Nonlocal effective medium approximation for metallic nanorod metamaterials

We present an analytical nonlocal effective medium approximation to describe the optical nonlocal effects in metallic nanorod metamaterials based on Mie scattering theory. It is shown that the developed nonlocal effective medium theory can predict a coexistence state of two modes around the epsilon-near-zero region, where strong optical nonlocal effects lead to the behavior of both positive refraction and negative refraction in the nanorod metamaterials. Outside of the coexistence region, only one mode can be excited and its behavior can be well described using the local effective medium theory.