Mathematical analysis of plasmon resonances for curved nanorods

TL;DR

This paper provides a rigorous mathematical analysis of plasmon resonances in curved anisotropic nanorods, deriving sharp asymptotic formulas and resonance conditions that relate geometry, material parameters, and wave frequency.

Contribution

It is the first theoretical study analyzing plasmon resonances in anisotropic nanostructures using spectral and asymptotic analysis of layer potential operators.

Findings

Resonance conditions depend on geometry, material parameters, and frequency.

Different parts of the nanorod induce varying resonance strengths.

Resonance at the nanorod ends is more pronounced than at the facade.

Abstract

We investigate plasmon resonances for curved nanorods which present anisotropic geometries. We analyze quantitative properties of the plasmon resonance and its relationship to the metamaterial configurations and the anisotropic geometries of the nanorods. Based on delicate and subtle asymptotic and spectral analysis of the layer potential operators, particularly the Neumann-Poincar\'e operators, associated with anisotropic geometries, we derive sharp asymptotic formulae of the corresponding scattering field in the quasi-static regime. By carefully analyzing the asymptotic formulae, we establish sharp conditions that can ensure the occurrence of the plasmonic resonance. The resonance conditions couple the metamaterial parameters, the wave frequency and the nanorod geometry in an intricate but elegant manner. We provide thorough resonance analysis by studying the wave fields both inside and outside the nanorod. Furthermore, our quantitative analysis indicates that different parts of the nanorod induce varying degrees of resonance. Specifically, the resonant strength at the two end-parts of the curved nanorod is more outstanding than that of the facade-part of the nanorod. This paper presents the first theoretical study on plasmon resonances for nanostructures within anisotropic geometries.