Related papers: Effective Maxwell's equations in general periodic …
We study the sense in which the continuum limit of a broad class of discrete materials with periodic structures can be viewed as a nonlinear elastic material. While we are not the first to consider this question, our treatment is more…
We study a transmission problem for the time harmonic Maxwell's equations between a classical positive material and a so-called negative index material in which both the permittivity $\varepsilon$ and the permeability $\mu$ take negative…
We establish the well-posedness, the finite speed propagation, and a regularity result for Maxwell's equations in media consisting of dispersive (frequency dependent) metamaterials. Two typical examples for such metamaterials are materials…
We derive and interpret solutions of time-harmonic Maxwell's equations with a vertical and a horizontal electric dipole near a planar, thin conducting film, e.g. graphene sheet, lying between two unbounded isotropic and non-magnetic media.…
A waveguide coincides with a three-dimensional domain G having finitely many cylindrical outlets to infinity; the boundary of G is smooth. In G, we consider the stationary Maxwell system with real spectral parameter k and identity matrices…
Topological metamaterials have invaded the mechanical world, demonstrating acoustic cloaking and waveguiding at finite frequencies and variable, tunable elastic response at zero frequency. Zero frequency topological states have previously…
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…
Using electromagnetism to study analogue space-times is tantamount to considering consistency conditions for when a given (meta-)material would provide an analogue space-time model or --- vice versa --- characterizing which given metric…
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…
This paper provides a general framework for deriving effective material properties of one-dimensional, time-modulated systems of subwavelength resonators. It applies to subwavelength resonator systems with a general form of time-dependent…
The goal of this work is to study the electromagnetic scattering problem of time-domain Maxwell's equations in an unbounded structure. An exact transparent boundary condition is developed to reformulate the scattering problem into an…
The scattering of electromagnetic waves from obstacles with wave-material interaction in thin layers on the surface is described by generalized impedance boundary conditions, which provide effective approximate models. In particular, this…
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…
Electromagnetic properties of periodic two-dimensional sub-wavelength structures consisting of closely-packed inclusions of materials with negative dielectric permittivity $\epsilon$ in a dielectric host with positive $\epsilon_h$ can be…
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…
To design a uniaxial anisotropic metamaterial a layered cylindrical metamaterial is introduced for TE polarization. Unlike to the previous work, which the layers were in radial direction, here the layers are in azimuthal direction.…
In a bounded domain $\mathcal{O}\subset\mathbb{R}^3$ of class $C^{1,1}$, we consider a stationary Maxwell system with the boundary conditions of perfect conductivity. It is assumed that the magnetic permeability is given by a constant…
In electromagnetism, the model of Maxwell's equations yields accurate and trustworthy predictions. Numerical solvers can reach electromagnetic solutions far beyond the set of analytical closed-form solutions; this is crucial in…
To discuss the properties of metamaterials on physical grounds and to consider them in applications, effective material parameters are usually introduced and assigned to a given metamaterial. In most cases, only weak spatial dispersion is…
We consider the time-harmonic Maxwell equations with impedance boundary conditions on a bounded Lipschitz domain $\Omega$ with analytic boundary $\Gamma$. We suppose that $\Omega$ consists of multiple subdomains, and that the permeability…