Analysis of plasmon resonance on smooth domains using spectral properties of the Neumann–Poincaré operator

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.

Spectral Properties of Neumann-Poincaré Operator and Anomalous Localized Resonance in Elasticity Beyond Quasi-Static Limit

“…Beyond the spherical geometry, it is rather unpractical to derive the required spectral results. In fact, even in the simplest electro-static case, only the radical geometry [3] and ellipse geometry [7] were considered. For more general geometries, one may resort to the assistance of numerical simulations; see [11] for the electro-static case.…”

Mathematical and numerical framework for metasurfaces using thin layers of periodically distributed plasmonic nanoparticles

“…Recently, there have been several interesting mathematical works on plasmonic resonances for nanoparticles [2][3][4][5][6][7][8][9]. On the other hand, scattering of waves by periodic structures plays a central role in optics [10].…”

Spectrum of the Neumann–Poincaré Operator for Ellipsoids and Tunability

“…The new inner product in two dimensions is defined in a similar but slightly different way (see, for example, [5]). If ∂Ω is C 1,α -smooth for some α > 0, then K * ∂Ω is a compact operator on H −1/2 (∂Ω).…”

“…Since S ∂Ω is a unitary operator from H −1/2 (∂Ω) onto H 1/2 (∂Ω), Plemelj's symmetrization principle (1.4) shows that K ∂Ω on H 1/2 (∂Ω) and K * ∂Ω on H −1/2 (∂Ω) have the same spectra (see [5]). We also emphasize that the NP operator in [12] is 2 times that of this paper.…”