In this thesis, a detailed description of acoustic cloaking is put forth using a coating consisting of discrete layers, enabling the cancellation of the scattered field around the object. This particular approach has previously only been applied to electromagnetic waves, for which it was observed that cloaking could be achieved using isotropic materials over a finite bandwidth. The analysis begins with a presentation of the theoretical formulation, which is developed using classical scattering theory for the scattered acoustic field of an isotropic sphere coated with multiple layers. Unlike previous works on acoustic scattering from spherical bodies, the criteria for acoustic cloaking is that the scattered field in the surrounding medium be equal to zero, and seeking a solution for the layer properties which achieve this condition. To effectively investigate this situation, approximate solutions are obtained by assuming either quasi-static limits or thin shells, which provide valuable insight into the fundamental nature of the scattering cancellation. In addition, using these approximate solutions as a guide, exact numerical solutions can be obtained, enabling the full dynamics of the parameter space to be evaluated. Based on this analysis, two distinct types of acoustic cloaking were found: a plasmonic cloak and an anti-resonance cloak. The plasmonic cloak is a non-resonant type of cloak, named plasmonic because of its analogous behavior to the non-resonant cloak observed in electromagnetic waves which utilizes plasmonic materials to achieve the necessary properties. Due to the non-resonant behavior, this type of cloak offers the possibility of a much broader range of cloaking. To expand this design beyond wavelengths on the order of the uncloaked scatterer, multilayered cloak designs are investigated. The anti-resonance cloak, as the name suggests, uses the anti-resonances of the modes within the cloaking layer to supplement the non-resonant plasmonic cloaking of the scattered field. Although somewhat more limited in bandwidth due to the presence of anti-resonances (and the accompanying resonances), this type of cloak enables a larger reduction in the scattering strength, compared with using a single elastic layer utilizing only non-resonant cloaking. A thorough investigation of the design space for a single isotropic elastic cloaking layer is performed, and the necessary elastic properties are discussed. The work in this thesis describes the investigation of the theoretical formulation for acoustic cloaking, expanding upon the use of scattering cancellation previously developed for the cloaking of electromagnetic waves. This work includes a detailed look at the different physical phenomena, including both resonant and non-resonant mechanisms, that can be used to achieve the necessary scattering cancellation and which can be applied to a wide range of scattering configurations for which cloaking would be desirable. In addition to laying out a broad theoretical foundation, the use of limiting cases and practical examples demonstrates the effectiveness and feasibility of such an approach to the acoustic cloaking of a spherical object. / text

Le travail dans cette thèse a consisté à l'étude de la propagation des ondes, en particulier la considération d'un problème de cloaking d'une part et d'un problème inverse d’identification de fissure d'autre part. Nous nous intéressons particulièrement à appliquer une stratégie qui est basé sur un changement de variable pour rendre un objet invisible, la validation numérique des résultats de ce problème a été réalisée par la librairie éléments finies XLiFE++. L'analyse de différents aspects mathématiques du problème de cloaking pour une équation elliptique non linéaire a fait l'objet du chapitre deux. La détermination de l'opérateur Dirichlet-Neumann associé à l'opérateur quasi-linéaire nous a permis d'adapter la technique de transformation utilisé pour le cadre des équations différentielles elliptiques linéaire afin de définir la notion de cloaking pour un problème non linéaire. Pour la dernière partie nous nous sommes intéressés à la reconstruction de fissures pour un problème thermique, pour cela un lien entre l'écart à la réciprocité et la transformée de Fourier du saut de la température à travers la fissure a été établi, ce qui nous a amené à développer un algorithme rapide pour la résolution numérique. / We are concerned with the study of the propagation of waves, in particular the consideration of a cloaking problem on the one hand and of a problem of cracks reconstruction on the second hand. We focus more particularly in applying a strategy that is based on a change of variable to cloak an object. The validation with numerical results has been achieved by the nite element library XLiFE++. The analysis of different mathematical aspects of the cloaking problem for a quasilinear elliptic equation has been the subject of chapter two. The determination of the Dirichlet-Neumann operator associated with the quasilinear operator allowed us to adapt the transformation technique used for the frame-work of linear elliptic differential equations to define the notion of cloaking for our nonlinear problem. For the last part we are interested in crack reconstruction for a thermal problem. For that, a link between the reciprocity gap and the Fourier transform of the temperature jump through the cracks was established, which has led to the development of a fast algorithm for numerical resolution.

