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A mathematical and numerical framework for near-field optics

by H. Ammari and D. Choi and S. Yu

(Report number 2018-08)

Abstract
This paper is concerned with the inverse problem of reconstructing small and local perturbations of a planar surface using the field interaction between a known plasmonic particle and the planar surface. The aim is to perform a super-resolved reconstruction of these perturbations from shifts in the plasmonic frequencies of the particle-surface system. In order to analyze the interaction between the plasmonic particle and the planar surface, a well chosen conformal mapping, which transforms the particle-surface system into a coated structure, is used. Then the even Fourier coefficients of the transformed domain are related to the shifts in the plasmonic resonances of the particle-surface system. A direct reconstruction of the perturbations of the planar surface is proposed. Its viability and limitations are documented by numerical examples.

Keywords: Near-field optics, plasmonic sensing, super-resolution, M\"{o}bius transformation, generalized polarization tensors, plasmonic resonances.

@Techreport{ACY18_762,
  author = {H. Ammari and D. Choi and S. Yu},
  title = {A mathematical and numerical framework for near-field optics},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2018-08},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2018/2018-08.pdf },
  year = {2018}
}

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