A mathematical and numerical framework for near-field optics

Habib Ammari, Doo Sung Choi, Sanghyeon Yu

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


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
Issue number2217
Publication statusPublished - 2018 Sept 1
Externally publishedYes

Bibliographical note

Funding Information:
Data accessibility. Supporting data are available on the electronic supplementary material. Authors’ contributions. All authors developed the theory and performed numerical computation. All authors wrote the manuscript. Competing interests. We have no competing interests. Funding. The work of D.S.C. is supported by the Korean Ministry of Science, ICT and Future Planning through NRF grant No. 2016R1A2B4014530.

Publisher Copyright:
© 2018 The Author(s) Published by the Royal Society. All rights reserved.


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

ASJC Scopus subject areas

  • General Mathematics
  • General Engineering
  • General Physics and Astronomy


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