Plasmon resonance with finite frequencies: a validation of the quasi-static approximation for diametrically small inclusions

Abstract

We study resonance for the Helmholz equation with a finite frequency in a plasmonic material of negative dielectric constant in two and three dimensions. We show that the quasi-static approximation is valid for diametrically small inclusions. In fact, we quantitatively prove that if the diameter of a inclusion is small compared to the loss parameter, then resonance occurs exactly at eigenvalues of the Neumann-Poincaré operator associated with the inclusion.

arXiv comment15 pages

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• On Absence and Existence of the Anomalous Localized Resonance without the Quasi-static Approximation
• Mathematical analysis of plasmonic nanoparticles: the scalar case