The resolution of optical instruments is normally limited by the wave nature of light. Circumventing this limit, known as the diffraction limit of imaging, is of tremendous practical importance for modern science and technology. One method, super-resolved fluorescence microscopy was distinguished with the Nobel Prize in Chemistry in 2014, but there is plenty of room for alternatives and complementary methods such as the pioneering work of Prof. J. Pendry on the perfect lens based on negative refraction that started the entire research area of metamaterials. In this thesis, we have used analytical techniques to solve several important challenges that have risen in the discussion of the microwave experimental demonstration of absolute optical instruments and the controversy surrounding perfect imaging. Attempts to overcome or circumvent Abbe's diffraction limit of optical imaging, have traditionally been greeted with controversy. In this thesis, we have investigated the role of interacting sources and detectors in perfect imaging. We have established limitations and prospects that arise from interactions and resonances inside the lens. The crucial role of detection becomes clear in Feynman's argument against the diffraction limit: “as Maxwell's electromagnetism is invariant upon time reversal, the electromagnetic wave emitted from a point source may be reversed and focused into a point with point-like precision, not limited by diffraction.” However, for this, the entire emission process must be reversed, including the source: A point drain must sit at the focal position, in place of the point source, otherwise, without getting absorbed at the detector, the focused wave will rebound and the superposition of the focusing and the rebounding wave will produce a diffraction-limited spot. The time-reversed source, the drain, is the detector which taking the image of the source. In 2011-2012, experiments with microwaves have confirmed the role of detection in perfect focusing. The emitted radiation was actively time-reversed and focused back at the point of emission, where, the time-reversed of the source sits. Absorption in the drain localizes the radiation with a precision much better than the diffraction limit. Absolute optical instruments may perform the time reversal of the field with perfectly passive materials and send the reversed wave to a different spatial position than the source. Perfect imaging with absolute optical instruments is defected by a restriction: so far it has only worked for a single–source single–drain configuration and near the resonance frequencies of the device. In chapters 6 and 7 of the thesis, we have investigated the imaging properties of mutually interacting detectors. We found that an array of detectors can image a point source with arbitrary precision. However, for this, the radiation has to be at resonance. Our analysis has become possible thanks to a theoretical model for mutually interacting sources and drains we developed after considerable work and several failed attempts. Modelling such sources and drains analytically had been a major unsolved problem, full numerical simulations have been difficult due to the large difference in the scales involved (the field localization near the sources and drains versus the wave propagation in the device). In our opinion, nobody was able to reproduce reliably the experiments, because of the numerical complexity involved. Our analytic theory draws from a simple, 1–dimensional model we developed in collaboration with Tomas Tyc (Masaryk University) and Alex Kogan (Weizmann Institute). This model was the first to explain the data of experiment, characteristic dips of the transmission of displaced drains, which establishes the grounds for the realistic super-resolution of absolute optical instruments. As the next step in Chapter 7 we developed a Lagrangian theory that agrees with the simple and successful model in 1–dimension. Inspired by the Lagrangian of the electromagnetic field interacting with a current, we have constructed a Lagrangian that has the advantage of being extendable to higher dimensions in our case two where imaging takes place. Our Lagrangian theory represents a device-independent, idealized model independent of numerical simulations. To conclude, Feynman objected to Abbe's diffraction limit, arguing that as Maxwell's electromagnetism is time-reversal invariant, the radiation from a point source may very well become focused in a point drain. Absolute optical instruments such as the Maxwell Fisheye can perform the time reversal and may image with a perfect resolution. However, the sources and drains in previous experiments were interacting with each other as if Feynman's drain would act back to the source in the past. Different ways of detection might circumvent this feature. The mutual interaction of sources and drains does ruin some of the promising features of perfect imaging. Arrays of sources are not necessarily resolved with arrays of detectors, but it also opens interesting new prospects in scanning near-fields from far–field distances. To summarise the novel idea of the thesis: • We have discovered and understood the problems with the initial experimental demonstration of the Maxwell Fisheye. • We have solved a long-standing challenge of modelling the theory for mutually interacting sources and drains. • We understand the imaging properties of the Maxwell Fisheye in the wave regime. Let us add one final thought. It has taken the scientific community a long time of investigation and discussion to understand the different ingredients of the diffraction limit. Abbe's limit was initially attributed to the optical device only. But, rather all three processes of imaging, namely illumination, transfer and detection, make an equal contribution to the total diffraction limit. Therefore, we think that for violating the diffraction limit one needs to consider all three factors together. Of course, one might circumvent the limit and achieve a better resolution by focusing on one factor, but that does not necessary imply the violation of a fundamental limit. One example is STED microscopy that focuses on the illumination, another near–field scanning microscopy that circumvents the diffraction limit by focusing on detection. Other methods and strategies in sub-wavelength imaging –negative refraction, time reversal imaging and on the case and absolute optical instruments –are concentrating on the faithful transfer of the optical information. In our opinion, the most significant, and naturally the most controversial, part of our findings in the course of this study was elucidating the role of detection. Maxwell's Fisheye transmits the optical information faithfully, but this is not enough. To have a faithful image, it is also necessary to extract the information at the destination. In our last two papers, we report our new findings of the contribution of detection. We find out in the absolute optical instruments, such as the Maxwell Fisheye, embedded sources and detectors are not independent. They are mutually interacting, and this interaction influences the imaging property of the system.

