Eigenwaves in Waveguides with Dielectric Inclusions: Spectrum

TL;DR

This paper investigates the spectral properties of eigenwaves in waveguides with dielectric inclusions, formulating the problem as an eigenvalue problem for an operator pencil and analyzing the spectrum's structure.

Contribution

It introduces a mathematical framework for eigenwaves in waveguides with inclusions, characterizing the spectrum as isolated points within a specific region.

Findings

Spectrum consists of isolated points in a strip

Spectrum has finitely many real points

Eigenwaves are defined via eigenvectors and associated vectors

Abstract

We consider fundamental issues of the mathematical theory of the wave propagation in waveguides with inclusions. Analysis is performed in terms of a boundary eigenvalue problem for the Maxwell equations which is reduced to an eigenvalue problem for an operator pencil. We formulate the definition of eigenwaves and associated waves using the system of eigenvectors and associated vectors of the pencil and prove that the spectrum of normal waves forms a nonempty set of isolated points localized in a strip with at most finitely many real points.