Le travail présenté dans cette thèse comporte différents attrayant sujetsde l'optique comme les métamatériaux, l’optique transformationnelle, lescristaux photoniques, la réfraction négative et les interactions thermoplasmoniques.Nous avons développé plusieurs métamatériaux pour les plasmons desurface basés sur l'optique de transformation. Tout d'abord, nous avonsdémontré théoriquement, numériquement et expérimentalement certainsdispositifs mettant en scène le phénomène d’invisibilité.Deuxièmement, nous avons démontré la réfraction négative des plasmonsde surface en utilisant le concept d'espace de pliage (space folding) pourdes lentilles plates et anisotropes et enfin avec seulement desmétamatériaux diélectriques. Additionnellement, nous avons démontréqu’un damier structuré de films d'or peut exhiber une transmission extraordinairesur toute la gamme de fréquences visible.Enfin, nous avons étudié un problème multiphysique en mixant l'optiqueet thermique et leurs effets induits. Nous avons pu montrer que joueravec l'amplitude d'une onde électromagnétique ou une impulsion, peutinduire un gradient de température et le contrôle parfait d’un tel dispositifthermo-plasmonique. / The work which has been presented in this thesis includes differentappealing subjects of optics such as metamaterials, transformationaloptics, photonic crystals, negative refraction and thermo-plasmonicinteractions. In this manuscript we have developed several metamaterialsfor Surface Plasmon Polaritons based on the transformational optics.Firstly we have demonstrated theoretically, numerically andexperimentally some SPP cloaking devices. Secondly, we havedemonstrated SPP negative refraction using the concept of space foldingthen with some dielectric metamaterial, flat and anisotropic SPP lenses.Additionaly we have demonstrated that subwavelength checkerboardstructured thick gold films have demonstrated an extra-ordinarytransmission over the visble range of frequencies.Finally, we have investigated a general multiphysics problem to mix opticsand thermally induced effects. We have been able to show that playingwith the amplitude of an electromagnetic wave or a pulse, we can inducea gradient of temperature and control heat of a plasmonic device.

Doctor of Philosophy / Department of Mechanical and Nuclear Engineering / Liang-Wu Cai / Acoustic scattering by a cylindrical scatterer comprising isotropic acoustic and orthotropic elastic layers is theoretically solved. The orthotropic material is used for the scattering problem because the sound speeds along radial and tangential axes can be different; which is an important property for acoustic cloaking design. A computational system is built for verifying the solutions and conducting simulations. Scattering solutions are obtained based on two theoretical developments. The first one is exact solutions for elastic waves in cylindrically orthotropic elastic media, which are solved using Frobenius method. The second theoretical development is a set of two canonical problems for acoustic-orthotropic-acoustic media. Based on the two theoretical developments, scattering by three specially selected simple multilayer scatterers are analyzed via multiple-scattering approach. Solutions for the three scatterers are then used for solving a “general” multilayer scatterer through a recursive solution procedure. The word “general” means the scatterer can have an arbitrary number of layers and each layer can be either isotropic acoustic or orthotropic elastic. No approximations have been used in the process. The resulting analytically-exact solutions are implemented and verified. As an application example, acoustic scattering by a scatterer with a single orthotropic layer is presented. The effects on the scattering due to changing parameters of the orthotropic layer are studied. Acoustic scattering by a specially designed multilayer scatterer is also numerically simulated. Ratios of the sound speeds of the orthotropic layers along r and θ directions are defined to satisfy the requirement of the Cummer-Schurig cloaking design. The simulations demonstrate that both the formalism and the computational implementation of the scattering solutions are correct.

Dans la première partie, on s'intéresse à la multi-diffusion d'une onde acoustique avec une matrice homogène 2D contenant N inclusions. Dans le cas particulier de deux inclusions, on met alors en évidence l'importance du contraste matrice/inclusion dans les termes d'interactions entre inclusions. Le cas général de la multi-diffusion, pour distribution aléatoire de N inclusions, est ensuite développé dans l'esprit de Foldy-Lax basé sur des moyennes d'ensembles. Ainsi on cherche à déterminer le nombre d'onde effectif de l'onde effective, définie comme la moyenne du champ total, dans le cas d'une onde incidente émise par un point source. La deuxième partie est consacrée au cloaking actif dans une plaque. On détermine ainsi les amplitudes modales des sources multipolaires afin d'éteindre une onde plane ou émise par un point source, dans une région donnée. En outre, cette méthode peut s'appliquer pour éteindre l'onde diffractée par un défaut. Enfin dans la dernière partie, on se propose d'étudier la propagation d'onde au sein d'un milieu comportant des dislocations. On utilise la géométrie de Riemann-Cartan afin de modéliser ce milieu continu. Afin d'illustrer les différences que peuvent induire deux définitions possibles de la déformation (spatiale et matérielle), nous étudions la propagation d'ondes 3D dans l'exemple simple d'un milieu continu avec une densité uniforme et stationnaire de défauts. L'anisotropie et l'atténuation sont présentes dans les deux modèles mais sous forme différente. Enfin la déformation matérielle induit des modes de respiration et, en régime haute fréquence, des ondes transverses qui suivent l'escalier en spirale de Cartan. / In the first part, we investigate the multiple scattering of an acoustic wave within an homogeneous matrix containing N obstacles. In the particular case with 2 obstacles, we show the importance of the contrast matrix /obstacle in the coupling terms between inclusions. The general case of multiple scattering by N obstacles randomly distributed is then developed following the Foldy-Lax theory based on ensemble averaging. We aim to evaluate the effective wavenumber of the effective wave, defined as the average of the total field, in the case where the incoming wave is emitted by a point-like source. The second part is dedicated to the active cloaking in a thin plate. Hence we determine the modal amplitudes of the sources in order to extinct an incoming wave in a given region. This method can be applied to extinct the wave scattered by an obstacle. Finally, in the last part, the Riemann-Cartan geometry is used to model continuum with dislocations. In order to illustrate the differences induced by two possible definitions for the strain (spatial or material) in this framework, propagation of 3D waves is studied for a simple example of infinite continuum with uniform and stationary defects density. Anisotropy and attenuation are caught by both models even if these effects are quite different. Furthermore the material strain uniform breathing modes and, in the high frequency regime, transverse waves which follow the Cartan's spiral staircase.

