Analysis of plasmon resonance on smooth domains using spectral properties of the Neumann-Poincar\'e operators

TL;DR

This paper provides a detailed spectral analysis of plasmon resonance on smooth domains using the Neumann-Poincaré operator, revealing differences in resonance behavior at eigenvalues and the essential spectrum, with implications for cloaking and resonance phenomena.

Contribution

It extends the symmetrization principle for the Neumann-Poincaré operator and analyzes resonance behavior at the essential spectrum on various domains.

Findings

Resonance at the essential spectrum is weaker than at eigenvalues.

Anomalous localized resonance occurs at the essential spectrum on ellipses.

Resonance does not occur at the essential spectrum on three-dimensional balls.

Abstract

We investigate in a quantitative way the plasmon resonance at eigenvalues and the essential spectrum (the accumulation point of eigenvalues) of the Neumann-Poincar\'e operator on smooth domains. We first extend the symmetrization principle so that the single layer potential becomes a unitary operator from $H^{-1/2}$ onto $H^{1/2}$. We then show that the resonance at the essential spectrum is weaker than that at eigenvalues. It is shown that anomalous localized resonance occurs at the essential spectrum on ellipses, but cloaking does not occur on ellipses unlike the core-shell structure considered in [20]. It is shown that resonance does not occur at the essential spectrum on three dimensional balls.