Relations between co- and cross-polarizabilites of electrically small scatterers demonstrated from a multipole expansion of the electromotive force

Prof. Juan Domingo Baena Doello (Universidad Nacional de Colombia) 

'Relations between co- and cross-polarizabilites of electrically small scatterers demonstrated from a multipole expansion of the electromotive force'

Abstract: For bianisotropic electrically small scatterers, some symmetry and reciprocity properties use to be held. For instance, it is usually true that the product of co-polarizabilities equals the product of cross-polarizabilities (α_ee * α_mm = α_me * α_em). However, it is well known that it is possible to find cases that violate it. Still, it is not understood in depth why it happens. In this talk, we demonstrate the origin of the bianisotropy of a general scatterer by using a multiple expansion of the electromotive force of an equivalent circuit equation. The equivalent circuit comes from the complex Poynting’s theorem and have meaning for any general shape of the scatterer. We will show some dyadic expresions for the polarizability tensors. Finally, we analyze why such properties are valid sometimes but not always.