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

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−1/2H−1/2 onto H1/2H1/2. 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, and cloaking due to anomalous localized resonance does occur on ellipses like on the core-shell structure considered in [19]. It is shown that cloaking due to anomalous localized resonance does not occur at the essential spectrum on three dimensional balls.