Effective Medium Response of Metallic Nanowire Arrays with a Kerr-type Dielectric Host

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.