Localization and geometrization in plasmon resonances and geometric structures of Neumann-Poincaré eigenfunctions

Emilia Blåsten, Hongjie Li, Hongyu Liu*, Yuliang Wang

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

15 Citations (Scopus)


This paper reports some interesting discoveries about the localization and geometrization phenomenon in plasmon resonances and the intrinsic geometric structures of Neumann-Poincaré eigenfunctions. It is known that plasmon resonance generically occurs in the quasi-static regime where the size of the plasmonic inclusion is sufficiently small compared to the wavelength. In this paper, we show that the global smallness condition on the plasmonic inclusion can be replaced by a local high-curvature condition, and the plasmon resonance occurs locally near the high-curvature point of the plasmonic inclusion. We link this phenomenon with the geometric structures of the Neumann-Poincaré (NP) eigenfunctions. The spectrum of the Neumann-Poincaré operator has received significant attentions in the literature. We show that the Neumann-Poincaré eigenfunctions possess some intrinsic geometric structures near the high-curvature points. We mainly rely on numerics to present our findings. For a particular case when the domain is an ellipse, we can provide the analytic results based on the explicit solutions.

Original languageEnglish
Pages (from-to)957-976
Number of pages20
JournalESAIM: Mathematical Modelling and Numerical Analysis
Issue number3
Publication statusPublished - 1 May 2020

Scopus Subject Areas

  • Analysis
  • Numerical Analysis
  • Modelling and Simulation
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Geometrization
  • High-curvature
  • Localization
  • Neumann-Poincaré eigenfunctions
  • Plasmonics


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