and can be written in terms of extinction contributions from each nanoparticle σ i . Note that though σ i is assigned to nanoparticle i, it is a collective quantity that is a function of the positions of all other nanoparticles. Both σ(ω) and σ i (ω) are spectra, and we define an ensemble resonance frequency ω res and individual particle resonance frequencies ω res,i as the frequency of maximum extinction cross-section ω res = arg max σ(ω), ω res,i = arg max σ i (ω)