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

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