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Scatterers on the substrate: Far field formulas

by R. Hiptmair and S. Sargheini

(Report number 2015-02)

Abstract
The near-field to far-field mapping is a tool used to describe radiation at far distances from scatterers. We consider the geometric setting of a bounded scatterer mounted on a substrate, illuminated by a monochromatic plane wave. For such an structure, the far-field functional consists of different asymptotic terms including surface waves. We investigate all contributions closely and show that the only important term at far distances is the spherical wave. A closed form representation is given based on the Green's function of a dipole over a half space. The far-field functional is stated in terms of both volume and boundary integrals. When finite element methods are used to solve Maxwell's equations approximately, the volume based expression is more accurate than the boundary integral. We confirmed the validity of our results by performing several numerical experiments and compared them with other numerical and experimental results.

Keywords: Far field, Scattering, radiation integrals, Nannoparticles

@Techreport{HS15_592,
  author = {R. Hiptmair and S. Sargheini},
  title = {Scatterers on the substrate: Far field formulas},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2015-02},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2015/2015-02.pdf },
  year = {2015}
}

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