A class of rigorous formulas for the efficient extraction of the full polarizability matrix of electrically small particles is introduced in this paper. After the dipole approximation of the scatterer, under study, the latter is placed on a two-dimensional square array, illuminated by four normally incident plane waves, and eventually its polarizabilities are expressed in terms of induced dipole moments. Then, by applying an equivalent surface model for the array, the induced dipoles are calculated as a function of the reflection/transmission coefficients from the array. Lastly, the combination of the previous formulations leads to the final expressions for the polarizability matrix of the particle. In order to verify the featured methodology, the extracted polarizabilities are involved in radar cross section and total radiated power calculations for various incidences and are compared with their simulated counterparts.
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