Surface Plasmon Resonance of Nanoparticles and Applications in Imaging

TL;DR

This paper develops a mathematical framework for localized surface plasmon resonance in nanoparticles, analyzing scattering and absorption enhancements, with numerical simulations for multiple particles to inform imaging applications.

Contribution

It introduces a new mathematical approach using layer potential techniques for analyzing plasmon resonance in nanoparticles, including multiple particle interactions.

Findings

Derived small-volume electromagnetic field expansions valid for various relaxation rates.

Analyzed scattering and absorption enhancements due to plasmon resonance.

Provided numerical simulations illustrating resonance behavior in multi-particle systems.

Abstract

In this paper we provide a mathematical framework for localized plasmon resonance of nanoparticles. Using layer potential techniques associated with the full Maxwell equations, we derive small-volume expansions for the electromagnetic fields, which are uniformly valid with respect to the nanoparticle's bulk electron relaxation rate. Then, we discuss the scattering and absorption enhancements by plasmon resonant nanoparticles. We study both the cases of a single and multiple nanoparticles. We present numerical simulations of the localized surface plasmonic resonances associated to multiple particles in terms of their separation distance.