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We investigate plasmon-emitter interactions in a nanoparticle-on-a-mirrorcavity. We consider two different sorts of emitters, those that sustain dipolartransitions, and those hosting only quadrupolar, dipole-inactive, excitons. Bymeans of a fully analytical two-dimensional transformation optics approach, wecalculate the light-matter coupling strengths for the full plasmonic spectrumsupported by the nanocavity. We reveal the impact of finite-size effects in theexciton charge distribution and describe the population dynamics in aspontaneous emission configuration. Pushing our model beyond the quasi-staticapproximation, we extract the plasmonic dipole moments, which enables us tocalculate the far-field scattering spectrum of the hybrid plasmon-emittersystem. Our findings, tested against fully numerical simulations, reveal thesimilarities and differences between the strong coupling phenomenology forbright and dark excitons in nanocavities.

Dipolar and Quadrupolar Excitons Coupled to a Nanoparticle-on-a-Mirror Cavity