Related papers: On the low-frequency spatial dispersion in wire me…
Electromagnetic waves in vacuum and most materials have transverse polarization. Longitudinal electromagnetic waves with electric field parallel to wave vector are very rare and appear under special conditions in a limited class of media,…
The aim of this article is to study the attenuation of transient low-frequency waves in 2D lattices in both plane and antiplane problems. The main idea of this article is that analytical solutions to problems of mechanics of discrete…
In media with strong spatial dispersion the electric displacement vector and the electric field are typically linked by a partial differential equation in the bulk region. The objective of this work is to highlight that in the vicinity of…
In the framework of multiple-scattering theory, we show that the dispersion relations of certain electromagnetic (EM) and elastic metamaterials can be obtained analytically in the long-wavelength limit. Specific examples are given to the…
We study two-dimensional wave propagation in materials whose properties vary periodically in one direction only. High order homogenization is carried out to derive a dispersive effective medium approximation. One-dimensional materials with…
We study the coherence in time and space of electromagnetic fields propagated through complex media. Whether for localization, imaging or telecommunication, the development of dedicated numerical techniques is generally based on the…
Coherent wave propagation in disordered media gives rise to many fascinating phenomena as diverse as universal conductance fluctuations in mesoscopic metals and speckle patterns in light scattering. Here, the theory of electromagnetic wave…
This paper is dedicated to the study of the semilinear fractional diffusion-wave equation. We provide estimates on the families of linear operators related to the problem in the fractional power scale associated with the Laplace operator.…
We formulate an effective medium (mean field) theory of a material consisting of randomly distributed nodes connected by straight slender rods, hinged at the nodes. Defining novel wavelength-dependent effective elastic moduli, we calculate…
The spectral properties of the Laplacian operator on ``small-world'' lattices, that is mixtures of unidimensional chains and random graphs structures are investigated numerically and analytically. A transfer matrix formalism including a…
The geometric representation at a fixed frequency of the wavevector (or dispersion) surface $\omega(\vec k)$ for lossless, homogeneous dielectric--magnetic uniaxial materials is explored, when the elements of the relative permittivity and…
In this work, we investigate mathematical models for electromagnetic wave propagation in dispersive isotropic media. We emphasize the link between physical requirements and mathematical properties of the models. A particular attention is…
A mathematical model for wire rolling is developed, focusing on predicting the lateral spread. This provides, for the first time, an analytic model of lateral spread without any fitting parameters. The model is derived directly from the…
We discuss the propagation of electromagnetic waves on a rectangular lattice of polarizable point dipoles. For wavelengths long compared to the lattice spacing, we obtain the dispersion relation in terms of the lattice spacing and the…
In this paper, a spatially dispersive finite-difference time-domain (FDTD) method to model wire media is developed and validated. Sub-wavelength imaging properties of the finite wire medium slabs are examined. It is demonstrated that the…
We show that technique of Dyson equation in wave multiple scattering by spatially disordered discrete medium statistical theory leads directly to a dielectric permittivity tensor, which is characterized by spatial dispersion and obeys the…
In this paper we suggest a simple analytical method for description of electromagnetic properties of a geometrically regular two-dimensional subwavelength arrays (metasurfaces) formed by particles with randomly fluctuating polarizabilities.…
A theoretical approach for describing the electromagnetic radiation produced by prolonged electron bunch propagating in the lattice of metallic wires of finite length is presented. This approach is based on vibrator antenna theory and…
We introduce the stochastic band structure, a method giving the dispersion relation for waves propagating in periodic media or along waveguides, and subject to material loss or radiation damping. Instead of considering an explicit or…
Dielectric relaxation in disordered dielectric mixtures are presented by emphasizing the interfacial polarization. The obtained results coincide with and cause confusion with those of the low frequency dispersion behavior. The considered…