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Describing meta-atoms using the exact higher-order polarizability tensors

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.