Mathematical analysis of plasmonic resonances for nanoparticles: the full Maxwell equations

TL;DR

This paper provides a rigorous mathematical analysis of plasmonic resonances in nanoparticles using full Maxwell equations, exploring how size, shape, and arrangement affect resonance behavior and establishing conditions for effective medium approximations.

Contribution

It introduces a precise mathematical framework for analyzing plasmonic resonances and derives conditions for the validity of Maxwell-Garnett theory at resonance frequencies.

Findings

Resonance shifts and broadening depend on nanoparticle properties.

Layer potential techniques effectively analyze plasmonic phenomena.

Conditions for Maxwell-Garnett theory validity at resonances are established.

Abstract

In this paper we use the full Maxwell equations for light propagation in order to analyze plasmonic resonances for nanoparticles. We mathematically define the notion of plasmonic resonance and analyze its shift and broadening with respect to changes in size, shape, and arrangement of the nanoparticles, using the layer potential techniques associated with the full Maxwell equations. We present an effective medium theory for resonant plasmonic systems and derive a condition on the volume fraction under which the Maxwell-Garnett theory is valid at plasmonic resonances.