Impedance Transformers

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Methods for the design and analysis of higher-order mode couplers applied to superconducting accelerating structures

Higher-order modes (HOMs) may affect beam stability and refrigeration requirements of superconducting proton linacs such as the SPL which is being studied at CERN. One option being considered to limit these effects is the use of coaxial HOM couplers. In this work, potentially dangerous modes are analyzed and corresponding damping requirements derived. The design process of coaxial HOM couplers is examined under new aspects. Several prototypes are elaborated and compared in terms of mode damping, thermal loads, structural deformations, mechanical tolerances, and multipacting.Moden höherer Ordnung (HOMs) können beträchtlich die Strahldynamik und Kühlanforderungen supraleitender Linearbeschleuniger, wie dem am CERN untersuchten SPL, beeinflussen. Koaxiale HOM Koppler sind eine Möglichkeit, um Auswirkungen entsprechender Moden zu begrenzen. Im Rahmen dieser Arbeit wurden potentiell gefährliche Moden analysiert und Dämpfungsanforderungen abgeleitet. Der Kopplerentwurf wurde unter neuen Gesichtspunkten aufgegriffen. Verschiedene Prototypen wurden bezüglich Modendämpfung, thermisches Verhaltens, strukturmechanischer Verformungen, Toleranzen und Multipactings verglichen

Photonic crystal antireflection coatings, surface modes, and impedances

We present a rigorous definition of a wave impedance for 2D rectangular and triangular lattice photonic crystals (PCs), in the form of a matrix. Reflection and transmission at an interface between PCs can be represented by matrices that relate the Bloch mode (eigenmode) amplitudes in the two PCs; we show that these matrices, which are multi-mode generalisations of reflection and transmission coefficients, may be calculated from the PCs' impedances that we define. Given the impedances and Bloch factors (propagation constants) of a collection of PCs, the reflection and transmission properties of arbitrary stacks of these PCs may be calculated efficiently using a few matrix operations. Therefore our definition enables PC-based antireflection coatings to be designed efficiently: some computationally expensive simulations are required in an initial step to find a range of PCs' impedances, but then the reflectances of every coating that consists of a stack of these PCs can be calculated without any further simulations. We first define the PC impedance from the transfer matrix of a single PC layer (i.e., a grating). Since transfer matrix methods are not especially widespread, we also present a method and associated source code to extract a PC's propagating and evanescent Bloch modes from a scattering calculation that can be performed by any off-the-shelf field solver, and to calculate impedances from the extracted modal fields. Finally, we put our method to use. We apply it to design antireflection coatings, nearly eliminating reflection at a single frequency for one or both polarisations, or lowering it across a larger bandwidth. We use it to find surface modes at interfaces between PCs and air, and their projected band structures. We use the impedance to define effective parameters for PC homogenisation, and we briefly describe how our definition has been used to dispersion engineer a PC waveguide

