Related papers: Effective Maxwell's equations in general periodic …
It is well known that defining a local refractive index for a metamaterial requires that the wavelength be large with respect to the scale of its microscopic structure (generally the period). However, the converse does not hold. There are…
The possibility of an incompletness of the equations of electromagnetism is analyzed using a thought experiment that shows a non-physical behavior according to classical electromagnetism. Basically, from Maxwell equations it is shown that a…
We consider time-harmonic Maxwell's equations set in an heterogeneous medium with perfectly conducting boundary conditions. Given a divergence-free right-hand side lying in $L^2$, we provide a frequency-explicit approximability estimate…
Propagation of monochromatic extraordinary light in a hyperbolic metamaterial is identical to propagation of massive particles in a three dimensional effective Minkowski spacetime, in which the role of a timelike variable is played by one…
In this paper, we consider near cloaking for the full Maxwell equations. We extend the recent results, where the quasi-static limit case and the Helmholtz equation are considered, to electromagnetic scattering problems. We construct very…
The convergence behaviour and the design of numerical methods for modelling the flow of light in photonic crystal fibres depend critically on an understanding of the regularity of solutions to time-harmonic Maxwell equations in a…
Maxwell's equations in curved space-time are invariant under electromagnetic duality transformations. We exploit this property to constraint the design parameters of metamaterials used for transformations optics. We show that a general…
In this paper, we present a unit cell showing a band-gap in the lower acoustic domain. The corresponding metamaterial is made up of a periodic arrangement of this unit cell. We rigorously show that the relaxed micromorphic model can be used…
In curved spacetime, Maxwell's equations can be expressed in forms valid in Minkowski background, with the effect of the metric (gravity) appearing as effective polarizations and magnetizations. The electric and magnetic (EM) fields depend…
We solve time-harmonic Maxwell's equations in anisotropic, spatially homogeneous media in intersections of $L^p$-spaces. The material laws are time-independent. The analysis requires Fourier restriction-extension estimates for perturbations…
A discussion is given of the conformal Einstein field equations coupled with matter whose energy-momentum tensor is trace-free. These resulting equations are expressed in terms of a generic Weyl connection. The article shows how in the…
We analyze the reflection and transmission coefficients calculated from transfer matrix simulations on finite lenghts of electromagnetic metamaterials, to determine the effective permittivity and permeability. We perform this analysis on…
We investigate the effects of mesoscopic inhomogeneities on the metal-superconductor transition occurring in several two-dimensional electron systems. Specifically, as a model of systems with mesoscopic inhomogeneities, we consider a…
We consider solutions to the time-harmonic Maxwell problem in $\R^3$. For such solution we provide a rigorous derivation of the asymptotic expansions in the practically interesting situation, where a finite number of inhomogeneities of…
We study the behaviour of the spectrum of a family of one-dimensional operators with periodic high-contrast coefficients as the period goes to zero, which may represent e.g. the elastic or electromagnetic response of a two-component…
We propose and investigate a new type of metamaterial structure composing of several interpenetrating wire meshes. Calculated band structures show that they exhibit index ellipsoids locating at nonzero k-point in long wavelength limit. We…
Numerical discretization of the large-scale Maxwell's equations leads to an ill-conditioned linear system that is challenging to solve. The key requirement for successive solutions of this linear system is to choose an efficient solver. In…
Efficient modeling of dispersive materials via time-domain simulations of the Maxwell equations relies on the technique of auxiliary differential equations. In this approach, a material's frequency-dependent permittivity is represented via…
Metamaterials are arrangement of basic building blocks that repeat in space, time, or both. These material systems serve as an excellent platform for controlling waves, such as engineering wavenumber band gaps, flat bands, and…
Electromagnetic field propagation through a transition layer between the positive-index and negative-index materials with linearly changing dielectric permittivity and magnetic permeability was investigated. It is shown that at oblique…