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A scattering problem for a local pertubation of an open periodic waveguide

Kirsch, Andreas

Abstract:

In this paper we consider the propagation of waves in an open waveguide in $\mathbb{R}^2$ where the index of refraction is a local perturbation of a function which is periodic along the axis of the waveguide (which we choose to be the $x_1$−axis) and equal to one for $|x_2| > h_0$ for some $h_0 > 0$. Motivated by the limiting absorption principle (proven in [17] for the case of an open waveguide in the half space $\mathbb{R} \times (0, \infty))$ we formulate a radiation condition which allows the existence of propagating modes and prove uniqueness, existence, and stability of a solution under the assumption that no bound states exist. In the second part we determine the order of decay of the radiating part of the solution in the direction of the layer and in the direction orthogonal to it. Finally, we show that it satisfies the classical Sommerfeld radiation condition and allows the definition of a far field pattern.


Volltext §
DOI: 10.5445/IR/1000141621
Veröffentlicht am 03.01.2022
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht/Preprint
Publikationsmonat/-jahr 01.2022
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000141621
Verlag Karlsruher Institut für Technologie (KIT)
Umfang 43 S.
Serie CRC 1173 Preprint ; 2022/2
Projektinformation SFB 1173/2 (DFG, DFG KOORD, SFB 1173/2 2019)
Externe Relationen Abstract/Volltext
Schlagwörter Helmholtz equation, periodic media, radiation condition
KIT – Die Forschungsuniversität in der Helmholtz-Gemeinschaft
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