Purcell effect for high-Q plasmon lattice modes in the coupled dipole approximation

We present a semi-analytical treatment of the spontaneous emission enhancement for collective lattice resonances of a linear 1D array of metallic nanoparticles in order to improve the physical understanding of these resonances, previously explored numerically. The treatment is based on the coupled-dipole approximation and Green's function formalism. We calculate the Purcell factor of the surface lattice resonance for localized emitters as a function of emitter position and compare it to the resonant enhancement for a localized plasmonic resonance of an isolated single nanoparticle. We find that the Purcell factor for a single emitter (or an incoherent ensemble of emitters) near the nanoparticle is typically smaller for the surface lattice resonance, although it can be higher for emitters nearly halfway between the particles. Nevertheless, in agreement with previous models, the lattice resonances display stronger emission in certain regions as well as a much narrower range of emission angles, which can lead to improved collection efficiency. Finally, we show that the “slow-propagating” modes of square 2D lattices of nanoparticles are capable of significantly stronger Purcell-enhanced emission.