Abstract
We present analytical expressions for the resonance frequencies of the plasmonic modes hosted in a cylindrical nanoparticle within the quasi-static approximation. Our theoretical model gives us access to both the longitudinally and transversally polarized dipolar modes for a metallic cylinder with an arbitrary aspect ratio, which allows us to capture the physics of both plasmonic nanodisks and nanowires. We also calculate quantum mechanical corrections to these resonance frequencies due to the spill-out effect, which is of relevance for cylinders with nanometric dimensions. We go on to consider the coupling of localized surface plasmons in a dimer of cylindrical nanoparticles, which leads to collective plasmonic excitations. We extend our theoretical formalism to construct an analytical model of the dimer, describing the evolution with the inter-nanoparticle separation of the resultant bright and dark collective modes. We comment on the renormalization of the coupled mode frequencies due to the spill-out effect, and discuss some methods of experimental detection.
Highlights
The optical properties of small metal clusters have been studied throughout the twentieth century [1], in a field which is referred to as plasmonics [2]
We present analytical expressions for the resonance frequencies of the plasmonic modes hosted in a cylindrical nanoparticle within the quasi-static approximation
We go on to consider the coupling of localized surface plasmons in a dimer of cylindrical nanoparticles, which leads to collective plasmonic excitations
Summary
The optical properties of small metal clusters have been studied throughout the twentieth century [1], in a field which is referred to as plasmonics [2]. The inevitable quantum corrections which arise at the nanoscale are addressed by accounting for the so-called spill-out effect [32] In this quantum size effect, the resonance frequency is modified due to a proportion of electrons spilling outside of the small metallic. In order to account analytically for such collective plasmonic effects, we adapt our aforementioned theory to the case of a dimer of cylindrical metallic NPs. We derive simple expressions for the bright and dark mode resonance frequencies of the system as a function of the interparticle separation, which allows for a clear description of how the plasmonic coupling scales with distance.
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