Mie Plasmons: Modes Volumes, Quality Factors, and Coupling Strengths (Purcell Factor) to a Dipolar Emitter

Abstract

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