Dispersion relations for plasmons in complex-shaped nanoparticle chains

A method for finding dispersion in chains of plasmonic particles of arbitrary shape is proposed. Our approach is based on analytic continuation via polylogarithms and is basically a generalization of the method known for spherical nanoparticle chains. As an example, we consider an axial chain of split-ring resonators. Three distinct solutions are distinguished, namely, two plasmons and a nonexponential wave. Dispersion relations, decay profiles, and spectra of excitation by a point source are obtained and compared with that in a spherical nanoparticle chain. The nuances of implementing the method are discussed.