The refraction properties of photonic crystal lattices offers methods to control the beam steering of light through use of non-linear dispersion contours. In this thesis new photonic crystal structures, such as the square and triangular superlattices, that provide novel refractive properties are analyzed. The property difference between rows in these structures is the hole radius Δr. The difference in hole sizes leads to observation of the superlattice effect, that is, a change in the refractive index Δn between opposite rows of holes. The index difference becomes a function of the size of the smaller r2 hole area or volume due to the addition of the higher index background material compared to the larger r1 holes. The difference in hole radii Δr = r1 - r2 is referred to as the static superlattice strength and is designated by the ratio of r2/r1. The superlattice strength increases as the ratio of r2/r1 decreases. The hole size modulation creates modified dispersion contours that can be used to fabricate advanced beam steering devices through the introduction of electro-optical materials and a controlled bias. A discussion of these superlattice structures and their optical properties will be covered, followed by both static and dynamic tunable device constructions utilizing these designs. Also, static tuning of the devices through the use of atomic layer deposition, as well as active tuning methods utilizing liquid crystal (LC) infiltration, sealed LC cells, and the addition of electro-optic material will be discussed. Also in this thesis we present designs to implement a simpler demonstration of cloaking, the carpet cloak, in which a curved reflective surface is compressed into a flat reflective surface, effectively shielding objects behind the curve from view with respect to the incoming radiation source. This approach eliminates the need for metallic resonant elements. These structures can now be fabricated using only high index dielectric materials by the use of electron beam lithography and standard cleanroom technologies. The design method, simulation analysis, device fabrication, and near field optical microscopy (NSOM) characterization results are presented for devices designed to operate in the 1400-1600nm wavelength range. Improvements to device performance by the deposition/infiltration of linear, and potentially non-linear optical materials, were investigated.

L’objectif de ce travail est le développement de dispositifs de contrôle de la diffusion des ondes acoustiques à l’aide de surfaces hétérogènes, pour des applications à l’acoustique urbaine. Pour remplir cet objectif, deux méthodes sont employées. La première à l’aide d’une métasurface, la direction d’une onde réfléchie est contrôlée. La seconde étude concerne l’influence d’un traitement inhomogène aux parois d’un guide ouvert sur les effets conjoints ou compétitifs d’absorption, de confinement et de rayonnement de l’onde. Nous montrons expérimentalement la possibilité de dissimuler un objet disposé sur un mur pour une onde acoustique audible. Pour y parvenir, une métasurface composée de différents résonateurs de Helmholtz est conçue et est réalisée de façon à être la plus fine possible. Ces travaux sont réalisés dans le domaine fréquentiel mais également dans le domaine temporel, ce qui permet de mettre en avant le caractère large bande de la métasurface. Il est démontré numériquement et expérimentalement que la direction des ondes réfléchies peut être contrôlée. Enfin la dernière partie est consacrée à l’influence d’une paroi hétérogène sur la propagation d’une onde acoustique à l’intérieur d’une rue. Une rue pouvant être assimilée à un guide d’onde ouvert engendre donc des modes de propagation complexes, dus aux pertes par rayonnement. La présence d’un matériau poreux sur les parois d’un guide vient perturber fortement la localisation spatiale des modes, ce qui les rend plus ou moins fuyants. / The aim of this thesis is to develop a scheme for controling the propagation of acoustic waves using heteregenous surfaces. Its results can be applied in the field of urban acoustic. The thesis is composed of two sections, each of them employing a different method. The first section focuses on controling the direction of a reflected wave, using a metasurface. The second concentrates on the influence of an inconsistent treatment to the side of an open waveguide on the wave joint and competitive effects of absorption, confinement and radiation. Part one provides experimental evidence that it is possible to conceal an object placed on a wall from an audible acoustic wave. To prove it, the thinest possible metasurface was constructed with Helmholtz resonators. The experimental results were compared to a numerical study realized with finite elements. This work was made in both temporal and frequency domains, allowing to point out the wide frequency characteristics of the metasurface. The numerical and experimental results show that the direction of a reflected wave can, indeed, be controled. Part two analyse the impact of a heterogeneous wall on the spreadinf of an acoustic wave in a street. Due to radiation losses, the street produces complex ways of propagation. The presence of a porous material on a waveguide‘ side deeply disrupt the spatial location of these waves, making them more or less fleeting. In particular, depending on the position of the material in the street, certain waves will be more confined to the inside of the street, radiating less towards the open external environment. They are consequently, less cushioned.

