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

Corresponding Author:[email protected]

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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.
29 Mar 2021Submitted to Mathematical Methods in the Applied Sciences
30 Mar 2021Submission Checks Completed
30 Mar 2021Assigned to Editor
05 Apr 2021Reviewer(s) Assigned
30 Sep 2021Review(s) Completed, Editorial Evaluation Pending
04 Oct 2021Editorial Decision: Revise Major
27 Oct 20211st Revision Received
27 Oct 2021Submission Checks Completed
27 Oct 2021Assigned to Editor
27 Oct 2021Reviewer(s) Assigned
06 Jan 2022Review(s) Completed, Editorial Evaluation Pending
07 Jan 2022Editorial Decision: Accept
15 Jul 2022Published in Mathematical Methods in the Applied Sciences volume 45 issue 10 on pages 5737-5773. 10.1002/mma.8137