Describing Meta-Atoms Using the Exact Higher-Order Polarizability Tensors

Abstract

In nanophotonics, multipole approach has become an indispensable theoretical framework for analyzing subwavelength meta-atoms and their radiation properties. Thus far, induced multipole moments have frequently used to illustrate the radiating properties of the meta-atoms, but they are excited at a specific illumination and do not fully represent anisotropic meta-atoms. On the other hand, dynamic polarizability (α) tensors contain complete scattering information of the metaatoms, but have not often been considered due to complicated retrieval procedures. In this study, we suggest that exact higher-order α-tensor can be efficiently obtained from T-matrix using simple basis transformation. These higher-order α-tensors are necessary to describe recently reported coupled plasmonic and high-refractive-index particles, which we demonstrate from their retrieved α-tensors. Finally, we show that description of meta-atoms using α-tensors incorporated with multiple-scattering theory vastly extends the applicability of the multipole approach in nanophotonics, allowing accurate and efficient depiction of complicated, random, multi-scale systems. Usage: Preprint.

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“…Due to the equivalence of Cartesian and spherical coordinates representations [54], polarizability and T matrices are interchangeable in the sense that they contain the same information. This equivalence has been explicitly documented up to quadrupolar order [55], and, more recently, up to octupolar order [56].…”

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