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.

Le domaine des métamatériaux acoustiques connaît un succès grandissant depuis maintenant une vingtaine d’années, notamment en raison de phénomènes exotiques aux perspectives d’applications plus que prometteuses : « l’invisibilité » acoustique en est l’exemple le plus manifeste. Dans cette thèse, nous présentons des métamatériaux acoustiques à résonances locales, et qui permettent de générer aussi bien de l’opacité que de la transparence acoustique. C’est plus particulièrement le couplage entre résonateurs de différentes formes qui est l’objet de nos investigations. Notre étude nous a permis de comprendre que la diffraction est l’une des principales limitation à l’omnidirectionalité des performances d’opacité, que nous avons caractérisé au moyen d’un banc ultrasonore motorisé. Un tel phénomène de diffraction est dû à la présence d’un réseau, et nous proposons dans notre étude des solutions qui permettent de dépasser cette limitation. A partir de cette étude, nous avons ainsi pu transposer au domaine sonore les résultats obtenus pour les ultrasons, ce qui nous a permis de réaliser deux principaux types de dispositifs : des métamatériaux acoustiques aux fonctions de réflecteur d’une part et d’absorbant basses fréquences d’autre part. Enfin, l’étude en homogénéisation de ce type de structure a aussi révélé un effet de densité effective quasi-nulle, dont les applications vont du contrôle de front d’onde, à la furtivité acoustique. De tels résultats offrent un potentiel d’application dans de nombreux champs, que ce soit pour le bâtiment ,l’automobile, l’aéronautique, ou l’acoustique sous-marine. / For more than twenty years now, Acoustic Metamaterials are experiencing a growing success, partlydue to exotic phenomena and their wide variety of extremely promising applications: “InvisibilityCloak” is the most vivid example of this. In this thesis, we report on designs of locally resonantacoustic metamaterials, that enable us to generate both sound opacity and transparency. It is moreparticularly coupling between resonators having different forms which is the focus of our work.This study permit us to understand that diffraction is one of the main limitation of omnidirectionalcapabilities involving locally resonant perforated plates, as supported by experimental investigationsrealized using a motorized ultrasonic set-up. We proposed solutions to overcome such a limitation,in the case where the opacity mechanism uses diffraction gratings. From this, we transposed theresults obtained in ultrasonic frequencies to the audible range, which permits us to develop twomain kinds of acoustic devices based on metamaterials: broadband reflectors and low-frequencyabsorbers. Finally, homogenization study of such structures revealed an effect of density near-zero,with applications from shaping wave front, to acoustic furtiveness. Such results paves the way forpromising applications in various field, including construction, automotive and aeronautical industries,submarine acoustics and so on.

This report examines the cross sections of silver microresonators subjected to an incident light with different polarization. The microresonators had different geometries with and without broken symmetries. Cross section profiles for different microresonator configurations are interesting for the division of Material Physics, Uppsala University, when designing metamaterials to tune the optical response of the material. The goal is to form an insight of how the optical response can be tuned by choosing different geometries, varying the size and polarization of the incident light. In this project computer simulations in COMSOL were made to simulate the optical response of different microresonators. When the incident light interact with the silver microresonators plasmonic excitations is generated which in turn interacts with the light changing the phase and therefore the optical response. By increasing the radius of the disk silver microresonantors the resonance was found to shift to lower energies. For a geometry with a disk microresonator inside a ring microresonator the Fano resonances were dependent of the radius of the disk microresonator.

When a nanostructure is coupled between two leads, the electron transmission probability as a function of energy, E, is used in the Landauer formula to obtain the electrical conductance of the nanodevice. The electron transmission probability as a function of energy, T (E), is calculated from the appropriate solution of the time independent Schrödinger equation. Recently, a large class of nanostructures called quantum dragons has been discovered. Quantum dragons are nanodevices with correlated disorder but still can have electron transmission probability unity for all energies when connected to appropriate (idealized) leads. Hence for a single channel setup, the electrical conductivity is quantized. Thus quantum dragons have the minimum electrical conductance allowed by quantum mechanics. These quantum dragons have potential applications in nanoelectronics. It is shown that for dimerized leads coupled to a simple two-slice (l = 2, m = 1) device, the matrix method gives the same expression for the electron transmission probability as renormalization group methods and as the well known Green's function method. If a nanodevice has m atoms per slice, with l slices to calculate the electron transmission probability as a function of energy via the matrix method requires the solution of the inverse of a (2 + ml) (2 + ml) matrix. This matrix to invert is of large dimensions for large m and l. Taking the inverse of such a matrix could be done numerically, but getting an exact solution may not be possible. By using the mapping technique, this reduces this large matrix to invert into a simple (l + 2) (l + 2) matrix to invert, which is easier to handle but has the same solution. By using the map-and-tune approach, quantum dragon solutions are shown to exist for single-layer planar rectangular crystals with different boundary conditions. Each chapter provides two different ways on how to find quantum dragons. This work has experimental relevance, since this could pave the way for planar rectangular nanodevices with zero electrical resistance to be found. In the presence of randomness of the single-band tight-binding parameters in the nanodevice, an interesting quantum mechanical phenomenon called Fano resonance of the electron transmission probability is shown to be observed.

In this thesis devices for controlling the flow of surface plasmon polaritons are described. Dielectric and metallic nanostructures were designed for this purpose, and characterized by leakage radiation microscopy in real and in reciprocal spaces. Manipulation of surface plasmons by dielectric lenses and gradient index elements is presented, and negative refraction, steering and self-collimation of surface plasmons in one- and two-dimensional plasmonic crystals is demonstrated. The achieved degree of control was applied for routing of nanoparticles by optical forces, as well as for two methods of enhancing the figures of merit of plasmonic refractive index sensors, based on the one hand on Fano resonances natural to leakage radiation microscopy, and on the other hand on anisotropie plasmonic bandstructures.

Ce manuscrit s'inscrit dans le contexte du contrôle de la propagation des plasmons de surface. A cet effet, des nanostructures diélectriques et métalliques ont été conçues et caractérisées par microscopie à champ de fuite dans les espaces réels et réciproques. La manipulation des plasmons de surface à l'aide de lentilles diélectriques et d' éléments à gradient d'indice est présentée, et la réfraction négative, la direction et l'auto-collimation des plasmons de surface dans des cristaux plasmoniques à une ou deux dimensions sont démontrées. Ces résultats ont été utilisés pour le guidage de nanoparticules à l'aide de forces optiques, ainsi que pour deux méthodes permettant de renforcer le facteur de mérite de sondes plasmoniques de variation d'indice de réfraction, basées l' une sur les résonances de Fano naturelles de la microscopie à champ de fuite, et pour la seconde sur les structures des bandes plasmoniques anisotropes. / In this thesis devices for controlling the flow of surface plasmon polaritons are described. Dielectric and metallic nanostructures were designed for this purpose, and characterized by leakage radiation microscopy in real and in reciprocal spaces. Manipulation of surface plasmons by dielectric lenses and gradient index elements is presented, and negative refraction, steering and self-collimation of surface plasmons in one- and two-dimensional plasmonic crystals is demonstrated. The achieved degree of control was applied for routing of nanoparticles by optical forces, as well as for two methods of enhancing the figures of merit of plasmonic refractive index sensors, based on the one hand on Fano resonances natural to leakage radiation microscopy, and on the other hand on anisotropie plasmonic bandstructures.