Related papers: Maxwell eigenmodes in product domains

Eigenmodes of electromagnetic field with perfectly conducting or infinitely permeable conditions on the boundary of a D-dimensional spherically symmetric cavity is derived explicitly. It is shown that there are (D-2) polarizations for TE…

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…

This paper describes recent progress in the analysis of relativistic gauge conditions for Euclidean Maxwell theory in the presence of boundaries. The corresponding quantum amplitudes are studied by using Faddeev-Popov formalism and…

We prove that for bounded and convex domains in three dimensions, the Maxwell constants are bounded from below and above by Friedrichs' and Poincar\'e's constants. In other words, the second Maxwell eigenvalues lie between the square roots…

The Newtonian potential operator for the Helmholtz equation, which is represented by the volume integral with fundamental solution as kernel function, is of great importance for direct and inverse scattering of acoustic waves. In this…

We consider a Riemannian cylinder endowed with a closed potential 1-form A and study the magnetic Laplacian with magnetic Neumann boundary conditions associated with those data. We establish a sharp lower bound for the first eigenvalue and…

The homogenization of eigenvalues of non-Hermitian Maxwell operators is studied by the H-convergence method. It is assumed that the Maxwell systems are equipped with suitable m-dissipative boundary conditions, namely, with Leontovich or…

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…

Resonant electromagnetic modes are analyzed inside a dielectric cavity of equilateral triangular cross section and refractive index n, surrounded by a uniform medium of refractive index n'. The field confinement is determined only under the…

We formulate an optimization problem for the dependence of the eigenvalues of Maxwell's equations in a cavity upon variation of the electric permittivity and we prove a corresponding Maximum Principle.

New results for scalar Casimir self-energies arising from interior modes are presented for the three integrable tetrahedral cavities. Since the eigenmodes are all known, the energies can be directly evaluated by mode summation, with a…

- The purpose of this article is to study possible concentrations of eigenfunc-tions of Laplace operators (or more generally quasi-modes) on product manifolds. We show that the approach of the first author and Zworski [10, 11] applies…

Resonances usually result from wave superpositions in cavities where they are due to the wave spatio-temporal folding imposed by the boundaries. These energy accumulations are the signature of the cavity eigenmodes. Here we study a…

This work considers the Neumann eigenvalue problem for the weighted Laplacian on a Riemannian manifold $(M,g,\partial M)$ under the singular perturbation. This perturbation involves the imposition of vanishing Dirichlet boundary conditions…

We study a class of localized solutions of the wave equation, called eigenwavelets, obtained by extending its fundamental solutions to complex spacetime in the sense of hyperfunctions. The imaginary spacetime variables y, which form a…

Motivated by various applications, this article develops the notion of boundary control for Maxwell's equations in the frequency domain. Surface curl is shown to be the appropriate regularization in order for the optimal control problem to…

We study time dependence of various measures of entanglement (covariance entanglement coefficient, purity entanglement coefficient, normalized distance coefficient, entropic coefficients) between resonantly coupled modes of the…

The asymptotic behavior of the first eigenvalues of magnetic Laplacian operators with large magnetic fields and Neumann realization in polyhedral domains is characterized by a hierarchy of model problems. We investigate properties of the…

We consider a product of an arbitrary number of independent rectangular Gaussian random matrices. We derive the mean densities of its eigenvalues and singular values in the thermodynamic limit, eventually verified numerically. These…

After presenting various concepts and results concerning the classical Steklov eigenproblem, we focus on analogous problems for time-harmonic Maxwell's equations in a cavity. In this direction, we discuss recent rigorous results concerning…