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We present analytical expressions for the resonance frequencies of theplasmonic modes hosted in a cylindrical nanoparticle within the quasistaticapproximation. Our theoretical model gives us access to both the longitudinallyand transversally polarized dipolar modes for a metallic cylinder with anarbitrary aspect ratio, which allows us to capture the physics of bothplasmonic nanodisks and nanowires. We also calculate quantum mechanicalcorrections to these resonance frequencies due to the spill-out effect, whichis of relevance for cylinders with nanometric dimensions. We go on to considerthe coupling of localized surface plasmons in a dimer of cylindricalnanoparticles, which leads to collective plasmonic excitations. We extend ourtheoretical formalism to construct an analytical model of the dimer, describingthe evolution with the inter-nanoparticle separation of the resultant brightand dark collective modes. We comment on the renormalization of the coupledmode frequencies due to the spill-out effect, and discuss some methods ofexperimental detection.

Plasmonic modes in cylindrical nanoparticles and dimers