Determining polarizability tensors for an arbitrary small electromagnetic scatterer

In order to design metamaterials, one needs to investigate electromagnetic properties of each single meta-atom forming these structures. There have been proposed several techniques of extracting electromagnetic properties (such as polarizability) of a single meta-atom. All of them are based on numerical calculations of scattered fields from the inclusion. The main disadvantage of the previous techniques is quite complicated procedures of extracting the polarizabilities that implies determination of scattered fields at a large number of points around the inclusion. We have developed a method to retrieve the polarizabilities for an arbitrary-shaped meta-atom. In order to find one polarizability component, our technique needs information of scattered fields only at two points. Utilizing this simple method, we have succeeded in precise tuning of the properties of meta-atoms which ensure the desired electromagnetic response for composite metamaterials.