  In nanophotonics, multipole framework has become an indispensable theoretical
tool for analyzing subwavelength meta-atoms and their radiation properties.
This work presents higher-order exact dynamic polarizability (alpha) tensors,
which can fully represent anisotropic meta-atoms with higher-order multipole
transitions. By using the irreducible exact Cartesian multipoles and field
components as the basis, the exact alpha-tensor rigorously reflects symmetry
information of particles including reciprocity. In addition, the exact
alpha-tensor can be obtained from T-matrix simply using basis transformation.
Finally, we show that description of meta-atoms using alpha-tensors
incorporated with multiple-scattering theory vastly extends the applicability
of the multipole framework in nanophotonics, allowing accurate and efficient
depiction of complicated, random, multi-scale systems.
