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

<p>Complex artificial materials (metamaterials) strongly interact with light and can be used to fabricate structures which mimic a material response that has no natural equivalent. Classical tools for the design of optical or radio frequency devices are often ill-suited to utilize such media or have shortcomings in their ability to capture important physics in the device behavior. Recently it has been demonstrated that the structure of Maxwell's equations can be used to exploit this newly available freedom. By leveraging the `form-invariance' of Maxwell's equations under coordinate transforms, it is possible to develop material distributions in which light will behave as though flowing through warped coordinates. This design process is termed `transformation optics' and has inspired the creation of many novel electromagnetic structures such as the invisibility cloak.</p><p>In this dissertation the tools used in the field of transformation optics will be explored and expanded. Several new designs are discussed, each of which expands upon the ideas that have previously been employed in the field. To begin, I show that the explicit use of a transformation which extends throughout all space may be used to reduce the overall size of an optical device without changing its optical properties. A lens is chosen as a canonical device to demonstrate this behavior. For this work I provided the original idea for a compressing transformation as well as its dielectric-only implementation. I then mentored Dan Roberts as he confirmed the device properties through simulation. I further demonstrate that currents may be succesfully employed within the framework of transformation optics-resulting in novel antenna designs. For this work I suggested handling the sheet currents as the limit of a volumetric current density. I also demonstrated how an intermediate coordinate system could be used to easily handle the types of transformatios which were being explored.</p><p>For a particular functionality the choice of transformation is, in general, not unique. It is natural, then, to seek optimized transformations which reduce the complexity of the final structure. It was recently demonstrated that for some transformations a numerical scheme could be employed to find quasi-conformal transformations for which the requisite complex material distribution could be well approximated by an isotropic, inhomogeneous media. This process was previously used to demonstrate a carpet cloak-a device which masks a bump in a mirror surface. Unlike the more common transformation optical media, which exhibit strong losses at high frequencies, isotropic designs can be readily made to function at infrared or even optical frequencies.</p><p>The prospect of leveraging transformation optics in devices which operate at high frequencies, into the infrared and visible, motivates the use of quasi-conformal transformations in lens design. I demonstrate how transformation optics can be used to take a classical lens design based on spherical symmetry, such as a Luneburg lens, and warp it to suit the requirements of a planar imaging array. I report on the experimental demonstration of this lens at microwave frequencies. In the final design a lens is demonstrated in a two-dimensional field mapping waveguide to have a field of view of ~140 degrees and a bandwidth exceeding a full decade. In this work I proposed the idea of using the inverse of the quasi-conformal transform to arrive at the lens index profile. I performed all necessary simulations and wrote ray tracing code to confirm the properties of the lens. I proposed the metamaterial realization of the lens and performed the necessary retrievals for material design. I wrote code which would create the layout for an arbitrary gradient index structure in a standard computer aided drafting format. I fabricated three lenses-two of which are described in this thesis-and took all of the data shown in the thesis.</p><p>The most well known example of a transformation optical device is the invisibility cloak. Despite the great deal of attention paid to the cloak in the literature, the most natural way in which to quantify the efficacy of the cloak-its cross-section-has never been experimentally determined. This measurement is of practical interest because the cloak provides a useful canonical example of a medium which relies on the unique properties of metamaterials-strong anisotropy, inhomogeneity and both magnetic and electric response. Thus, a cloaking cross-section measurement provides a useful way to quantify advancements in the effective medium theories which form the basis for metamaterials. I report on the first such measurements, performed on the original microwave cloaking design. The experiments were carried out in a two-dimensional TE waveguide. Explicit field maps are used to determine the Bessel decomposition of the scattered wave. It is found that the cloak indeed reduces the scattering cross-section of a concealed metal cylinder in a frequency band from 9.91 to 10.14 GHz. The maximum cross-section reduction was determined to be 24%. The total cross-section and the Bessel decomposition of the scattered wave are compared to an analytical model for the cloaking design which assumes a discrete number of loss-less, homogenized cylinders. While the qualitative features of the cloak-a reduced cross-section at the cloaking frequency-are realized, there is significant deviation from the homogenized calculation. These deviations are associated with loss and inaccuracies of the effective-medium-model for metamaterials. In this work I proposed of direct integration of the fields to perform cross-section measurements. I worked out the necessary formulas to determine the coefficients in the Bessel expansion and the resulting scattering cross-section. I mentored an undergraduate student, Dan Gaultney, who scripted the application of the cross-section analysis and took the necessary data. All of the data in this thesis, however, is based on my own implementation of the data analysis.</p> / Dissertation

