Polarizability calculation of arbitrary individual scatterers, scatterers in arrays, and substrated scatterers

We develop a semi-analytical approach for calculation of polarizability tensors of individual scatterers, scatterers in arrays, and substrated scatterers. The approach is based on the integration from induced charges and currents on the scatterer. By taking advantage of the present approach we calculate the individual polarizability tensors of isolated scatterers in a homogeneous isotropic medium. Moreover, we present the procedure of obtaining the polarizability tensors of substrated scatterers: scatterers located between two different isotropic media. Furthermore, using the proposed method we determine the surface susceptibility tensors of scatterers in a periodic metasurface. To compare and verify the results of arrays, we also investigate two other methods for calculating surface susceptibilities of scatterers in arrays. We examine the validity of the proposed approach using some examples and compare the results with other approaches. The proposed approach, in comparison to other reported approaches, is simpler, easily implemented, and does not require spherical harmonics expansion or complicated far-field calculations. (C) 2016 Optical Society of America