Scattering by a periodic tube in R3: part ii. A radiation condition. (9th September 2019)

• Record Type: Journal Article
• Authors: Kirsch, Andreas
• Is Part Of: Inverse problems. Volume 35:Number 10(2019)
• Publication Date: 2019-09-09
• Subjects: Helmholtz equation -- periodic wave guide -- radiation condition; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/ab2e27
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: 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 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.