Related papers: The Maxwell system in waveguides with several ends
A numerical technique is described that can efficiently compute solutions in interface problems. These are problems with data, such as the coefficients of differential equations, discontinuous or even singular across one or more interfaces.…
This paper is concerned with the time-dependent Maxwell's equations for a plane interface between a negative material described by the Drude model and the vacuum, which fill, respectively, two complementary half-spaces. In a first paper, we…
In this paper we extend for the case of Maxwell equations the "X-shaped" solutions previously found in the case of scalar (e.g., acoustic) wave equations. Such solutions are localized in theory, i.e., diffraction-free and particle-like…
We consider two inverse boundary value problems for the time-harmonic Maxwell equations in an infinite slab. Assuming that tangential boundary data for the electric and magnetic fields at a fixed frequency is available either on subsets of…
We are interested in the homogenization of energy like quantities for electromagnetic waves in the high frequency limit for Maxwell's equations with various boundary conditions. We use a scaled variant of H-measures known as semi classical…
This paper provides a rigorous analysis of boundary element methods for the magnetic field integral equation on Lipschitz polyhedra. The magnetic field integral equation is widely used in practical applications to model electromagnetic…
An inverse obstacle scattering problem for the electromagnetic wave governed by the Maxwell system over a finite time interval is considered. It is assumed that the wave satisfies the Leontovich boundary condition on the surface of an…
We present a high order, Fourier penalty method for the Maxwell's equations in the vicinity of perfect electric conductor boundary conditions. The approach relies on extending the smooth non-periodic domain of the equations to a periodic…
We consider the inverse problem of determining the isotropic inhomogeneous electromagnetic coefficients of the non-stationary Maxwell equations in a bounded domain of R^3, from a finite number of boundary measurements. Our main result is a…
Equilateral triangular waveguides are one of the very few special kind of waveguides, whose field solutions can be constructed without necessarily solving the Maxwell's equations. Solutions can be obtained simply by superposing some plane…
We introduce a new notion of "matrix potential" to nonlinear optical systems. In terms of a matrix potential $g$, we present a gauge field theoretic formulation of the Maxwell-Bloch equation that provides a semiclassical description of the…
In this article, we extend the results of both Shao and Holzegel-Shao to the AdS-Einstein-Maxwell system $({M}, g, F)$. We study the asymptotics of the metric $g$ and the Maxwell field $F$ near the conformal boundary ${I}$ for the fully…
This paper is concerned with analysis of electromagnetic wave scattering by an obstacle which is embedded in a two-layered lossy medium separated by an unbounded rough surface. Given a dipole point source, the direct problem is to determine…
We analyse the response of laser interferometric gravitational wave detectors using the full Maxwell equations in curved spacetime in the presence of weak gravitational waves. Existence and uniqueness of solutions is ensured by setting up a…
Topologically protected waves in the linearly polarized Maxwell's equations with gyrotropic, magneto-optic media were studied a decade ago both computationally and experimentally. This paper develops a robust tight-binding model for this…
We study the free boundary problem for a plasma-vacuum interface in ideal incompressible magnetohydrodynamics. Unlike the classical statement when the vacuum magnetic field obeys the div-curl system of pre-Maxwell dynamics, to better…
The paper formulates Maxwell's equations in 4-dimensional Euclidean space by embedding the electromagnetic vector potential in the frame vector $g_0$. Relativistic electrodynamics is the first problem tackled; in spite of using a geometry…
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…
We propose a new class of fundamental solutions for the numerical analysis of boundary value problems for the Maxwell equations. We prove completeness of systems of such fundamental solutions in appropriate Sobolev spaces on a smooth…
We prove a uniqueness theorem for an inverse boundary value problem for the Maxwell system with boundary data assumed known only in part of the bound- ary. We assume that the inaccessible part of the boundary is either part of a plane, or…