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Polarizability Tensor Calculation: Induced Local Charge and Current Distributions

We develop a semi-analytical approach to calculate the polarizability tensors of an arbitrary individual scatterer. The approach is based on the calculation of induced electric and/or magnetic dipole moments on the scatterer. By taking the advantages of the present approach, we calculate the individual polarizability tensors of an isolated scatterer in a homogeneous isotropic medium. Moreover, we obtain the polarizability tensors of scatterers located between two different isotropic media. Furthermore, due to the nature of the proposed method, we may determine the effective polarizability of a scatterer in a periodic array. To this end and for comparison reasons, we investigate two other methods for calculating effective polarizability tensors of scatterers in a two-dimensional periodic array. The proposed approach, in comparison to other reported approaches, is simpler, easily implemented, and does not require spherical harmonic expansion or complicated far-field calculations. We examine the validity of the proposed approach using several examples and compare the results with other approaches.