Circuit modeling of periodic structures

In the present dissertation the main goal consists in the derivation of analytical circuit models for di_erent types of 1-D periodic structures by a method based on the integral equation. Thus, in Chapter 1 the techique to derive equivalent circuits is described in detail. It is applied for 1-D periodic structures, although for 2-D periodic structures it can be applied in a similar manner. Single-slit gratings and compound gratings are analyzed by using a slit-array formulation. For the derivation of the model we assume the grating to be sandwiched by two semi- in_nite dielectric susbtrates. Extensions to more complex environments are left for the following chapters. We will also present in the same chapter the strip-array formulation, which is adequate for slit gratings with large slit apertures. The obtaining of the circuits will be explained in detail, step by step, in order to see clearly the implicit physical insights. In Chapter 2 the investigation is focused on the study of the scattering response of a periodic single slit- and strip-grating under TE and TM nor- mal and oblique incidence. Their corresponding circuit models, derived in Chapter 1 assuming that the array is sandwiched by two semi-in_nite dielec- tric slabs, are now extended to account for multilayer systems. Additionally, we will also consider a pair of coupled gratings, which, under certain sym- metry conditions, can be studied from the perspective of a single grating by using an analysis based on even and odd excitations. It will be checked the excellent agreement shown by the circuit model in comparison with results provided by HFSS. In particular, the appearance of some kind of resonances such as Wood's anomaly or anomalous extraordinary transmission are well catched by the model. Finally, a discussion about the range of validity of the models is provided. In Chapter 3, the scattering response of the well-known mushroom struc- ture under TM normal and oblique incidence is analyzed in depth. The mushroom periodic structure is actually a periodic corrugated surface. Its corresponding equivalent circuit will be used not only to check the excellent performance and the reliability to reproduce complex resonant behaviors but also as an e_cient design tool. In order to corroborate this, an absorber is easily designed by _lling the corrugations with a lossy silicon dielectric. The model also incorporate modi_cations in order to account for possible ohmic losses in the metallic surfaces. At the end of the chapter a brief discussion about the performance of the model is carried out. Chapter 4 is devoted to the study of the scattering response of com- pound gratings under TM incidence. Periodic compound gratings contain more than one slit per period. The existence of two, three, or a more num- ber of slit apertures per each period and its mutual coupling introduces a new type of resonant: the so-called phase resonance. The appearance of pha- se resonance is accompanied with several phenomena whose study is quite interesting. The circuit model will provide an alternative explanation of pha- se resonance, and will allow us to undertand the associated complexity in a simple manner. The inclusion of ohmic and dielectric losses are incoporated in the model. Furthermore, it will also be checked that the model is capable to work accurately for frequencies close to the optic regime, by taking into account the properties of metals at these frequencies by the Drude model. This fact reveals that the Microwave Network Theory can be sucessfully extended to other frequency ranges under certain circumstances. Finally, Chapter 5 shows an exhaustive study about the scattering pro- perties of coupled slit gratings under TE and TM incidence. Departing from the model of a single slit grating, a _ topology is mathematically deduced to account for a pair of coupled gratings. These gratings can be geometrically di_erent and be misaligned each other, but their period must coincide. Sys- tems containing several gratings stacked will also be considered. From the circuit point of view, a stack of gratings is readily modelled by cascading their corresponding _ circuits. A brief discussion about the limits of validity of the model is also provided

Bio-inspired nanophotonics : manipulating light at the nanoscale with plasmonic metamaterials

textMetals interact very differently with light than with radio waves and finite conductivities and losses often limit the way that RF concepts can be directly transferred to higher frequencies. Plasmonic materials are investigated here for various optical applications, since they can interact, confine and focus light at the nanoscale; however, regular plasmonic devices are severely limited by frequency dispersion and absorption, and confined signals cannot travel along plasmonic lines over few wavelengths. For these reasons, novel concepts and materials should be introduced to successfully manipulate and radiate light in the same flexible way we operate at lower frequencies. In line with these efforts, optical metamaterials exploit the resonant wave interaction of collections of plasmonic nanoparticles to produce anomalous light effects, beyond what naturally available in optical materials and in their basic constituents. Still, these concepts are currently limited by a variety of factors, such as: (a) technological challenges in realizing 3-D bulk composites with specific nano-structured patterns; (b) inherent sensitivity to disorder and losses in their realization; (c) not straightforward modeling of their interaction with nearby optical sources. In this study, we develop a novel paradigm to use single-element nanoantennas, and composite nanoantenna arrays forming two-dimensional metasurfaces and three-dimensional metamaterials, to control and manipulate light and its polarization at the nanoscale, which can possibly bypass the abovementioned limitations in terms of design procedure and experimental realization. The final design of some of the metamaterial concepts proposed in this work was inspired by biological species, whose complex structure can exhibit superior functionalities to detect, control and manipulate the polarization state of light for their orientation, signaling and defense. Inspired by these concepts, we theoretically investigate and design metasurfaces and metamaterial models with the help of fully vectorial numerical simulation tools, and we are able to outline the limitations and ultimate conditions under which the average optical surface impedance concept may accurately describe the complex wave interaction with planar plasmonic metasurfaces. We also experimentally explore various technological approaches compatible with these goals, such as the realization of lithographic single-element nanoantenna and nanoantenna arrays with complex circuit loads, periodic arrays of plasmonic nanoparticles or nanoapertures, and stacks of rotated plasmonic metasurfaces. At the conclusion of this effort, we have theoretically analyzed, designed and experimentally realized and characterized the feasibility of using discrete metasurfaces to realize phenomena and performance that are not available in natural materials, oftentimes inspired by the biological world.Electrical and Computer Engineerin

Theory, design and measurement of near-optimal graphene reconfigurable and non-reciprocal devices at terahertz frequencies

