Trapped modes in electromagnetic waveguides

TL;DR

This paper investigates the existence of electromagnetic trapped modes in three-dimensional waveguides, demonstrating how specific geometries and dielectric perturbations can support such modes, with some mechanisms unique to Maxwell's equations.

Contribution

The paper introduces new geometric and dielectric configurations that support trapped modes in Maxwell's equations, highlighting mechanisms unique to electromagnetic waveguides.

Findings

Existence of trapped modes in certain geometries

Identification of dielectric perturbations supporting trapped modes

Mechanisms unique to Maxwell's equations for trapping

Abstract

We consider the Maxwell's equations with perfect electric conductor boundary conditions in three-dimensional unbounded domains which are the union of a bounded resonator and one or several semi-infinite waveguides. We are interested in the existence of electromagnetic trapped modes, i.e. $L^2$ solutions of the problem without source term. These trapped modes are associated to eigenvalues of the Maxwell's operator, that can be either below the essential spectrum or embedded in it. First for homogeneous waveguides, we present different families of geometries for which we can prove the existence of eigenvalues. Then we exhibit certain non homogeneous waveguides with local perturbations of the dielectric constants that support trapped modes. Let us mention that some of the mechanisms we propose are very specific to Maxwell's equations and have no equivalent for the scalar Dirichlet or Neumann Laplacians.