Mie plasmons: modes volumes, quality factors and coupling strengths (Purcell factor) to a dipolar emitter

TL;DR

This paper analyzes localized surface plasmons in metallic nanoparticles using quasi-static and Mie theory, focusing on mode volumes, quality factors, and their impact on emitter coupling, with insights into losses and energy conservation.

Contribution

It introduces a method to estimate mode volumes and quality factors for Mie plasmons, linking these to emitter coupling strength via the Purcell factor.

Findings

Mode volumes and quality factors are characterized for Mie plasmons.

Coupling strength is proportional to the ratio Q/V, elucidating the Purcell effect.

Energy conservation and loss mechanisms are discussed in detail.

Abstract

Using either quasi-static approximation or exact Mie expansion, we characterize the localized surface plasmons supported by a metallic spherical nanoparticle. We estimate the quality factor $Q_n$ and define the effective volume $V_n$ of the $n^{th}$ mode in a such a way that coupling strength with a neighbouring dipolar emitter is proportional to the ratio $Q_n/V_n$ (Purcell factor). The role of Joule losses, far-field scattering and mode confinement in the coupling mechanism are introduced and discussed with simple physical understanding, with particular attention paid to energy conservation.