期刊
INVERSE PROBLEMS
卷 35, 期 10, 页码 -出版社
IOP PUBLISHING LTD
DOI: 10.1088/1361-6420/ab2e27
关键词
Helmholtz equation; periodic wave guide; radiation condition
资金
- Deutsche Forschungsgemeinschaft (DFG) [CRC 1173]
This second part of a pair of papers complements the first part (see Kirsch 2018 (35 104004)) but can be read independently. Scattering of time-harmonic waves from periodic structures at some fixed real-valued wave number becomes analytically difficult 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. As in the first part we consider a medium described by a refractive index which is periodic along the axis of an infinite cylinder in R-3 and constant outside of the cylinder. We formulate a proper radiation condition which allows the existence of traveling modes (and is motivated by the limiting absorption principle proven in the first part) and prove uniqueness and existence.
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