nous avons notamment donné un critère de stabilité théorique, étudié sa convergence théorique et fait une analyse de l’erreur de dispersion. Pour tenircompte des possibilités d’ordre d’approximation spatiale variable par direction, nous avons mis en placeune stratégie d’affectation des ordres suivant le maillage donné. Ceci nous a permis d’obtenir un pas detemps optimal pour une précision souhaitée tout en réduisant les coûts de calcul. Après avoir porté ceschéma sur des machines de production, différents problèmes de CEM, antennes, IEM ou foudre ont ététraités afin de montrer les avantages et le potentiel de celui-ci. En conclusion de ces expérimentationsnumériques, il s’avère que la méthode est limitée par le manque de précision pour prendre en comptedes géométries courbes. Afin d’améliorer cela, nous avons proposé une hybridation entre ce schéma et leschéma GD que l’on peut étendre aux autres schémas comme les méthodes différences finies (FDTD) etvolumes finis (FVTD). Nous avons montré que la technique d’hybridation proposée conserve l’énergie etest stable sous une condition que nous avons évaluée de manière théorique. Des exemples de validationont ensuite été montrés. Enfin, pour tenir compte des réseaux de câbles, un modèle de fils minces d’ordred’approximation spatiale élevé a été proposé. Malheureusement, celui-ci ne peut pas couvrir l’ensembledes cas industriels et pour remédier à cela, nous avons proposé une hybridation de notre approche avecune équation de ligne de transmission. L’intérêt de cette hybridation a été montré sur un certain nombred’exemples, que nous n’aurions pas pu traiter par un modèle de structure filaire simple. / In this thesis, we study the improvement of the Yee’s scheme to treat efficiently and in arelevant way the industrial issues we are facing nowadays. For that, we first of all try to reduce thenumerical errors of dispersion and then to improve the modeling of the curved surfaces and of theharness networks. To answer these needs, a solution based on a Galerkin Discontinuous (GD) methodhas been first considered. However, the use of such method on the entire modeling volume is quite costly ;moreover the wires are not taken into account in this method. That is the reason why, with the objectiveof an industrial tool and after a large bibliographic research, we headed for the study of finite elementsscheme (FEM) on a Cartesian mesh which has all the good properties of the Yee’s scheme. Especially,this scheme is exactly the Yee’s scheme when the spatial order of approximation is set to zero. Forthe higher orders, this new scheme allows to greatly reduce the numerical error of dispersion. In theframe of this thesis and for this scheme, we give a theoretical criterion of stability, study its theoreticalconvergence and we perform an analysis of the error of dispersion. To take into account the possibilityof the variable spatial orders of approximation in each direction, we put in place a strategy of orderaffectation according to the given mesh. This strategy allows to obtain an optimal time step for a givenselected precision while reducing the cost of the calculations. Once this new scheme has been adaptedto large industrial computing means, different EMC, antennas, NEMP or lightning problems are treatedto demonstrate the advantages and the potential of this scheme. As a conclusion of these numericalsimulations we demonstrate that this method is limited by a lack of precision when taking into accountcurved geometries. To improve the treatment of the curved surfaces, we propose an hybridization between this scheme andthe GD scheme. This hybridization can also be applied to other methods such as Finite Differences(FDTD) or Finite Volumes (FVTD). We demonstrate that the technique of hybridization proposed,allows to conserve the energy and is stable under a condition that we study theoretically. Some examplesare presented for validation. Finally and to take into account the cables, a thin wire model with a highorder of spatial approximation is proposed. Unfortunately, this model does not allow to cover all theindustrial cases. To solve this issue we propose an hybridization with a transmission line method. Theadvantage of this hybridization is demonstrated thanks to different cases which would not have beenfeasible with a more simple thin wire method.

L’objectif de cette thèse est de développer une méthode Galerkine discontinue d’ordre élevé capable de prendre en considération des simulations réalistes liées à la nanophotonique. Au cours des dernières décennies, l’évolution des techniques de lithographie a permis la création de structure géométriques de tailles nanométriques, révélant ainsi une large gamme de phénomènes nouveaux nés de l’interaction lumière-matière à ces échelles. Ces effets apparaissent généralement pour des objets de taille égale ou (très) inférieure à la longueur d’onde du champ incident. Ce travail repose sur le développement et l’implémentation de modèles de dispersion appropriés (principalement pour les métaux), ainsi que sur un large éventail de méthodes computationnelles classiques. Deux développements méthodologiques majeurs sont présentés et étudiés en détails: (i) les éléments courbes, et (ii) l’ordre d’approximation local. Ces études sont accompagnées de plusieurs cas-tests réalistes tirés de la nanophotonique. / The goal of this thesis is to develop a discontinuous Galerkin time-domain method to be able to handle realistic nanophotonics computations. During the last decades, the evolution of lithography techniques allowed the creation of geometrical structures at the nanometer scale, thus unveiling a variety of new phenomena arising from light-matter interactions at such levels. These effects usually occur when the device is of comparable size or (much) smaller than the wavelength of the incident field. This work relies on the development and implementation of appropriate models for dispersive materials (mostly metals), as well as on a large panel of classical computational techniques. Two major methodological developments are presented and studied in details: (i) curvilinear elements, and (ii) local order of approximation. This work is complemented with several physical studies of real-life nanophotonics applications.