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A Scattering Problem for a Local Perturbation of an Open Periodic Waveguide
  • Andreas Kirsch
Andreas Kirsch
KIT
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Abstract

In this paper we consider the propagation of waves in an open waveguide in R^2 where the index of refraction is a local perturbation of a function which is periodic along the axis of the waveguide and equal to one outside a strip of finite width. Motivated by the limiting absorption principle (proven in an ealier paper by the author for the case of an open waveguide in the half space) we formulate a radiation condition which allows the existence of propagating modes and prove uniqueness, existence, and stability of a solution. In the last part we investigate the decay properties of the radiating part in the direction of periodicity and orthogonal to it.

Peer review status:UNDER REVIEW

29 Mar 2021Submitted to Mathematical Methods in the Applied Sciences
30 Mar 2021Assigned to Editor
30 Mar 2021Submission Checks Completed
05 Apr 2021Reviewer(s) Assigned