Mathematical aspects of the theory of wave propagation in metal-dielectric waveguides

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 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. We show the importance of these results for the theory of wave propagation in open guiding structures and consider in more detail the surface wave spectrum of the Goubau line.