Describing the dispersion of plasmonic nanorod arrays via coupling of elementary excitations

Abstract

Metamaterials such as metal-dielectric multilayers and cylindrical nanowires are well known, for instance because of their hyperbolic dispersion. Here we examine in detail the mode characteristics in an array of square and rectangular metallic nanorods. In particular we propose a method to describe the dispersion via the coupling of specific elementary excitations. Apparently, these fundamental modes depend on the size and shape of the nanorods, and on the particular symmetry of the Bloch modes. Specifically, we show that arrays of relatively small square nanorods are associated with coupling of single rod modes. In contrast, large nanorod arrays correspond with a basic structure consisting of four metallic corners. In the medium size case, the nature of the elementary excitation depends on the frequency range and Bloch mode symmetry. Finally, we study rectangular nanorods, which turn out to derive from a basic geometry with two semi-infinite rods. The analysis method is thus useful for a better comprehension of many other types of metamaterials.