A scattering problem for a local perturbation of an open periodic waveguide

In this paper, we consider the propagation of waves in an open waveguide in ℝ2 where the index of refraction is a local perturbation of a function which is periodic along the axis of the waveguide (which we choose to be the x1 axis) and equal to one for |x2| > h0 for some h0  >  0. Motivated b...

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Bibliographic Details
Published inMathematical methods in the applied sciences Vol. 45; no. 10; pp. 5737 - 5773
Main Author Kirsch, Andreas
Format Journal Article
LanguageEnglish
Published Freiburg Wiley Subscription Services, Inc 15.07.2022
Subjects
Far fields
periodic refractive index
Perturbation
Propagation modes
radiation condition
Refractivity
scattering
Wave propagation
waveguide
Waveguides
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Summary:In this paper, we consider the propagation of waves in an open waveguide in ℝ2 where the index of refraction is a local perturbation of a function which is periodic along the axis of the waveguide (which we choose to be the x1 axis) and equal to one for |x2| > h0 for some h0  >  0. Motivated by the limiting absorption principle (proven in an earlier paper by the author), we formulate a radiation condition which allows the existence of propagating modes and prove uniqueness, existence, and stability of a solution under the assumption that no bound states exist. In the second part, we determine the order of decay of the radiating part of the solution in the direction of the layer and in the direction orthogonal to it. Finally, we show that it satisfies the classical Sommerfeld radiation condition and allows the definition of a far field pattern.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.8137