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Resonant states in waveguide transmission problems
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
2015 (English)In: Progress in Electromagnetics Research B, ISSN 1937-6472, E-ISSN 1937-6472, Vol. 64, 119-143 p.Article in journal (Refereed) PublishedText
Abstract [en]

We prove the existence of complex eigenfrequencies of open waveguide resonators in the form of parallel-plate waveguides and waveguides of rectangular crosssection containing layered dielectric inclusions. It is shown that complex eigenfrequencies are finite-multiplicity poles of the analytical continuation of the operator of the initial diffraction problem and its Green's function to a multi-sheet Riemann surface, and also of the transmission coefficient extended to the complex plane of some of the problem parameters. The eigenfrequencies are associated with resonant states (RSs) and eigenvalues of distinct families of Sturm-Liouville problems on the line; they form countable sets of points in the complex plane with the only accumulation point at infinity and depend continuously on the problem parameters. The set of complex eigenfrequencies is similar in its structure to the set of eigenvalues of a Laplacian in a rectangle. The presence of a resonance domain in the form of a parallel-plane layered dielectric insert removes the continuous frequency spectrum and gives rise to a discrete set of points shifted to (upper half of) the complex plane.

Place, publisher, year, edition, pages
New York: Institute of Electrical and Electronics Engineers (IEEE), 2015. Vol. 64, 119-143 p.
Keyword [en]
applied mathematics, waveguide
National Category
Mathematical Analysis
URN: urn:nbn:se:hig:diva-21190DOI: 10.2528/PIERB15083001ISI: 000380563800051ScopusID: 2-s2.0-84958980348ISBN: 978-9-0900-8628-6OAI: oai:DiVA.org:hig-21190DiVA: diva2:900845
2015 URSI Atlantic Radio Science Conference (URSI AT-RASC), 16-24 May 2015, Gran Canaria, Spain
Available from: 2016-02-05 Created: 2016-02-05 Last updated: 2016-11-28Bibliographically approved

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Shestopalov, Yury V.
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