Extraordinary refractive properties of photonic crystals of metallic nanorods

Abstract

By applying a homogenization method based on systematic full-electrodynamic complex-band-structure calculations, we deduce the effective permittivity tensor of a uniaxial photonic crystal consisting of consecutive hexagonal arrays of aligned metallic nanorods of finite length. The form of the obtained permittivity tensor over a relatively broad low-frequency region, where homogenization is applicable, suggests the occurrence of unconventional refractive behavior, namely, negative refraction and self-collimation. This behavior is corroborated by straightforward calculation of the relevant group velocities in the actual photonic crystal. Moreover, it is shown that, in the frequency region where negative refraction occurs, a finite slab of the crystal possesses eigenmodes that form flat bands outside the light cone, as many as the number of its constituent layers. These eigenmodes allow for transfer of the evanescent components of an incident wave field to the other side of the slab, thus enabling subwavelength imaging.