Polarizability Tensor Retrieval for Subwavelength Particles of Arbitrary Shape

We present a semianalytical method to determine the full polarizability tensor of subwavelength particles with arbitrary shape and composition. This method extracts both co-and cross-coupling terms of the polarizability tensor, retrieving the full 6 × 6 polarizability tensor with three measurements, by appropriately rotating the inclusions, when embedded in a planar periodic array, with respect to their principle axes. In order to validate this method, we present four examples, including a magnetodielectric sphere, a magnetodielectric spheroid, a conducting helix and pairs of split-ring resonators, and discuss the relation with fundamental constraints such as reciprocity and Onsager's relations. We also discuss how this retrieval method may be useful for the design and homogenization of periodic metamaterials and two-dimensional (2-D) metasurfaces formed by subwavelength inclusions.