Eigenwaves in waveguides with dielectric inclusions: spectrum

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 non-empty set of isolated points localized in a strip with at most finitely many real points.

Keywords:

• eigenwave
• waveguide
• pencil
• spectrum
• dielectric
• inclusion

AMS Subject Classifications:

• 45E99
• 31B20
• 83C50
• 74S10

Acknowledgments

This work is supported by the Visby Programme of the Swedish Institute, Russian Foundation for Basic Research, projects 11-07-00330-a and 12-07-97010-p-a, and the Ministry of Education and Science of the Russian Federation, grant 14.B37.21.1950.