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1 results

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

  • Carlos Jerez-Hanckes, Jean-Claude Nédélec
  • Journal:
    Communications in Computational Physics / Volume 11 / Issue 2 / February 2012
    Published online by Cambridge University Press:
    20 August 2015, pp. 629-646
    Print publication:
    February 2012

  • 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.