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Applicable Analysis
An International Journal
Volume 93, 2014 - Issue 2
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Articles

Eigenwaves in waveguides with dielectric inclusions: spectrum

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Pages 408-427 | Received 21 Sep 2012, Accepted 18 Feb 2013, Published online: 01 May 2013
 

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.

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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.

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