LOCALIZATION AND GEOMETRIZATION IN PLASMON RESONANCES AND GEOMETRIC STRUCTURES OF NEUMANN-POINCARE EIGENFUNCTIONS

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journal

2 Scopus Citations
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Original languageEnglish
Pages (from-to)957-976
Journal / PublicationMathematical Modelling and Numerical Analysis
Volume54
Issue number3
Online published16 Apr 2020
Publication statusPublished - May 2020

Abstract

This paper reports some interesting discoveries about the localization and geometrization phenomenon in plasmon resonances and the intrinsic geometric structures of Neumann-Poincare 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.

Research Area(s)

  • Plasmonics, localization, geometrization, high-curvature, Neumann-Poincare eigenfunctions, QUASI-STATIC APPROXIMATION, CLOAKING, NANOPARTICLES, OPERATOR, SYSTEMS

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