Modified multipoles in metamaterials

Multipole decomposition method is a promising tool for investigation of radiating or scattering response of electromagnetic sources or particles. It works even in the case of relatively complicated and compound scatterers like multilayer particles, clusters, asymmetrical systems, and metamaterials [1]. Commonly, the radiation fields of point electric or magnetic sources are decomposed only into electric or magnetic dipole moments, while real sources can be described by series of multipoles, including higher multipoles and toroidal moments. For instance, toroidal or anapole metamaterials cannot be correctly described without taking into consideration toroidal multipoles [2].