Mie resonance-based dielectric metamaterials

Preface 1. Introduction 2. FDTD Method for periodic structure analysis 3. EBG Characterizations and classifications 4. Design and optimizations of EBG structures 5. Patch antennas with EBG structures 6. Low profile wire antennas on EBG surfaces 7. Surface wave antennas Appendix: EBG literature review.

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Electromagnetic Band Gap Structures in Antenna Engineering

We study a composite medium consisting of insulating magnetodielectric spherical particles embedded in a background matrix. Using results from the literature going back as far as Lewin (1947), we show that the effective permeability and permittivity of the mixture can be simultaneously negative for wavelengths where the spherical inclusions are resonant and that the medium results in an effective "double negative (DNG) media". Materials of this type are also called negative-index materials, backward media (BW), and left-handed materials. This type of material belongs to a more general class of metamaterials. The theoretical results presented here show that composite media having much simpler structure than those reported in the literature can exhibit negative permeability and permittivity over significant bandwidths.

A double negative (DNG) composite medium composed of magnetodielectric spherical particles embedded in a matrix

We develop an effective medium description of a two-dimensional photonic band-gap medium composed of dielectric cylinders of large dielectric constant. Using the transfer matrix method we have calculated reflection coefficients for a slab of the composite and plane-wave incidence, as well as the (complex) wavevector for the infinite system. From these quantities we derive an effective permittivity and permeability for the composite. In the case of p-polarized incidence the composite displays a negative magnetic permeability at microwave frequencies due to single-scatterer resonances in the medium.

https://iopscience.iop.org/article/10.1088/0953-8984/14/15/317/pdf

Photonic band-gap effects and magnetic activity in dielectric composites

Recently, an electromagnetic metamaterial was fabricated and demonstrated to exhibit a “left-handed” (LH) propagation band at microwave frequencies. A LH metamaterial is one characterized by material constants—the permeability and permittivity—which are simultaneously negative, a situation never observed in naturally occurring materials or composites. While the presence of the propagation band was shown to be an inherent demonstration of left handedness, actual numerical values for the material constants were not obtained. In the present work, using appropriate averages to define the macroscopic fields, we extract quantitative values for the effective permeability and permittivity from finite-difference simulations using three different approaches.

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Direct calculation of permeability and permittivity for a left-handed metamaterial

A system of N dielectric layers imprinted with a transverse lattice of planar metallic scatterers and stacked monolithically along the longitudinal direction of a rectangular waveguide is examined in this paper. This monolithically constructed photonic crystal exhibits valuable filtering properties. The resulting optimized filters are inexpensive to fabricate because the building block (printed layer) is ideal for mass production. The complete filter contains no air gaps (monolithic) and can be modularly built up, or reconfigured, by simple stacking requiring no adhesives (modular). The filter response is designed using our analytical expressions and fast software, as well as using commercial software such as HFSS. A comparison of the two design methods shows that our approach is five orders of magnitude faster than HFSS and significantly reduces the memory requirements. Prototype measurements in the Ka-band show excellent agreement with predictions of our design method. Optimized designs displaying reduced size, extremely flat passbands (0.25 dB), and great isolation (-100 dB) are also presented.

Monolithic waveguide filters using printed photonic-bandgap materials

Printed metallo-dielectric photonic bandgap (PBG) materials are analyzed using an analytical approach based on multipole expansions for the scattered fields of individual scatterers and a transfer-matrix method for reconstructing the total scattered fields created by successive lattice planes of the artificial crystal. An effective description of the PBG medium is derived and its correspondence with natural crystals is further advanced through an analysis based on Lorentzian response functions, which characterize natural crystals. The effective wave impedance and bulk reflection coefficient of the medium are provided and their properties inside and outside the bandgaps are examined. The presented treatment for these effective response functions extends far beyond the traditional effective medium theory (EMT) limits.

Artificial versus natural crystals: effective wave impedance of printed photonic bandgap materials

An effective description is developed for a metalodielectric photonic bandgap (PBG) material far beyond the quasi-static limit of traditional effective-medium theories. An analytic approach, recently presented by the authors, is further advanced to provide the complete effective permittivity and permeability functions. Reflection and transmission coefficients are presented for both TM and TE oblique plane-wave incidence, based on the determination of the equivalent impedance for each lattice plane in the crystal and the transfer-matrix method for reconstructing the effect of successive lattice planes. An analysis of the semi-infinite and slab observables yields the anisotropic effective refractive index, effective permittivity, and effective permeability, thus completing the macroscopic description of the interaction of electromagnetic waves with the medium. Among the novel aspects of the analysis is the equivalence of our PBG system with a physically dispersive system at ultraviolet frequencies and the derivation and explanation of the development of high dispersive magnetization (permeability) for these media, independently of the microscopic magnetic properties of the metallic implants.

Effective response functions for photonic bandgap materials

A magnetic interface generator (400) generates a magnetic interface (410) at a center frequency f0 The magnetic interface generator (400) is a passive array of spirals that are deposited on a substrate surface The magnetic interface (410) is generated in a plane at a distance (Z) above the surface of the substrate (406) The distance (Z) where the magnetic interface (410) is created is determined by the cell size (A) of the spiral array, where the cell size is based on the spiral arm length and the spacing (S) between the spirals (402) The center frequency of the magnetic interface (410) is determined by the average track length DAV of the spirals (402) in the spiral array The spacing (S) of the spiral array is chosen to project the magnetic interface (410) to another layer in the multi-layer substrate so as to improve performance of a circuit in the plane of the magnetic interface (410)

Apparatus for generating a magnetic interface and applications of the same

This paper presents the theoretical design of an artificial dielectric exhibiting narrowband frequency selective properties in the bulk without relying on periodic placement of elements. In this manner, it initiates a novel approach that bypasses the drawbacks of the traditional frequency selective surfaces (FSS), namely, unwanted passbands, dependence on excitation angle and polarization, and difficulties in conversion from planar to curved geometries. The key design elements are the concentric geometry of the inclusions and the use of Lorentzian resonant media. A discussion of physical resonant materials is presented, substantiating the credibility of the theoretical design. To illustrate the approach, a novel complex medium is synthesized as an ensemble of spherical particles composed of a lossy core coated with a highly resonant dielectric layer and embedded into a dielectric host. The resulting structure is an amorphous substance, lossy over its entire spectrum except for two narrow-band transparency windows, where it may become as lossless as desired. The parameter space of the system is thoroughly analyzed which determines the type of constitutive materials and geometries for tailor-designing the windows according to specifications (shape, positioning and overall normalization). In this sense, the lossy concentric structure forms an ideal candidate for thin absorbing films (TAFs) with extensive applications in antenna systems, RF absorbers, and anechoic chambers.

C.A. Kyriazidou

Papers

Monolithic waveguide filters using printed photonic-bandgap materials

Artificial versus natural crystals: effective wave impedance of printed photonic bandgap materials

Effective response functions for photonic bandgap materials

Apparatus for generating a magnetic interface and applications of the same

Novel material with narrow-band transparency window in the bulk