Second harmonic generation in metamaterials based on homogeneous centrosymmetric nanowires

We present a comprehensive theoretical study of the second harmonic generation (SHG) in metamaterials consisting of arbitrary distributions of cylindrical nanowires made of centrosymmetric materials. The electromagnetic field at both the fundamental frequency (FF) and second harmonic (SH), as well as the total cross section, the absorption cross section, and the scattering cross section, are calculated by means of a numerical algorithm based on the multiple scattering method. Our algorithm fully describes the nonlinear optical response of the metamaterial by incorporating the contributions of both the surface and bulk nonlinear polarizations and can be applied to both s- and p-polarized incident waves. We use this numerical method to investigate the SHG in a series of particular cases of practical interest, namely, a single metallic cylinder, chains of metallic cylinders, and periodic and random distributions of such cylinders. In particular, we study the relation between the local field enhancement, via the excitation of surface plasmon-polariton modes, and the amount of energy absorbed or scattered in the far-field, at the FF and the SH.