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.

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.

Monocentric lenses provide compact, broadband, high resolution, wide-field imaging. However, they produce a curved image surface and have found limited use. The use of an appropriately machined fiber bundle to relay the curved image plane onto a flat focal plane array (FPA) has recently emerged as a potential solution. Unfortunately the spatial sampling that is intrinsic to the fiber bundle relay can have a negative effect on image resolution, and vignetting has been identified as another potential shortcoming of this solution. This thesis describes a metamaterial lens yielding a high-performance image relay from a curved surface to a flat focal plane. Using quasi-conformal transformation optics, a Maxwell's fish-eye lens is transformed into a concave-plano shape. A design with a narrower range of constitutive parameters is deemed more likely to be manufacturable. Therefore, the way in which the particular shape of the concave-plano reimager influences the range of needed constitutive parameters is explored. Finally, image quality metrics, such as spot size and light efficiency, are quantified.

With the increasing demand on wireless and portable devices, the radio frequency front end blocks are required to feature properties such as wideband, high frequency, multiple operating frequencies, low cost and compact size. However, the current radio frequency system blocks are designed by combining several individual frequency band blocks into one functional block, which increase the cost and size of devices. To address these issues, it is important to develop novel approaches to further advance the current design methodologies in both space and spectrum domains. In recent years, the concept of artificial materials has been proposed and studied intensively in RF/Microwave, Terahertz, and optical frequency range. It is a combination of conventional materials such as air, wood, metal and plastic. It can achieve the material properties that have not been found in nature. Therefore, the artificial material (i.e. meta-materials) provides design freedoms to control both the spectrum performance and geometrical structures of radio frequency front end blocks and other high frequency systems. In this dissertation, several artificial materials are proposed and designed by different methods, and their applications to different high frequency components and circuits are studied. First, quasi-conformal mapping (QCM) method is applied to design plasmonic wave-adapters and couplers working at the optical frequency range. Second, inverse QCM method is proposed to implement flattened Luneburg lens antennas and parabolic antennas in the microwave range. Third, a dual-band compact directional coupler is realized by applying artificial transmission lines. In addition, a fully symmetrical coupler with artificial lumped element structure is also implemented. Finally, a tunable on-chip inductor, compact CMOS transmission lines, and metamaterial-based interconnects are proposed using artificial metal structures. All the proposed designs are simulated in full-wave 3D electromagnetic solvers, and the measurement results agree well with the simulation results. These artificial material-based novel design methodologies pave the way toward next generation high frequency circuit, component, and system design.

