  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.
