  We derive an effective medium model to characterize the macroscopic
electromagnetic response of metallic nanowire arrays embedded in a host
dielectric with a Kerr-type nonlinear permittivity function. It is shown that
the macroscopic electromagnetic fields are coupled to the conduction current in
the nanowires and to an additional quasi-static potential through a system of
nonlinear equations. We prove that a weak nonlinearity leads to an
electromagnetic response closer to that of an indefinite medium, and to
isofrequency contours with increased hyperbolicity. For high-field intensities
the negative refraction of electromagnetic waves at an air nanowire material
interface is enhanced when the nanowires are embedded in a self-focusing Kerr
medium.
