Tunable focusing in natural hyperbolic magnetic media

While optical effects such as negative refraction and imaging obtained from slab lenses with plane parallel sides are widely studied using metamaterials, it is less well known that these effects can occur naturally in certain materials. We discuss a class of natural hyperbolic materials that not only display similar effects but also allow one to modify the focal length of a slab lens with an externally applied magnetic field. This is possible because antiferromagnets are gyrotropic and support magnetic polaritons whose frequencies are sensitive to magnetic fields. In addition, a rich caustic structure emerges at low temperatures, when damping should be small. These materials also produce slab focusing at higher temperatures, although the caustic structure disappears

Studies of metamaterial structures

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Magnetism in one-dimensional metamaterials: Double hyperbolic media and magnetic surface states

Metamaterials with magnetic properties have been widely investigated with rather complex two- and three-dimensional resonant structures. Here we propose conceptually and demonstrate experimentally a mechanism for broadband optical magnetism in simpler one-dimensional systems. We experimentally demonstrate that alternating high-index dielectric/metal multilayer hyperbolic metamaterials can exhibit a strong magnetic response including variously µ>1 to µ<0. By engineering the electric permittivity as well, we reveal an epsilon and mu near zero regime. We show that modifications of internal metamaterial structure can lead to either type I or type II magnetic hyperbolic dispersion, thereby generalizing the notion of a hyperbolic metamaterial to encompass both TE and TM polarizations in simple multilayer geometries. Finally, we show that a negative magnetic response can give rise to TE interface-bound states, analogous to their TM counterparts, surface plasmon polaritons

Oriented asymmetric wave propagation and refraction bending in hyperbolic media

Crystal quartz is a well-known anisotropic medium with optically active phonons in the THz region where hyperbolic phonon-polaritons can be excited. Here, we use this material to illustrate how the behavior of bulk and surface hyperbolic polaritons can be drastically modified by changing the orientation of the crystal’s anisotropy axis with respect to its surface. We demonstrate, both theoretically and experimentally, phenomena associated with the orientation of hyperbolic media. We show the consequences of changes in the crystal’s orientation in various ways, such as the modification of the effective reststrahl regions and associated surface phonon polariton dispersion. Of particular significance, however, is the transmission behavior of radiation passing through a rotated hyperbolic crystal. Here, even a small rotation of the optical axes with respect to the crystal surface can lead to a very large degree of asymmetry in the transmitted intensity. In addition, the refracting angle (which in a hyperbolic medium may correspond to negative refraction and slab lensing behavior) itself becomes asymmetric, so that a slab lens with a laterally displaced image becomes possible. We discuss some of the possible consequences of these types of effects

Generalized homogenization theory and inverse design of periodic electromagnetic metamaterials

textArtificial metamaterials composed of specifically designed subwavelength unit cells can support an exotic material response and present a promising future for various microwave, terahertz and optical applications. Metamaterials essentially provide the concept to microscopically manipulate light through their subwavelength inclusions, and the overall structure can be macroscopically treated as homogeneous bulk material characterized by a simple set of constitutive parameters, such as permittivity and permeability. In this dissertation, we present a complete homogenization theory applicable to one-, two- and three-dimensional metamaterials composed of nonconnected subwavelength elements. The homogenization theory provides not only deep insights to electromagnetic wave propagation among metamaterials, but also allows developing a useful and efficient analysis method for engineering metamaterials. We begin the work by proposing a general retrieval procedure to characterize arbitrary subwavelength elements in terms of a polarizability tensor. Based on this system, we may start the macroscopic analysis of metamaterials by analyzing the scattering properties of their microscopic building blocks. For one-dimensional linear arrays, we present the dispersion relations for single and parallel linear chains and study their potential use as sub-diffractive waveguides and leaky-wave antennas. For two-dimensional arrays, we interpret the metasurfaces as homogeneous surfaces and characterize their properties by a complete six-by-six tensorial effective surface susceptibility. This model also offers the possibility to derive analytical transmission and reflection coefficients for metasurfaces composed of arbitrary nonconnected inclusions with TE and TM mutual coupling. For three-dimensional metamaterials, we present a generalized theory to homogenize arrays by effective tensorial permittivity, permeability and magneto-electric coupling coefficients. This model captures comprehensive anisotropic and bianisotropic properties of metamaterials. Based on this theory, we also modify the conventional retrieval method to extract physically meaningful effective parameters of given metamaterials and fundamentally explain the common non-causality issues associated with parameter retrieval. Finally, we conceptually propose an inverse design procedure for three-dimensional metamaterials that can efficiently determine the geometry of the inclusions required to achieve the anomalous properties, such as double-negative response, in the desired frequency regime.Electrical and Computer Engineerin

