Asymptotics for helmholtz and maxwell solutions in 3-D open waveguides

Carlos Jerez-Hanckes, Jean Claude Nedelec

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


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= (x 1,x2,x3) ∈ℝ3, with x 3 denoting the direction orthogonal to the layers, standard conditions only hold for the outer layers in the region |x3| > ||x||γ, for γ∈ (1/4,1/2) and x large. For |x 3| ≤ ||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.

Original languageEnglish
Pages (from-to)629-646
Number of pages18
JournalCommunications in Computational Physics
Issue number2
StatePublished - Feb 2012
Externally publishedYes


  • Helmholtz equation
  • Open waveguide
  • Radiation condition


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