Reconstructing fine details of small objects by using plasmonic spectroscopic data. Part II: The strong interaction regime

Habib Ammari, Matias Ruiz, Sanghyeon Yu, Hai Zhang

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


This paper is concerned with the inverse problem of reconstructing a small object from far-field measurements by using the field interaction with a plasmonic particle which can be viewed as a passive sensor. It is a follow-up of the work [H. Ammari et al., SIAM J. Imaging Sci., 11 (2018), pp. 1–23], where the intermediate interaction regime was considered. In that regime, it was shown that the presence of the target object induces small shifts to the resonant frequencies of the plasmonic particle. These shifts, which can be determined from the far-field data, encode the contracted generalized polarization tensors of the target object, from which one can perform reconstruction beyond the usual resolution limit. The main argument is based on perturbation theory. However, the same argument is no longer applicable in the strong interaction regime as considered in this paper due to the large shift induced by strong field interaction between the particles. We develop a novel technique based on conformal mapping theory to overcome this difficulty. The key is to design a conformal mapping which transforms the two-particle system into a shell-core structure, in which the inner dielectric core corresponds to the target object. We show that a perturbation argument can be used to analyze the shift in the resonant frequencies due to the presence of the inner dielectric core. This shift also encodes information of the contracted polarization tensors of the core, from which one can reconstruct its shape, and hence the target object. Our theoretical findings are supplemented by a variety of numerical results based on an efficient optimal control algorithm. The results of this paper make the mathematical foundation for plasmonic sensing complete.

Original languageEnglish
Pages (from-to)1931-1953
Number of pages23
JournalSIAM Journal on Imaging Sciences
Issue number3
Publication statusPublished - 2018
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2018 Society for Industrial and Applied Mathematics.


  • Far-field measurement
  • Generalized polarization tensors
  • Plasmonic sensing
  • Superresolution

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


Dive into the research topics of 'Reconstructing fine details of small objects by using plasmonic spectroscopic data. Part II: The strong interaction regime'. Together they form a unique fingerprint.

Cite this