Generalized Brewster effect in high-refractive-index nanorod-based metasurfaces

The interference between electric and magnetic dipolar fields is known to lead to asymmetric angular distributions of the scattered intensity from small high refractive index (HRI) particles. Properly designed all-dielectric metasurfaces based on HRI spheres have been shown to exhibit zero reflectivity, a generalized Brewster's effect, potentially for any angle, wavelength and polarization of choice. At normal incidence, the effect is related to the absence of backscattering from small dielectric spheres or disks at the, so-called, first Kerker condition. In contrast, homogeneous HRI cylinders do not fulfil the first Kerker condition due to the mismatch between the local electric and magnetic density of states. In this work, we show that although a zero back-scattering condition can never be achieved for individual cylinders, when they are arranged in a periodic array their mutual interaction leads to an anomalous Kerker condition, leading to a generalized Brewster's effect in a nanorod-based metasurface. We derive a coupled electric and magnetic dipole (CEMD) analytical formulation to describe the properties of a periodic array of HRI nanorods in full agreement with exact numerical calculations.