Super-resolution from Quantum Metamaterials

Negative refraction and sub-wavelength resolution have been demonstrated with metamaterials throughout the past decade. This thesis introduces a quantum metamaterial, based on quantum mechanical principles, which exhibits negative refraction and sub-wavelength resolution with reduced absorption compared to non-quantum metamaterials. In particular, this thesis introduces a novel method of achieving sub-wavelength resolution using the quantum metamaterial. This method of superresolution does not require a negative permittivity or permeability, as the predecessors require, but is instead based on a dispersion curve with a high elliptical eccentricity. This thesis uses an effective medium approach to calculate the quantum metamaterial’s permittivity, which is then used to model super-resolution and negative refraction. After considerable design, optimisation and epitaxial growths, a GaAs based quantum metamaterial is fabricated into a superlens. A scanning near-field optical microscope is used to measure the sub-wavelength imaging capability of the quantum metamaterial superlens.Open Acces

DYADIC GREEN\u27S FUNCTIONS FOR LAYERED GENERAL ANISOTROPIC MEDIA AND THEIR APPLICATION TO RADIATION OF DIPOLE ANTENNAS

In this dissertation, the dyadic Green‟s functions (DGFs) for unbounded and layered anisotropic media, with no restriction imposed on the medium property, are derived. Utilizing the obtained DGFs, the radiation problems of a Hertzian dipole and a microstrip antenna in the presence of an anisotropic substrate are solved. After a brief introduction, the eigenvector dyadic Green‟s functions (E-DGFs) for an unbounded general anisotropic medium through the eigen-decomposition method are derived. The E-DGFs of a layered anisotropic geometry are then constructed based on the derivation of the unbounded E-DGFs using two different approaches. One is through the symmetrical property of the DGFs and the other is through the direct construction method. Rigorous proof and detailed derivation of the formulation for the E-DGFs are presented. The usage and limitation of each approach as well as the relationships between the corresponding E-DGFs are discussed. Applying the method of stationary phase to the associated E-DGFs, we formulate the radiation fields of an arbitrarily oriented Hertzian dipole located either above or inside the layered anisotropic medium. The important new findings include the analysis of the radiation field in terms of the reflection coefficients as a function of incidence angle, and the use of the biasing magnetic field to improve the broadside directivity for a z-directed source when a gyroelectric medium is involved. In addition to solving the radiation of a Hertzian dipole in the presence of a layered anisotropic medium, the layered E-DGFs derived here are also utilized to solve the more practical problem of a microstrip dipole printed on an anisotropic substrate. A method of moment solution is formulated with the E-DGF in the spectral domain. To demonstrate the feasibility of this method applicable to a general anisotropic medium, the current distribution, input impedances, and radiation patterns are numerically calculated for a microstrip dipole printed on various anisotropic substrates. Furthermore, a detailed parametric study of the effect of frequency, and direction and magnitude of the biasing magnetic field is provided for a dipole printed on a gyroelectric substrate. The parametric analysis in this dissertation may lead to a method whereby the additional freedom introduced by the gyroelectric medium can be utilized effectively to adjust the resonant length and radiation pattern of a printed dipole antenna