Related papers: Effective Maxwell's equations in general periodic …
In this work we study linear Maxwell equations with time- and space-dependent matrix-valued permittivity and permeability on domains with a perfectly conducting boundary. This leads to an initial boundary value problem for a first order…
We carry out the homogenization of time-harmonic Maxwell's equations in a periodic, layered structure made of two-dimensional (2D) metallic sheets immersed in a heterogeneous and in principle anisotropic dielectric medium. In this setting,…
We develop a finite volume method for Maxwell's equations in materials whose electromagnetic properties vary in space and time. We investigate both conservative and non-conservative numerical formulations. High-order methods accurately…
The aim of this article is to investigate the well-posedness, stability and convergence of solutions to the time-dependent Maxwell's equations for electric field in conductive media in continuous and discrete settings. The situation we…
In this note we consider the scattering of electromagnetic waves (governed by the time-harmonic Maxwell equations) by a thin periodic layer of perfectly conducting obstacles. The size of the obstacles and the distance between neighbouring…
A rigorous homogenization theory of metamaterials -- artificial periodic structures judiciously designed to control the propagation of electromagnetic waves -- is developed. All coarse-grained fields are unambiguously defined and effective…
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…
We use a homogenization procedure for Maxwell's equations in order to obtain in the local limit the frequency ($\omega$) dependent macroscopic dielectric response $\epsilon^M(\omega)$ of metamaterials made of natural constituents with any…
We consider a quasilinear nonhomogeneous, anisotropic Maxwell system in a bounded smooth domain of $\mathbb{R}^{3}$ with a strictly positive conductivity subject to the boundary conditions of a perfect conductor. Under appropriate…
Here, we present an overview of a first principles homogenization theory of periodic metamaterials. It is shown that in a rather general context it is possible to formally introduce effective parameters that describe the time evolution of…
At zero energy the Dirac equation has interesting behaviour. The asymmetry in the number of spin up and spin down modes is determined by the topology of both space and the gauge field in which the system sits. An analogous phenomenon also…
We study the frequency dependence of the effective electromagnetic parameters of left-handed and related meta-materials of the split ring resonator and wire type. We show that the reduced translational symmetry (periodic structure) inherent…
This paper focuses on the time-harmonic electromagnetic (EM) scattering problem in a general medium which may possess a nontrivial topological structure. We model this by an inhomogeneous and possibly anisotropic medium with embedded…
Many properties of photonic structures rely on band topology characterized by the integer invariants that can change during the topological transitions and give rise to the disorder-robust topological edge, corner, or interface states.…
We consider the time dependent Maxwell system in the sense of distributions in the context of temporal interfaces. Just as with spatial interfaces, electromagnetic waves at temporal interfaces scatter and create a transmitted and reflected…
We consider field localizing and concentration of electromagnetic waves governed by the time-harmonic anisotropic Maxwell system in a bounded domain. It is shown that there always exist certain boundary inputs which can generate…
We present an effective medium theory that can predict the effective permittivity and permeability of a geometrically anisotropic two-dimensional metamaterial composed with a rectangular array of elliptical cylinders. It is possible to…
Metamaterial effective parameters may exhibit freedom from typical dispersion constraints. For instance, the emergence of a magnetic response in arrays of split-ring resonators for long wavelengths cannot be attained in a passive continuous…
In the work, a modified effective medium theory is constructed for calculating the effective properties of thermoelectric composites with different values of percolation thresholds. It is shown that even at concentrations beyond the…
A unified homogenization procedure for split ring metamaterials taking into account time and spatial dispersion is introduced. The procedure is based on two coupled systems of equations. The first one comes from an approximation of the…