A radiation condition arising from the limiting absorption principle for a closed full‐ or half‐waveguide problem

In this paper, we consider the propagation of waves in a closed full or half waveguide where the index of refraction is periodic along the axis of the waveguide. Motivated by the limiting absorption principle, proven in the Appendix by a functional analytic perturbation theorem, we formulate a radia...

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Bibliographic Details
Published inMathematical methods in the applied sciences Vol. 41; no. 10; pp. 3955 - 3975
Main Authors Kirsch, Andreas, Lechleiter, Armin
Format Journal Article
LanguageEnglish
Published Freiburg Wiley Subscription Services, Inc 15.07.2018
Subjects
Absorption
Boundary value problems
closed waveguide
Constraining
limiting absorption principle
Mathematical analysis
Perturbation methods
Propagation modes
radiation condition
Refractivity
Singular perturbation
Wave propagation
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Summary:In this paper, we consider the propagation of waves in a closed full or half waveguide where the index of refraction is periodic along the axis of the waveguide. Motivated by the limiting absorption principle, proven in the Appendix by a functional analytic perturbation theorem, we formulate a radiation condition that assures uniqueness of a solution and allows the existence of propagating modes. Our approach is quite different to the known one as, eg, considered recently by Fliss and Joly and allows an extension to open wave guides. After application of the Floquet‐Bloch transform, we consider the Bloch variable α as a parameter in the resulting quasiperiodic boundary value problem and study the behaviour of the solution when α tends to an exceptional value by a singular perturbation result, which goes back to Colton and Kress.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.4879