Electromagnetic sources beyond common multipoles

TL;DR

This paper explores the full spectrum of electromagnetic multipole sources, emphasizing the significance of mean-square radii and their role in non-radiating sources, expanding the understanding beyond conventional multipole terms.

Contribution

It introduces a comprehensive geometrical framework for visualizing mean-square radii and highlights their importance in electromagnetic source expansions beyond traditional multipoles.

Findings

Mean-square radii are crucial in electromagnetic multipole expansions.

A new geometrical visualization method for mean-square radii is proposed.

Mean-square radii contribute to non-radiating electromagnetic sources.

Abstract

The complete dynamic multipole expansion of electromagnetic sources contains more types of multipole terms than it is conventionally perceived. The toroidal multipoles are one of the examples of such contributions that have been widely studied in recent years. Here we inspect more closely the other type of commonly overlooked terms known as the mean-square radii. In particular, we discuss both quantitative and qualitative aspects of the mean-square radii and provide a general geometrical framework for their visualization. We also consider the role of the mean-square radii in expanding the family of non-trivial non-radiating electromagnetic sources.