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Here, we present an overview of recent developments in the characterization of electromagnetic and quantum metamaterials using effective medium methods. It is highlighted that both electromagnetic and electronic systems can be homogenized…

Mesoscale and Nanoscale Physics · Physics 2017-11-23 Mario G. Silveirinha

Metamaterials are artificial composite structures designed for controlling waves or fields, and exhibit interaction phenomena that are unexpected on the basis of their chemical constituents. These phenomena are encoded in effective material…

Materials Science · Physics 2015-12-21 Mihai Caleap , Bruce W Drinkwater

It is discussed that the classical effective medium theory for the elastic properties of random heterogeneous materials is not congruous with the effective medium theory for the electrical conductivity. In particular, when describing the…

Materials Science · Physics 2020-02-17 Snarskii Andrei , Shamonin Mikhail , Yuskevich Pavel

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

While the properties of materials at microscopic scales are well described by fundamental quantum mechanical equations and electronic structure theories, the emergent behavior of mesoscopic or macroscopic composites is no longer governed…

Applied Physics · Physics 2025-07-10 Lifeng Hao , Fan Li , Yongqi Li , Siyong Wang , Xiaodong He

Scattering of electromagnetic (EM) waves by many small particles (bodies) embedded in a homogeneous medium is studied. Physical properties of the particles are described by their boundary impedances. The limiting equation is obtained for…

Mathematical Physics · Physics 2011-01-18 A. G. Ramm

Although the invention of the metamaterials has stimulated the interest of many researchers and possesses many important applications, the basic design idea is very simple: composing effective media from many small structured elements and…

Optics · Physics 2015-05-20 Hui Liu , Tao LI , Shu-ming Wang , Shi-ning Zhu

The problem of definition of effective material parameters (permittivity and permeability) for composite layers containing only one-two parallel arrays of complex-shaped inclusions is discussed. Such structures are of high importance for…

Classical Physics · Physics 2009-11-13 Elena Saenz , Pekka Ikonen , Ramon Gonzalo , Sergei Tretyakov

The relationship between magnetoelectricity and electromagnetism is a subject of a strong interest and numerous discussions in microwave and optical wave physics and material sciences. The definition of the energy and momentum of the…

Materials Science · Physics 2020-04-22 E. O. Kamenetskii

Reflection and refraction of electromagnetic waves by artificial periodic composites (metamaterials) can be accurately modeled by an effective medium theory only if the boundary of the medium is explicitly taken into account and the two…

Optics · Physics 2013-09-24 Vadim A. Markel , Igor Tsukerman

In the past two decades, artificial structures known as metamaterials have been found to exhibit extraordinary material properties that enable the unprecedented manipulation of electromagnetic waves, elastic waves, molecules, and particles.…

Applied Physics · Physics 2022-11-08 Jade E. Holliman , H. Todd Schaef , B. Peter McGrail , Quin R. S. Miller

Scattering of electromagnetic (EM) waves by many small particles, embedded in a given medium, is studied. Physical properties of the particles are described by their boundary impedances. The limiting equation is obtained for the effective…

Optics · Physics 2011-01-25 A. G. Ramm

High-fidelity numerical methods that model the physical layout of a device are essential for the design of many technologies. For methods that characterize electromagnetic effects, these numerical methods are referred to as computational…

We study the propagation of electromagnetic (EM) waves in extremely dense exotic systems with very unique properties. These EM waves develop a longitudinal component due to interactions with the medium. Renormalization scheme of QED is used…

Plasma Physics · Physics 2017-05-16 Samina Masood , Iram Saleem

In electrical engineering metamaterials have been developed that offer unprecedented control over electromagnetic fields. Here we show that general relativity lends the theoretical tools for designing devices made of such versatile…

Materials Science · Physics 2009-11-11 Ulf Leonhardt , Thomas G. Philbin

Fully harnessing the vast design space enabled by metamaterials to control electromagnetic (EM) fields remains an open problem for researchers. Inverse-design techniques have shown to best exploit the degrees of freedom available in design,…

Optics · Physics 2025-11-27 Jorge Ruiz-Garcia , Anthony Grbic

Within a decade of fruitful developments, metamaterials became a prominent area of research, bridging theoretical and applied electrodynamics, electrical engineering and material science. Being man-made structures, metamaterials offer a…

This article discusses electromagnetic properties of volumetric metamaterial samples with essentially discrete structure, that is, assembled as a periodic array of electromagnetic resonators. We develop an efficient numerical procedure for…

Applied Physics · Physics 2025-09-19 Aleksander O. Makarenko , Maxim A. Yurkin , Alexey A. Shcherbakov , Mikhail Lapine

Controlling electromagnetic energy is essential for an efficient and sustainable society. A key requirement is concentrating magnetic energy in a desired volume of space in order to either extract the energy to produce work or store it.…

Superconductivity · Physics 2015-06-17 Jordi Prat-Camps , Carles Navau , Alvaro Sanchez

The boundary element method (BEM) enables solving three-dimensional electromagnetic problems using a two-dimensional surface mesh, making it appealing for applications ranging from electrical interconnect analysis to the design of…

Numerical Analysis · Mathematics 2021-12-14 Shashwat Sharma , Piero Triverio
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