The role of angular momentum in the construction of electromagnetic multipolar fields

TL;DR

This paper clarifies the connection between different derivations of electromagnetic multipolar fields and their relation to angular momentum operators, enhancing understanding of their fundamental properties and applications.

Contribution

It explicitly demonstrates the relation between two common derivations of multipolar solutions and their connection to angular momentum operators.

Findings

Clarifies the relation between derivations of multipolar solutions

Shows the explicit connection to angular momentum operators

Facilitates comparison of different solution expressions

Abstract

Multipolar solutions of Maxwell's equations are used in many practical applications and are essential for the understanding of light-matter interactions at the fundamental level. Unlike the set of plane wave solutions of electromagnetic fields, the multipolar solutions do not share a standard derivation or notation. As a result, expressions originating from different derivations can be difficult to compare. Some of the derivations of the multipolar solutions do not explicitly show their relation to the angular momentum operators, thus hiding important properties of these solutions. In this article, the relation between two of the most common derivations of this set of solutions is explicitly shown and their relation to the angular momentum operators is exposed.