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A radiation condition arizing from the limiting absorption principle for a closed full- or half-waveguide problem

Kirsch, Andreas; Lechleiter, Armin

Abstract:
In this paper we consider the propagation of waves in a closed full- or half-waveguide where the index of refraction is periodic along the axis of the waveguide. Motivated by the limiting absorption principle, proven in the Appendix by a functional analytic perturbation theorem, we formulate a radiation condition which assures uniqueness of a solution and allows the existence of propagating modes. Our approach is quite different to the known one as, e.g., considered in [6] and allows an extension to open wave guides (see [10]). After application of the Floquet-Bloch transform we consider the Floquet-Bloch variable α as a parameter in the resulting quasi-periodic boundary value problem and study the behaviour of the solution when α tends to an exceptional value by a singular perturbation result which we have found in [4].


Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht
Jahr 2017
Sprache Englisch
Identifikator DOI(KIT): 10.5445/IR/1000071358
ISSN: 2365-662X
URN: urn:nbn:de:swb:90-713587
KITopen ID: 1000071358
Verlag KIT, Karlsruhe
Umfang 20 S.
Serie CRC 1173 ; 2017/17
Schlagworte wave propagation, closed waveguide, radiation condition, periodic structure, limiting absorption principle
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