Simple Composite Dipole Model for the Optical Modes of Strongly-Coupled Plasmonic Nanoparticle Aggregates

Self-assembled strongly coupled plasmonic aggregates exhibit optical spectra which show complex plasmonic resonances. To understand the optics of such systems, we introduce an effective composite dipole model extending previous effective models of aggregates into the plasmonic domain. The ingredients in this model are found by comparing the time-resolved extinction of self-assembling growing aggregates of gold nanoparticles spaced by rigid sub-nm gaps to recent rigorous electromagnetic simulations of this geometry. The highly reproducible spectral signatures from experiments match our simulations, confirming that the electromagnetic response of such fractal plasmonic clusters can be well-understood in terms of embedded straight chains of plasmonically coupled nanoparticles surrounded by an optically decoupled halo of dimers. We show how to derive simple analytical formulas that lead to rapid extraction of key parameters from such experimental spectra and which properly account for the long-wavelength lineshapes. In particular, we find these effective parameters describe the extent of plasmon delocalization along such chains, the eccentricity of these optically dominant cores, and the fraction of nanoparticles active within them. This underpins applications which depend on spectral selectivity and field enhancements in such tightly coupled plasmonic systems.