An elliptical coordinate transformation was chosen to produce an elliptical cylindrical quantum cloak. Since an ellipse can become to a circle geometrically, research on elliptical quantum cloak provides another way to test the feasibility of the quantum cloak. In this study, it was shown that the effective mass of an elliptical cylindrical quantum cloak is simpler than an circular cylindrical one. Hence, an elliptical quantum cloak is easier to achieve experimentally.

In general, Dual-Band technology enables microwave components to work at two different frequencies. This thesis introduces novel dual-band microwave components and their applications. Chapter 2 presents a novel compact dual-band balun (converting unbalanced signals to balanced ones). The ratio between two working frequencies is analyzed. A novel compact microstrip crossover (letting two lines to cross each other with very high isolation) and its dual-band application is the subject of chapter 3. A dual-frequency cloak based on lumped LC-circuits is introduced in chapter 4. In chapter 5, a dual-band RF device to detect dielectric constant changes of liquids in polydimethylsiloxane (PDMS) microfluidic channels has been presented. Such a device is very sensitive, and it has significantly improved the stability. Finally, conclusion of this thesis and future works are given in chapter 6.

Ce travail de thèse constitue une contribution originale et importante à la compréhension de la transformation d’espace et ouvre la voie au design de nouvelles structures éléctromagnétiques. Le couplage entre cette technique innovante et les métamatériaux a permis la réalisation de prototypes aux propriétés uniques. C’est ainsi que nous avons pu concevoir une cape d’invisibilité polygonale, un adapteur de modes ou encore une antenne directive ou isotrope. La fabrication de notre antenne très directive par cette méthode est le seul prototype dans la littérature qui allie le contrôle de la permittivité et la perméabilité à partir de résonnateurs électriques et magnétiques. Ce contrôle ultime de la lumière à partir d’une ingénierie de l’espace trouvera son utilité dans la recherche fondamentale mais aussi pour les ingénieurs et dévellopeurs recherchant plus de précision dans leur conception de dispositifs électromagnétiques. / This phD work is an original and important contribution to the understanding of transformation optics and paves the way to the design of new electromagnetic structures. The coupling between this innovative technique and metamaterials has led to prototypes with unique properties. We have thus developed an invisibility polygonal cloak, an electromagnetic taper, a directional antenna and isotropic source. The realization of our high-directive antenna with this method is the only prototype in the literature that combines controlled variations of the permittivity and permeability from electric and magnetic resonators. The ultimate control of light from an engineering space will find its usefulness in fundamental research but also for engineers and developers who are looking for more precision in the design of electromagnetic devices.

