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The limiting absorption principle and a radiation condition for the scattering by a periodic layer

Kirsch, Andreas; Lechleiter, Armin

Scattering of time-harmonic waves from periodic structures at some fixed real-valued wave number becomes analytically diffcult whenever there arise surface waves: These non-zero solutions to the homogeneous scattering problem physically correspond to modes propagating along the periodic structure and clearly imply non-uniqueness of any solution to the scattering problem. In this paper, we consider a medium that is defined in the upper two-dimensional half-space by a penetrable and periodic contrast. We prove that there is a so-called limiting absorption solution to the associated scattering problem. By definition, such a solution is the limit of a sequence of unique solutions for artificial complex-valued wave numbers tending to the above-mentioned real-valued wave number. Our method of proof seems to be new: By the Floquet-Bloch transform we first reduce the scattering problem to a finite-dimensional one that is set in the linear space spanned by all surface waves. In this space, we then compute explicitly which modes propagate along the periodic structure to the left or to the right. This finally yields a representation for our li ... mehr

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/1000068129
ISSN: 2365-662X
URN: urn:nbn:de:swb:90-681296
KITopen ID: 1000068129
Verlag KIT, Karlsruhe
Umfang 32 S.
Serie CRC 1173 ; 2017/8
Schlagworte scattering theory, Helmholtz equation, periodic media, Floquet-Bloch transform, limiting absorption principle, radiation condition
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