Analysis of plasmon resonance on smooth domains using spectral properties of the Neumann-Poincaré operators

Abstract

We investigate in a quantitative way the plasmon resonance at eigenvalues and the essential spectrum (the accumulation point of eigenvalues) of the Neumann-Poincaré 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.

18 pages

References in corpus (1)

• Spectral bounds for the Neumann-Poincaré operator on planar domains with corners

Cited by in corpus (2)

• Plasmon resonance with finite frequencies: a validation of the quasi-static approximation for diametrically small inclusions
• Mathematical analysis of plasmonic nanoparticles: the scalar case