This thesis explores the applications of graphene for terahertz and far infrared optical components and antennas, with particular emphasis on tunable and non-reciprocal devices. Both terahertz technologies and graphene are emerging fields which hold many promises for a number of future applications, including ultra-broadband communications, sensing and security. A very important amount of research has been devoted to explore the potential applications of graphene and its advantages over existing technologies. Conversely, there is a clear set of applications that could benefit from the development of terahertz technologies, but there are several technical challenges in terms of very limited availability of materials and components to generate, manipulate and detect terahertz waves. The main idea of this work is to bring these two topics together to demonstrate that terahertz and far infrared technologies can greatly benefit from the unique optical properties of graphene. The first original contribution of this thesis is an important theoretical upper bound for the performance of non-reciprocal and tunable devices, demonstrating that both these components can achieve a target performances at the expense of an unavoidable optical loss, which depends uniquely on the properties of graphene. If graphene with higher mobility is used, this unavoidable loss can be reduced; however, independently of the design geometry (waveguide devices, free space planar devices, ...), the loss will always appear. This theoretical limit is an important guideline for the design of graphene optical devices, as it can predict the best possible performances prior to any design effort or numerical simulation. It is also demonstrated that devices able to reach the upper bound are actually possible, and hence these devices (modulators, isolators among others) are optimal. The thesis explores then a number of designs of graphene antennas for terahertz and mid infrared frequencies, where it is shown that gated graphene can be used to achieve frequency reconfiguration in resonant plasmonic antennas and beam steering in graphene based reflectarrays. Circuit models are provided as a simple way to understand the behavior of the device in a simple way. Furthermore, an experimental technique able to measure the complex conductivity of graphene at infrared frequency is demonstrates, providing a very useful evaluation of graphene quality at those frequencies. The potential of graphene for non-reciprocal applications is then demonstrated experimentally, with the design, fabrication and measurement of the first terahertz isolator (operation frequency between 1 THz and 10 THz). The isolator is a device which allows the unilateral propagation of light, and for that reason is often called âoptical diodeâ. The isolator uses graphene immersed in a magnetostatic field, and exhibits approximately 7 dB of loss in one direction and more than 25 dB in the other. The device is shown to be quasi-optimum according to the theoretical bound and greatly improved performances are predicted for devices with next generation CVD graphene. Finally, the first tunable graphene reflectarray is presented, which is a metasurface able to steer in a desired direction an incoming beam of terahertz radiation. The device acts as a mirror, but, upon graphene gating, the direction of the reflected beam can be controlled and the beam itself can be modulated with complex modulation schemes

Time- and frequency-domain modeling of passive interconnection structures in field and circuit analysis

Die vorliegende Arbeit widmet sich den theoretischen Grundlagen und numerischen Verfahren zur Analyse passiver Verbindungsstrukturen auf der Basis der elektromagnetischen Feld- und Netzwerktheorie. Die Simulation elektromagnetischer Phänomene gewinnt eine immer stärkere Bedeutung sowohl im Entwicklungsprozess elektronischer Komponenten und Systeme als auch bei der EMV-Analyse. Ständig steigende Operationsfrequenzen erfordern die Einbeziehung der passiven Verbindungsstrukturen in die Analyse sowohl im Frequenz- als auch im Zeitbereich. Dabei wächst insbesondere die Bedeutung von Zeitbereichsmethoden bei der Behandlung elektrodynamischer Probleme infolge zunehmender Schaltfrequenzen und immer steilerer Anstiegsflanken. Frequenzbereichsmethoden in Kombination mit der Fourierrücktransformation erfordern bei extrem breiten Frequenzspektren einen hohen Rechenaufwand, um Zeitbereichslösungen mit hinreichender Genauigkeit zu erhalten. Im Falle von Nichtlinearitäten sind Zeitbereichsmethoden sogar die einzige Möglichkeit. Aus diesem Grunde wird in der vorliegenden Arbeit ein besonderer Schwerpunkt auf die Zeitbereichsmodellierung der Verbindungsstrukturen einschließlich der Schaltungsumgebung sowie die Behandlung mittels Netzwerksimulatoren gelegt.  Throughout the first period of electrical-engineering history, passive interconnections, i.e., conductors serving as the connection of electronic devices or system components, were typically not considered in the system modeling, except for some special cases and "electrically long" structures, which were successfully described via the transmission-line theory. This changed dramatically after the wide-spread introduction of digital, radio-frequency, and microwave technologies, which required transmission via the passive interconnection structures of high-frequency (HF) signals. The parasitic effects introduced by passive interconnections at high frequencies have motivated modern digital-system designers to consider such interconnections more precisely. &nbsp