Retrieval of Polarizability Matrix for Metamaterials

Exact retrieval of polarizability matrix is of critical importance in designing metamaterials and frequency-selective surfaces. We evaluate practical methods for effectively extracting the polarizability matrix of dielectric and metallic metamaterials. We focus on three approaches: analytical solutions, induced or displacement current distributions, and reflection/transmission parameters. The analytical solutions are limited to particles of canonical shapes; even minor alterations in the structure results in a different analytical model. In case of arbitrary shapes, it is useful to adopt the approach based on the calculation of the induced or displacement current distributions of the excited particle in response to plane wave illumination. A more rigorous estimate of the polarizability matrix for irregular shapes is possible via measured or simulated reflection/transmission parameters. We provide new insights related to the empirical and theoretical analysis of these algorithms. In particular, we show that, wherever applicable, these methods retrieve all components of polarizability matrix identically.