Surface plasmon resonances of an arbitrarily shaped nanoparticle: High frequency asymptotics via pseudo-differential operators

TL;DR

This paper analyzes surface plasmon resonances in arbitrarily shaped nanoparticles using pseudo-differential operators to derive high-frequency asymptotics, providing a mathematical framework for understanding these modes.

Contribution

It introduces a novel eigenvalue equation for surface plasmon modes using Dirichlet-Neumann operators and derives high-frequency asymptotics for arbitrary shapes.

Findings

Eigenvalue equation for plasmon modes derived

High-frequency asymptotic behavior characterized

Mathematical framework for arbitrary shapes established

Abstract

We study the surface plasmon modes of an arbitrarily shaped nanoparticle in the electrostatic limit. We first deduce an eigenvalue equation for these modes, expressed in terms of the Dirichlet-Neumann operators. We then use the properties of these pseudo-differential operators for deriving the limit of the high-order modes.