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Higher-order dynamic polarizability tensors are formulated using the irreducible Cartesian basis, which makes polarizability tensors and Green’s tensors to be symmetric. Basis transformation matrices are presented, which systematically transform Cartesian multipoles and local field quantities to spherical multipoles. These newly presented expressions allow systematic retrieval of higher-order dynamic polarizability tensors and formulation of coupled multipole method up to magnetic octupole. This multipole framework is (semi-)analytic and computationally efficient, allowing description of electromagnetically coupled meta-atoms. Meta-atoms in periodic or random lattices and those dispersed in three-dimensional random- and large-scale systems may be analyzed using this method.
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