Related papers: Trapped modes in electromagnetic waveguides
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 wave propagation of edge modes in a superlattice of 2D electron Gases in quantum Hall regime is investigated. After introducing surfaces charge and current densities at the edge, the Maxwell equations are solved for waves running along…
We introduce transversely structured all-dielectric waveguides which exploit the vectorial nature of light to achieve extreme sub-wavelength confinement in high index dielectrics, enabling characteristic mode dimensions below…
Whether there exist independent transverse electric (TE) and transverse magnetic (TM) modes in a metallic waveguide filled with an anisotropic medium is a fundamental question in electromagnetics waveguide theory, but so far no definitive…
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.…
We find solutions $E:\Omega\to\mathbb{R}^3$ of the problem \[ \left\{\begin{aligned} &\nabla\times(\nabla\times E) + \lambda E = \partial_E F(x,E) &&\quad \text{in}\Omega\\ &\nu\times E = 0 &&\quad \text{on}\partial\Omega \end{aligned}…
Based on the idea of the Abelian group theory in mathematics,this paper finds a sufficient condition of having independent TE and TM modes in a waveguide filled with homogenous anisotropic lossless medium. For independent TE modes, we prove…
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…
Electromagnetic waves, in vacuum or dielectrics, can be confined in unbounded cylinders in such a way that they turn around the main axis. For particular choices of the cylinder's section, interesting stationary configurations may be…
A planar waveguide with impedance boundary, composed of non-perfect metallic plates, and with passive or active dielectric filling is considered. We show the possibility of selective mode guiding and amplification when homogeneous pump is…
We study a Helmholtz-type spectral problem in a two-dimensional medium consisting of a fully periodic background structure and a perturbation in form of a line defect. The defect is aligned along one of the coordinate axes, periodic in that…
In this note we consider boundary value problems in electromagnetism. We prove well-posedness results for the time-harmonic Maxwell equations in the setting of Riemannian manifolds. We also consider the eigenvalue problem the homogeneous…
In the junction $\Omega$ of several semi-infinite cylindrical waveguides we consider the Dirichlet Laplacian whose continuous spectrum is the ray $[\lambda_\dagger, +\infty)$ with a positive cut-off value $\lambda_\dagger$. We give two…
In this paper we consider an abstract Cauchy problem for a Maxwell system modelling electromagnetic fields in the presence of an interface between optical media. The electric polarization is in general time-delayed and nonlinear, turning…
Inspired by recent developments in the theory of stability results in the context of certain wave type phenomena, we discuss abstract damped hyperbolic type equations given in a block operator matrix form with regards to asymptotic…
We discover a new wave localization mechanism in a periodic system without any disorder, which can produce a novel type of perfect flat band and is distinct from the known localization mechanisms, i.e., Anderson localization and flat band…
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…
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…
We consider Maxwell's equations in a 3-dimensional material, in which both, the electric permittivity, as well as the magnetic permeability, fluctuate in space. Differently from all previous treatments of the disordered electromagnetic…
This study presents a finite-difference-based numerical solver designed for the electric field formulation of vector wave equations in optically linear, non-magnetic, dielectric waveguides. We construct a generalized eigenvalue problem by…