<p>Acoustic metamaterials are engineered materials that were extensively investigated over the last years mainly because they promise properties otherwise hard or impossible to find in nature. Consequently, they open the door for improved or completely new applications (e.g. acoustic superlens that can exceed the diffraction limit in imaging or acoustic absorbing panels with higher transmission loss and smaller thickness than regular absorbers). Our objective is to surpass the limited frequency</p><p>operating range imposed by the resonant mechanism that s1ome of these materials have. In addition, we want acoustic metamaterials that could be experimentally demonstrated and used to build devices with overall performances better than the previous ones reported in the literature.</p><p>Here, we start by focusing on the need of engineered metamaterials in general and acoustic metamaterials in particular. Also, the similarities between electromagnetic metamaterials and acoustic metamaterials and possible ways to realize broadband acoustic metamaterials are briefly discussed. Then, we present the experimental realization</p><p>and characterization of a two-dimensional (2D) broadband acoustic metamaterial with strongly anisotropic effective mass density. We use this metamaterial to realize a 2D broadband gradient index acoustic lens in air. Furthermore, we optimize the lens design by improving each unit cell's performance and we also realize a 2D acoustic ground cloak in air. In addition, we explore the performance of some novel applications (a 2D acoustic black hole and a three-dimensional acoustic cloak) using the currently available acoustic metamaterials. In order to overcome the limitations of our designs, we approach the active acoustic metamaterials path, which offers a broader range for the material parameters values and a better control over them. We propose two structures which contain a sensing element (microphone) and an acoustic driver (piezoelectric membrane or speaker). The material properties are controlled by tuning the response of the unit cell to the incident wave. Several samples with interesting effective mass density and bulk modulus are presented. We conclude by suggesting few natural directions that could be followed for the future research based on the theoretical and experimental results presented in this work.</p> / Dissertation

The first part of this study is focused on numerical studies of light scattering from a single microscopic particle using the Discrete Dipole Approximation (DDA) method. The conventional DDA formalism is generalized to two cases: (a) inelastic light scattering from a dielectric particle and (b) light scattering from a particle with magnetic permeability u /= 1. The first generalization is applied to simulations of Raman scattering from bioaerosol particles, and the second generalization is applied to confi rmation of irregular invisibility cloaks made from metamaterials. In the second part, radiative transfer in a coupled atmosphere-ocean system is solved to study the asymptotic nature of the polarized light in deep oceans. The rate at which the radiance and the polarization approach their asymptotic forms in an ideal homogeneous water body are studied. Effects of the single scattering albedo and the volume scattering function are studied. A more realistic water body with vertical pro files for oceanic optical properties determined by a Case 1 water model is then assumed to study the e ffects of wavelength, Raman scattering, and surface waves. Simulated Raman scattering patterns computed from the generalized DDA formalism are found to be sensitive to the distribution of Raman active molecules in the host particle. Therefore one can infer how the Raman active molecules are distributed from a measured Raman scattering pattern. Material properties of invisibility cloaks with a few irregular geometries are given, and field distributions in the vicinity of the cloaked particles computed from the generalized DDA formalism con rm that the designated material properties lead to invisibility. The radiative transfer model calculation in deep oceans suggest that the underwater radiance approaches its asymptotic form more quickly than the polarization does. Therefore, a vector radiative transfer solution is necessary for asymptotic light field studies. For a typical homogeneous water body whose scattering property is characterized by the Petzold phase function, a single scattering albedo of w0 > 0:8 is required in order that the asymptotic regime can be reached before there are too few photons to be detected.

