been efficiently analyzed using the multipole decomposition technique [@Muhlig2011; @Grahn2012], because a few low-order multipole moments efficiently reconstruct the electromagnetic radiation and the relevant physics from a subwavelength localized current-charge source. Due to this feature, the multipole approach has become an useful and indispensable tool for nanophotonics [@Liu2017]. Manipulation of light in the nanoscale has been facilitated by interference of multipole radiations, which provides the underlying principles behind many optical phenomena and relevant applications. Notably, the multipole approach has given insights on directional scattering [@Liu2018], lattice Kerker effects [@Babicheva2017], non-radiating anapoles [@Gurvitz2019; @Baryshnikova2019], lattice invisiblity effects [@Terekhov2019], Fano-like resonances [@Gallinet2011a; @Suryadharma2019], optical anti-ferromagnetism [@Liu2017], optical nonlinearity [@Smirnova2016], radiative heat transfer, weak localization [@Mishchenko2008], photonic topological insulators [@Pocock2018], and bound states in the continuum [@Sadrieva2019].

Formulation of multipole radiation is a textbook problem [@Jackson1999], but given the importance of the multipole approach, expressions for multipoles are still under research [@Alaee2018; @Fruhnert2017; @Grahn2012] with possibility on toroidal multipoles as an extra multipole family [@Savinov2019; @Gurvitz2019]. In general, the multipoles under discussion are excited at a specific illumination, but they do not provide complete information of highly anisotropic meta-atoms. On the other hand, dynamic polarizability $\boldsymbol{\alpha}$ tensor (or transition $\mathbf{T}$ matrix) maps the 