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

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

La Transformation d’Espace appelée aussi Transformation Optique (TO) est un outil de conception électromagnétique puissant qui a permis la conception de nouveaux dispositifs tels que la célèbre “cape d'invisibilité”. Cette thèse s’inscrit dans la continuité directe de celle de M.D. Clemente Arenas (Application de la transformation d'espace à la conception d'antennes à diagramme de rayonnement contrôlé, 2014) et porte sur l’utilisation de la TO pour modifier drastiquement le rayonnement d’une antenne patch. Ces fortes modifications du rayonnement sont habituellement obtenues avec l’aide d’un superstrat encombrant et constitué de matériaux ayant une perméabilité et permittivité exotiques (métamatériaux). L’objectif est donc ici de réduire cet encombrement et de simplifier la réalisation en utilisant des matériaux diélectriques standards. Ainsi, grâce au superstrat développé, une antenne patch ayant un gain réalisé de 7 dB devient une antenne présentant deux lobes dans le plan azimutal de gain réalisé de 3.5 dB. Le superstrat, d’épaisseur 0.12λ, est conçu à l’aide de deux matériaux uniquement : Alumine (εr = 9.9) et Fullcure (εr = 2.8), alors que le profil initial comporte une permittivité variant entre 1 et 15 et une perméabilité entre 0.3 et 3. Divers degrés de libertés dans la conception permettent d'adapter notre solution pour concevoir d’autres superstrats avec des fonctionnalités différentes: diagramme ayant une ouverture de plus de 180° dans un plan, diagramme end-fire, etc. Les applications visées sont notamment celles de l’aéronautique pour lesquelles il existe aujourd’hui sur les aéronefs plusieurs dizaines d’antennes pour assurer toutes les liaisons nécessaires aux communications, à l’identification, au positionnement, etc. La géométrie du porteur conduit alors à utiliser plusieurs antennes protubérantes pour remplir cette mission. Cependant pour un avion, ces excroissances contribuent à dégrader l’aérodynamisme de l’appareil ce qui se traduit par une consommation plus importante. Le but est donc de proposer des solutions antennaires à rayonnement nonconventionnel et non protubérante compatible avec une intégration sur dérive ou fuselage. Le concept est validé à l'aide d'une maquette réalisée avec une imprimante 3D et avec le soutien d’Airbus Group Innovations. / Transformation Optics (TO) is a powerful electromagnetic design tool that enables the design of new devices such as the famous "invisibility cloak". This thesis is in direct continuation of that of M.D. Clemente Arenas (Application de la transformation d'espace à la conception d'antennes à diagramme de rayonnement contrôlé, 2014) and focuses on the use of the TO to drastically change radiation of a patch antenna. These sharp changes in radiation pattern are usually obtained using bulky superstrates made of metamaterials having exotic permeability and permittivity values. The objective of this thesis is to reduce the thickness of the superstrate and simplify the fabrication by enabling the use of standard dielectric materials. Thus, a patch antenna with realized gain of 7 dB is transformed, with the help of proposed superstrate, into an antenna having two lobes in the azimuth plane withrealized gain of 3.5 dB. The 0.12λ thick superstrate is designed using two standard dielectric materials only: Alumina (εr = 9.9) and FullCure (εr = 2.8), whereas the previous solution had variation in permittivity between 1 and 15 and in permeability between 0.3 and 3. Various degrees of freedom in the design allow adapting this solution to develop new superstrates for other applications: radiation pattern with HPBW greater than 180 ° in one plane, end-fire radiation pattern, etc. Target applications include those of aeronautics. Today, dozens of antennas on an aircraft are required to ensure the necessary communications links, identification, positioning and other purposes. The structure of the aircraft necessitates use multiple antennas to fulfill this mission, which are fixed and protrude on fuselage or wings. However, for an aircraft, these protuberances contribute to the aerodynamic drag, which results in higher fuel consumption. Therefore, the objective is to propose conformal antenna solutions with unconventional radiation pattern, which can be eventually integrated on fuselage or rudder. The concept is validated using a model made with a 3D printer and with the support of Airbus Group Innovations

