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Asymptotics for Helmholtz and Maxwell solutions in 3-D open waveguides

by C. Jerez-Hanckes and J.-C. Nédélec

(Report number 2010-07)

Abstract
We extend Sommerfeld and Silver-Müller radiation conditions to acoustic and electromagnetic fields propagating over three isotropic layers in $R^3$. In the outer layers, classical conditions only hold for waves propagating in the region $|x_3|>r^\gamma$ with $\gamma\in\left(\frac{1}{4},\frac{1}{2}\right)$. For $|x_3|>r^\gamma$ and inside the slab, asymptotic behaviors depend on the presence of surface or guided modes given by the discrete spectrum of the associated operator.

Keywords:

@Techreport{JN10_47,
  author = {C. Jerez-Hanckes and J.-C. Nédélec},
  title = {Asymptotics for Helmholtz and Maxwell solutions in 3-D open waveguides},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2010-07},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2010/2010-07.pdf },
  year = {2010}
}

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