Exact Multipolar Decompositions with Applications in Nanophotonics

The multipolar decomposition of electromagnetic sources is an important tool for the study of light–matter interactions in general, and optical materials in particular. Here, a report is given on recent progress in the multipolar decomposition of electromagnetic sources. First, the exact and simple expressions for the multipolar moments of electric current density distributions are reviewed, and then, the results are extended to multipolar moments of magnetization current density distributions due to intrinsic spin. The consideration of both electric and magnetic sources allows to establish the conditions for sources of pure handedness. Scripts are provided that facilitate the computation of multipolar moments of arbitrary order. The work and the included examples of use are placed in the context of nanophotonics and metamaterials, and an outlook for applications in these and other fields is provided. The multipole expansion is a valuable source of information to study light–matter interactions. In this Progress Report the authors give an overview of the latest developments, review exact expressions that have been recently derived, and complete the framework with new results. Furthermore, they demonstrate the use of the exact multipolar decomposition expressions in selected examples of contemporary research interest in nanophotonics, and sketch some possibilities for applications in diverse fields.