From Whitney Forms to Metamaterials: a Rigorous Homogenization Theory

A rigorous homogenization theory of metamaterials -- artificial periodic structures judiciously designed to control the propagation of electromagnetic waves -- is developed. All coarse-grained fields are unambiguously defined and effective parameters are then derived without any heuristic assumptions. The theory is an amalgamation of two concepts: Smith & Pendry's physical insight into field averaging and the mathematical framework of Whitney-Nedelec-Bossavit-Kotiuga interpolation. All coarse-grained fields are defined via Whitney forms and satisfy Maxwell's equations exactly. The new approach is illustrated with several analytical and numerical examples and agrees well with the established results (e.g. the Maxwell-Garnett formula and the zero cell-size limit) within the range of applicability of the latter. The sources of approximation error and the respective suitable error indicators are clearly identified, along with systematic routes for improving the accuracy further. The proposed approach should be applicable in areas beyond metamaterials and electromagnetic waves -- e.g. in acoustics and elasticity.Comment: 23 pages, 10 figure

Photo-designed terahertz devices

Technologies are being developed to manipulate electromagnetic waves using artificially structured materials such as photonic crystals and metamaterials, with the goal of creating primary optical devices. For example, artificial metallic periodic structures show potential for the construction of devices operating in the terahertz frequency regime. Here we demonstrate the fabrication of photo-designed terahertz devices that enable the real-time, wide-range frequency modulation of terahertz electromagnetic waves. These devices are comprised of a photo-induced, planar periodic-conductive structure formed by the irradiation of a silicon surface using a spatially modulated, femtosecond optical pulsed laser. We also show that the modulation frequency can be tuned by the structural periodicity, but is hardly affected by the excitation power of the optical pump pulse. We expect that our findings will pave the way for the construction of all-optical compact operating devices, such as optical integrated circuits, thereby eliminating the need for materials fabrication processes

Design and Optimization of Electromagnetic Band Gap Structures

Dizertační práce pojednává o návrhu a optimalizaci periodických struktur s elektromagnetickým zádržným pásmem (EBG – electromagnetic band gap) pro potlačení povrchových vln šířících se na elektricky tlustých dielektrických substrátech. Nepředvídatelné chování elektromagnetických vlastností těchto struktur v závislosti na parametrech elementární buňky činí jejích syntézi značně komplikovanou. Bez patřičného postupu je návrh EBG struktur metodou pokusu a omylu. V první části práce jsou shrnuty základní poznatky o šíření elektromagnetických vln v tzv. metamateriálech. Následně je diskutován správný způsob výpočtu disperzního diagramu ve vybraných komerčních programech. Jádrem dizertace je automatizovaný návrh a optimalizace EBG struktur využitím různých globálních optimalizačních algoritmů. Praktický význam vypracované metodiky je předveden na návrhových příkladech periodických struktur s redukovanými rozměry, dvoupásmovými EBG vlastnostmi, simultánním EBG a AMC (artificial magnetic conductor – umělý magnetický vodič) chováním a tzv. superstrátu. Poslední kapitola je věnována experimentálnímu ověření počítačových modelů.The thesis deals with the design and optimization of periodic structures for surface waves suppression on electrically dense dielectric substrates. The design of such structures is rather complicated due to the large factor of uncertainty how the electromagnetic band gap (EBG) properties change depending on the unit cell geometry. Without a proper approach, the design of EBGs is based on trial-and-error. In this thesis, the basic theory of electromagnetic wave propagation in metamaterials is presented first. Second, the correct dispersion diagram computation in the selected full-wave software tools is discussed. The main attention is turned then to the automated design and optimization of EBG structures using different global evolutionary algorithms. The practical exploitation of the developed technique is demonstrated on design examples of reduced-size and dual-band EBGs, periodic structures with simultaneous electromagnetic band gap and artificial magnetic conductor (AMC) properties and periodic structures acting as superstrates. The last chapter of the thesis is devoted to the experimental verification of computer models.

Tomorrow's Metamaterials: Manipulation of Electromagnetic Waves in Space, Time and Spacetime

Metamaterials represent one of the most vibrant fields of modern science and technology. They are generally dispersive structures in the direct and reciprocal space and time domains. Upon this consideration, I overview here a number of metamaterial innovations developed by colleagues and myself in the holistic framework of space and time dispersion engineering. Moreover, I provide some thoughts regarding the future perspectives of the area

Simple and accurate analytical model of planar grids and high-impedance surfaces comprising metal strips or patches

This paper introduces simple analytical formulas for the grid impedance of electrically dense arrays of square patches and for the surface impedance of high-impedance surfaces based on the dense arrays of metal strips or square patches over ground planes. Emphasis is on the oblique-incidence excitation. The approach is based on the known analytical models for strip grids combined with the approximate Babinet principle for planar grids located at a dielectric interface. Analytical expressions for the surface impedance and reflection coefficient resulting from our analysis are thoroughly verified by full-wave simulations and compared with available data in open literature for particular cases. The results can be used in the design of various antennas and microwave or millimeter wave devices which use artificial impedance surfaces and artificial magnetic conductors (reflect-array antennas, tunable phase shifters, etc.), as well as for the derivation of accurate higher-order impedance boundary conditions for artificial (high-) impedance surfaces. As an example, the propagation properties of surface waves along the high-impedance surfaces are studied.Comment: 12 pages, 10 figures, submitted to IEEE Transactions on Antennas and Propagatio