A mathematical and numerical framework for near-field optics

Habib Ammari, Doo Sung Choi, Sanghyeon Yu

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

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 analyse 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.

Original languageEnglish
Article number0150
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume474
Issue number2217
DOIs
Publication statusPublished - 2018 Sep 1
Externally publishedYes

Keywords

  • Generalized polarization tensors
  • Möbius transformation
  • Near-field optics
  • Plasmonic resonances
  • Plasmonic sensing
  • Super-resolution

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)
  • Physics and Astronomy(all)

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