Quantum ergodicity and localization of plasmon resonances

TL;DR

This paper investigates how surface plasmon resonances (SPR) tend to localize at high-curvature regions on interfaces, using quantum ergodicity and spectral theory to analyze their geometric and spectral properties.

Contribution

It introduces a novel analysis of SPR localization based on quantum ergodicity and spectral properties of the Neumann-Poincaré operator, extending previous theoretical frameworks.

Findings

SPR oscillations localize at high-curvature points

The work leverages quantum ergodicity principles for SPR analysis

Spectral properties of the Neumann-Poincaré operator are key to understanding SPR localization

Abstract

We are concerned with the geometric properties of the surface plasmon resonance (SPR). SPR is a non-radiative electromagnetic surface wave that propagates in a direction parallel to the negative permittivity/dielectric material interface. It is known that the SPR oscillation is very sensitive to the material interface. However, we show that the SPR oscillation asymptotically localizes at places with high magnitude of curvature in a certain sense. Our work leverages the Heisenberg picture of quantization and quantum ergodicity first derived by Shnirelman, Zelditch, Colin de Verdi\`ere and Helffer-Martinez-Robert, as well as certain novel and more general ergodic properties of the Neumann-Poincar\'e operator to analyze the SPR field, which are of independent interest to the spectral theory and the potential theory.