With the roll out of new technologies and the worldbecoming more connected, there is a rising demand for higherbandwidth and new frequency bands. To meet the demand,higher frequencies are used in new communication systems.Higher frequencies come with the need for new antenna designsand one promising type of antenna is the lens antenna. In thispaper, a modulated geodesic Luneburg lens with a novel feedingmethod is proposed for use between 8-10 GHz. Furthermore, themanufacturing of the lens explores the possibility of 3D printingas a method of producing cheap antennas.The paper verifies the viability of using a patch antenna andhorn as a feeding method for a parallel-plate waveguide lens.First the lens is modeled and simulated in CST Microwave Studioand is then 3D-printed in PLA plastic and taped with coppertape. The antenna achieves -5 dB S11-parameter between 8-10GHz. The antenna also achieves 60 scanning in the azimuthplane. The antenna achieves a HPBW of 15. / Med utvecklingen av nya tekniker och envärld som blir allt mer digital är efterfrågan på större bandbreddoch nya frekvensband hög. För att möta efterfrågananvänds högre frekvenser i nya kommunikationssystem. Medanvändningen av högre frekvenser behövs nya antenndesigneroch en lovande typ av antenn är linsantennen. I den härartikeln föreslås en modulerad geodesic Luneburg lins med enny typ av matningsmetod för användning mellan 8-10 GHz. Förtillverkningen av linsen utforskas 3D-printning som en billig ochenkel metod.Artikeln verifierar användningen av en patch-antenn och etthorn som matningsmetod för en lins av parallella metallplattor.Först simuleras linsen i CST Microwave Studio och 3Dprintassedan i PLA-plast och tejpas med koppartejp. Antennenåstakommer -5 dB i S11-parameter mellan 8-10 GHz. Antennenhar en skanning av 60 i azimut-planet och har en HPBW av15. / Kandidatexjobb i elektroteknik 2021, KTH, Stockholm

With the rise of 5G and the increasing number ofdevices, novel antenna designs are needed to meet the demandof the future. In this report, the authors present a design andexperimental verification of a 3D-printed Geodesic ModulatedReflective Luneburg lens antenna working at the X-Band, 8-12GHz. The lens profile is calculated from the refractive index of aflat system using transformation optics. Furthermore, the lens ismodulated to minimize the height and chamfers are implementedto reduce reflections. A sliding waveguide connected to a coaxialcable is used to excite the lens while the transmitted signal isradiated from a sinusoidal flare. A copper-lined PLA substrateconstitutes the 3D-printed lens. The authors achieved a S11 below-10 dB across the spectrum and a realized gain exceeding 10 dBacross the sweeping angles at 12 GHz, showcasing the usabilityas a directed antenna. / Med det nya 5G nätverket och den ökandemängden enheter behövs nya antenner för att möta framtidensefterfrågan. I denna rapport presenterar författarna en designoch experimentell verifiering av en 3D-printad geodesisk moduleradreflekterande Luneburg linsantenn i X-bandet, 8-12 GHz.Linsprofilen beräknas från brytningsindexet för ett platt systemmed transformationsoptik. Dessutom är linsen modulerad föratt minimera höjden och kantavfasningar implementeras föratt minska reflektioner. En glidande vågledare ansluten till enkoaxialkabel används för att excitera linsen medan den sända signalenutstrålas från en vågledare med sinusformad avrundning.Ett kopparfodrat PLA-substrat utgör den 3D-printade linsen.Författarna uppnådde en S11 under -10 dB över spektrumet ochen realiserad förstärkning överstigande 10 dB över svepvinklarnavid 12 GHz, vilket visar linsens användbarhet som riktad antenn. / Kandidatexjobb i elektroteknik 2021, KTH, Stockholm