Collective plasmonic modes in two-dimensional periodic arrays of metal nanoparticles

We investigate the collective plasmonic modes of metal nanoparticles in periodic two-dimensional (2D) arrays within a point-dipole description. The dynamic dispersion relations of the 2D arrays are obtained through a method which gives an effective polarizability describing the collective response of a system. Both the dispersion relations and mode qualities are simultaneously related to the imaginary part of the effective polarizability, which has contributions from the single-particle response as well as the interparticle coupling. The transverse long-range dipolar interaction is dominated by a wave term together with a purely geometrical constant representing the static geometrical contribution to resonant frequencies. As concrete examples, we considered small Ag spheres arranged in a square lattice. We find that inside the light cone, the transverse quasimode has a reasonably high mode quality, while the two in-plane modes show significant radiation damping. Near the light line, we observe strong coupling with free photons for the bands of the transverse mode and the transverse in-plane mode, and the longitudinal in-plane mode exhibits a negative group velocity inside the light cone. Vanishing group velocities in the light cone for all the quasimodes are found to be intrinsic properties of the 2D metal nanosphere dense arrays.