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On the Scattering of a Plane Wave by a Perturbed Open Periodic Waveguide
  • Andreas Kirsch
Andreas Kirsch
Karlsruhe Institute of Technology

Corresponding Author:[email protected]

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We consider the scattering of a plane wave by a locally perturbed periodic (with respect to x_1) medium. If there is no perturbation it is usually assumed that the scattered wave is quasi-periodic with the same parameter as the incident plane wave. As it is well known, one can show existence under this condition but not necessarily uniqueness. Uniqueness fails for certain incident directions (if the wavenumber is kept fixed), and it is not clear which additional condition has to be assumed in this case. In this paper we will analyze three concepts. For the Limiting Absorption Principle (LAP) we replace the refractive index n=n(x) by n(x)+iε in a layer of finite width and consider the limiting case when ε tends to zero. This will give an unsatisfactory condition. In a second approach we require continuity of the field with respect to the incident direction. This will give the same satisfactory condition as the third approach where we approximate the incident plane wave by an incident point source and let the location of the source tend to infinity.
04 Sep 2022Submitted to Mathematical Methods in the Applied Sciences
05 Sep 2022Submission Checks Completed
05 Sep 2022Assigned to Editor
20 Sep 2022Reviewer(s) Assigned
20 Dec 2022Review(s) Completed, Editorial Evaluation Pending
23 Dec 2022Editorial Decision: Revise Minor
06 Jan 20231st Revision Received
09 Jan 2023Submission Checks Completed
09 Jan 2023Assigned to Editor
09 Jan 2023Review(s) Completed, Editorial Evaluation Pending
10 Jan 2023Reviewer(s) Assigned
10 Feb 2023Editorial Decision: Accept