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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 and
Jean-Claude Nédélec
Carlos Jerez-Hanckes*
Affiliation:
Seminar für Angewandte Mathematik, ETH Zurich, Rämistrasse 101, 8092 Zurich, SwitzerlandEscuela 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:cjerez@math.ethz.ch
Email address:nedelec@cmap.polytechnique.fr
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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∣ > ∣∣x∣γ, 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.

Keywords

35C1535Q6078A45Open waveguideradiation conditionHelmholtz equation

Information

Type
Research Article
Information
Communications in Computational Physics , Volume 11 , Issue 2 , February 2012, pp. 629 - 646
Copyright
Copyright © Global Science Press Limited 2012

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