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.

One of the keys to successful commercialization of photonic devices is compatibility with complementary metal-oxide-semiconductor technology (CMOS), the major platform of the microelectronics industry. Silicon photonics, with plasmonic materials are promising candidates for next generation chip-scale technology. The majority of plasmonics research has focused on noble metals, which are not CMOS compatible. Transition metal nitrides are an emerging class of alternative plasmonic materials that are complementary metal-oxide-semiconductor compatible and have shown promising results when compared to devices utilizing noble metals. This dissertation highlights, a CMOS compatible method to produce such alternative plasmonic materials using atomic layer deposition (ALD), specifically ultrathin plasmonic titanium nitride, aluminum metal and zirconium nitride. A post-deposition hydrogen plasma treatment is also introduced to improve the metallic properties of the ultrathin films. Additionally, this dissertation proposes a core-multishell (CMS) nanowire (NW) device structure that utilizes these materials to enable the creation of photonic devices, specifically detailing designs for cloaking and photoelectrochemical (PEC) water splitting applications. It is shown theoretically that zirconium nitride cloaks a silicon nanowire without substantially compromising the absorption of light, resulting in a less-intrusive, better performing silicon nanowire photosensor, and outperforms a gold cloak in the wavelength region of 400-500 nm. It is demonstrated theoretically that emerging plasmonic materials TiN and ZrN are promising candidates to improve the ideal photocurrent density hematite photoanodes in core-multishell nanowire devices, allowing hematite to remain electrically thin enough to effectively transport charge carriers while absorbing light similar to thick hematite features.

Slippery liquid-infused porous surfaces (SLIPS) – a new class of bio-inspired liquid-repellent surfaces – comprise arbitrarily porous architectures filled with oils that exhibit high interfacial tensions to probe liquids and present ultralow contact angle hysteresis (<〖10〗^°). However, before practical technologies based on SLIPS can be designed at large-scale, a number of fundamental questions remain to be answered. For instance, depending on the sign of the spreading coefficient of the Vapor(V)-lubricant oil(O)-liquid(L) system, defined as S_(OL(V))=γ_LV-γ_LO-γ_OV>0, the lubricating layer forms a layer at the liquid-vapor interface (here, γ_LV is a liquid-vapor interfacial tension, γ_LO – liquid-oil, and γ_OV – oil-vapor). This “cloaking” of liquid drops can deplete SLIPS’ lubricant over time and contaminate the probed liquid. So far, cloaking has been investigated by contact angle goniometry and confocal microscopy, which cannot resolve films of molecular thickness and factors that govern the equilibrium thickness of those films are not entirely clear. Here, we report on the development and application of a reflective-mode SFA platform to characterize the cloaking of water droplets placed on SLIPS. A multilayer matrix method is utilized to analyze the interferometry data. Using this complementary experimental and analytical approach, we determined the thickness of the cloaking layer for the FDTS(solid)-VF-40(lubricant)-water(probe liquid)-air system to be z3= 7±1 nm. Towards deeper insights into the intermolecular and surface forces responsible for cloaking, we demonstrate that repulsive van der Waals interactions are responsible for stabilizing the cloaking film at the water-air interface. Our experimental platform and the analytical framework should facilitate investigations of other SLIPS and probe liquid systems down to the molecular-scale resolution. These findings might aid the rational design of SLIPS, e.g., for drag reduction, anti-biofouling, and anti-corrosion. In addition to investigating SLIPS, We addressed the following questions with the help of atomic force microscopy (AFM): (i) how do zwitterionic osmolytes modulate electrostatic and hydrophobic interactions in nanoscale confinement, and (ii) is it possible to have two negatively charged surfaces attract each other? Our findings are presented as appendices in this thesis.