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Asymptotics for Helmholtz and Maxwell Solutions in 3-D Open Waveguides

Published online by Cambridge University Press:  20 August 2015

Carlos Jerez-Hanckes*
Affiliation:
Seminar für Angewandte Mathematik, ETH Zurich, Rämistrasse 101, 8092 Zurich, Switzerland Escuela de Ingeniería, Pontificia Universidad Católica de Chile, Av. Vicuña Mackenna 4860, Santiago, Chile
Jean-Claude Nédélec*
Affiliation:
Escuela de Ingeniería, Pontificia Universidad Católica de Chile, Av. Vicuña Mackenna 4860, Santiago, Chile
*
Corresponding author.Email:[email protected]
Email address:[email protected]
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Abstract

We extend classic Sommerfeld and Silver-Müller radiation conditions for bounded scatterers to acoustic and electromagnetic fields propagating over three isotropic homogeneous layers in three dimensions. If X= (x1,x2,x3)ϵℝ3, with x3 denoting the direction orthogonal to the layers, standard conditions only hold for the outer layers in the region ∣x3∣ > ∣∣xγ, for γϵ(1/4,1/2) and x large. For ∣x3∣ < ∣∣x∣∣γ and inside the slab, asymptotic behavior depends on the presence of surface or guided modes given by the discrete spectrum of the associated operator.

Type
Research Article
Copyright
Copyright © Global Science Press Limited 2012

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