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Metamaterials are known to exhibit a variety of electromagnetic properties non-existing in nature. We show that an all-dielectric (non-magnetic) system consisting of deep subwavelength, high permittivity resonant spheres possess effective…

A small dielectric object with positive permittivity may resonate when the free-space wavelength is large in comparison with the object dimensions if the permittivity is sufficiently high. We show that these resonances are described by the…

The electromagnetic dispersion in periodic layered media can be tailored and their resonant properties can be considerably improved by utilizing anisotropic materials. Periodic structures with a photonic band edge split into two parts, or…

Optics · Physics 2009-11-13 A. A. Chabanov

Two methods are explained to exactly solve Maxwell's equations where permittivity, permeability and conductivity may vary in space. In the constitutive relations, retardation is regarded. If the material properties depend but on one…

Optics · Physics 2012-08-20 Ulrich Brosa

We estimate the electromagnetic fields generated by a cluster of dielectric nanoparticles embedded into a background made of a vacuum. The dielectric nanoparticles are small scaled but enjoy high contrast of their relative permittivity.…

Analysis of PDEs · Mathematics 2022-09-09 Xinlin Cao , Ahcene Ghandriche , Mourad Sini

A system of periodic poly-disperse coated nano-rods is considered. Both the coated nano-rods and host material are non-magnetic. The exterior nano-coating has a frequency dependent dielectric constant and the rod has a high dielectric…

Optics · Physics 2015-05-18 Yue Chen , Robert Lipton

We study the behavior of wave propagation in materials for which not all of the principle elements of the permeability and permittivity tensors have the same sign. We find that a wide variety of effects can be realized in such media,…

Materials Science · Physics 2009-11-07 D. R. Smith , D. Schurig

We analyze nonlinear properties of microstructured materials with negative refraction, the so-called left-handed metamaterials. We consider a two-dimensional periodic structure created by arrays of wires and split-ring resonators embedded…

Materials Science · Physics 2007-05-23 Alexander A. Zharov , Ilya V. Shadrivov , Yuri S. Kivshar

Recently, a theory for artificial magnetism in two-dimensional photonic crystals has been developed for large wavelength using homogenization techniques. In this paper we pursue this approach within a rigorous stochastic framework:…

Mathematical Physics · Physics 2013-05-31 Guy Bouchitte , Christophe Bourel , Luigi Manca

We consider a semi-infinite dielectric with multiple spatially dispersive resonances in the susceptibility. The effect of the boundary is described by an arbitrary reflection coefficient for polarization waves in the material at the…

Optics · Physics 2017-05-10 R. J. Churchill , T. G. Philbin

We investigate the interaction of polarized electromagnetic waves with hyperbolic metamaterial structures, whereby the in-plane permittivity component $\epsilon_x$ is opposite in sign to the normal component $\epsilon_z$. We find that when…

Optics · Physics 2015-06-19 Klaus Halterman , J. Merle Elson

Periodic structures are a type of metamaterial in which the physical properties depend not only on the details of the unit cell but also on how unit cells are arranged and interact with each other. In conventional engineering structures,…

Applied Physics · Physics 2022-05-27 Sudesh Pathak , Gagan Dangi , Farhad Farzbod

Composites are ideally suited to achieve desirable multifunctional effective properties since the best properties of different materials can be judiciously combined with designed microstructures. Here we establish cross-property relations…

Soft Condensed Matter · Physics 2020-05-13 Jaeuk Kim , Salvatore Torquato

We theoretically investigate the transmission of electromagnetic radiation through a metal plate with a zero-$\epsilon$ metamaterial slit, where the permittivity tends towards zero over a given bandwidth. Our analytic results demonstrate…

Optics · Physics 2008-09-15 Klaus Halterman , Simin Feng

Periodic structures with subwavelength features are instrumental in the versatile and effective control of electromagnetic waves from radio frequencies up to optics. In this paper, we theoretically evaluate the potential applications and…

Mesoscale and Nanoscale Physics · Physics 2013-01-04 Arya Fallahi , Julien Perruisseau-Carrier

We derive the electromagnetic medium equivalent to a cluster of all-dielectric nanoparticles (i.e. enjoying high refractive indices), distributed periodically in a smooth domain $\Omega$, while excited at nearly resonating dielectric…

Analysis of PDEs · Mathematics 2023-12-27 Xinlin Cao , Ahcene Ghandriche , Mourad Sini

A metamaterial with frequency dependent double negative effective properties is constructed from a sub-wavelength periodic array of coated rods. Explicit power series are developed for the dispersion relation and associated Bloch wave…

Analysis of PDEs · Mathematics 2012-02-06 Yue Chen , Robert Lipton

We analyse the resonance conditions of a long and narrow ribbon of finite length whether it is conductive or dielectric. This is accomplished by using a full wave approach based on the material independent modes that naturally discriminates…

Mesoscale and Nanoscale Physics · Physics 2019-09-04 Carlo Forestiere , Giovanni Miano , Mariano Pascale , Roberto Tricarico

Featuring dense spatial distributions of engineered metallic particles, electromagnetic metamaterials exhibit simultaneously negative values of both, dielectric permittivity and magnetic permeability, within a resonance frequency band…

We consider transverse propagation of electromagnetic waves through a two-dimensional composite material containing a periodic rectangular array of circular cylinders. Propagation of waves is described by the Helmholtz equation with the…

Mathematical Physics · Physics 2019-05-30 Yuri A. Godin , Boris Vainberg
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