Using the first-principles layer-multiple-scattering method we developed in previous work, we analyze recent experimental data on the extinction of light by rectangular two-dimensional arrays of gold nanoparticles on a dielectric waveguide. The theoretical results reproduce accurately the measured spectra and provide a transparent physical picture of the underlying processes.

We develop a Green’s function multiple-scattering formalism for the calculation of the density of states and the local density of states of the elastic field in periodic and nonperiodic structures consisting of nonoverlapping scatterers in a homogeneous host medium. The formalism is based on concepts and techniques developed in relation to the similar problem of electrons in solids. We apply the method to a specific example which demonstrates the existence of virtual bound states of the elastic field localized about a plane of nonoverlapping steel spheres in polyester. These states are manifested as dips in the transmission spectrum of the monolayer. They develop into narrow frequency bands in a phononic crystal built by a succession of such planes.