Σκοπός της παρούσας εργασίας είναι να παράσχει χρήσιμες πληροφορίες για την πρακτική κατασκευή συσκευών αορατότητας. Αρχικά, παρουσιάζονται οι διαφορετικοί τύποι των δισδιάστατων μέσων μετασχηματισμού (συσκευών αορατότητας) και διαπιστώνεται η υπεροχή του δισδιάστατου μανδύα αορατότητας επιπέδου από διηλεκτρικό. Προκειμένου να διερευνήσουμε αριθμητικά την οπτική συμπεριφορά αυτού του τύπου μανδύα, χρησιμοποιούμε τις εξισώσεις που εξάγονται από τη θεωρία της οπτικής μετασχηματισμών, και μέσω της μεθόδου F.D.T.D υπολογίζουμε το ηλεκτρομαγνητικό πεδίο σε όλα τα σημεία του υπολογιστικού πλέγματος. Στα όρια του πλέγματος αυτού τοποθετείται ένα στρώμα τέλειας προσαρμογής , έτσι ώστε να ελαχιστοποιούνται οι ανακλάσεις στα όρια αυτά, σε αναλογία με το πραγματικό πείραμα. Υλοποιώντας έναν κώδικα σε Μatlab, υπολογίζουμε την ένταση της σκεδαζόμενης ακτινοβολίας, για εγκάρσια μαγνητικά επίπεδα κύματα που προσπίπτουν υπό γωνία σε ένα αντικείμενο που περιβάλλεται από έναν μανδύα από διηλεκτρικό και είναι τοποθετημένο σε επίπεδο. Συγκεκριμένα, μελετάμε: την επίδοση της συσκευής συναρτήσει του βαθμού διακριτοποίησης του αριθμητικού πλέγματος, την επίδραση της απορρόφησης και της τυχαίας διαταραχής της επιτρεπτότητας των δομικών υλικών του μανδύα, καθώς και την επίδοση για πρόσπτωση υπό διαφορετικές γωνίες. Τέλος, εκτιμάμε τις ιδιότητες των στρώσεων από διηλεκτρικά που θα μπορούσαν να περιβάλουν τον μανδύα και να βελτιώσουν την αποδοτικότητά του στο ορατό φάσμα. / This work aims to provide useful information for the fabrication of practical cloaking devices. Initially, different types of two dimensional transformation media (invisibility devices) are presented and it is concluded that the all dielectric, two dimensional electromagnetic ground plane cloak dominates. In order to perform a numerical study of the sensitivity of this type of cloak, we use the equations deduced from the transformation optics via finite difference time domain method, for the electromagnetic wave, at every single point of the numerical domain. In the boundaries of this domain, we place a perfectly matched layer in order to minimize the reflections in those boundaries. That would replicate the real experiment with our simulations. By the application of a code written in Matlab, we calculate the scattering signature of an object surrounded by an all dielectric cloak and placed on a ground plane. Transverse magnetic plane waves are launched at an angle towards the object. In particular, we study the performance of the system as a function of the number of distinct components the cloak is divided into, the effects of lossy elements, the angle of incidence, as well as typical random variations of the permittivity of the building materials. Finally, we evaluate impedance matching layers that can surround the cloak and improve its effectiveness in the visible spectrum.

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.

Rubens' material reality culminates in the tableau which he named Het Pelsken (Flemish for 'The little Fur,' known also as La Pelisse). Of his vast oeuvre it is the most frequently cited work, described by one spectator as an "oil painting of a subject quite unusual...a beautiful woman naked beneath her dark fur." 1 Among art historians the tableau has been the subject of debate as to its 'meaning,' especially since the life-size image does not include narrative paraphernalia that would allow mythological interpretations. But as one scholar wrote, "most are relieved that the work was never meant to be sold."2 / This dissertation's trajectory is different. It points to Rubens' late style tableaux, of which Het Pelsken is one, as items painted in an exquisite technique effecting (bodily) presence, and conceived as commodities destined for circulation. Thus the works are heavily invested by producer(s) and buyer(s). Painted in a sophisticated allegorical language that simultaneously defies easy (narrative) access and yet keeps viewers continuously spellbound, Het Pelsken is being reframed together with some of Rubens' other paintings to establish a dialogue with today's audience. This study analyzes the allegorical paradigm by way of Walter Benjamin's dialectics in order to locate levels of truth---which are of relevance to current viewers---and also probes the forces that generate such an overt and repeated display of the feminine body. In so doing, the study also spotlights neo-allegorists, who in their' more recent art practice reconnect with Rubens and disconnect with some compositional and technical strategies of the Baroque master's paintings. These artists include contemporaries Robert Rauschenberg, Peter Dressler and Jean-Luc Godard. / 1Leopold von Sacher-Masoch, please see Chapter One for more of his commentary. 2Julius Held's research and response is also taken up in Chapter One.