Analytical properties of the plasmon decay profile in a periodic metal-nanoparticle chain

We show that the spatial decay of plasmons in a periodic metal-nanoparticle chain is composed of exponential and power-law decays. Our results show a high level of similarity between the absorptive and radiative decay channels. By analyzing the poles (and the corresponding residues) of the generating function for the lattice Green's function, we explain the details of the spatial decay profile. We also present an analytical formula for the decay profile.