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In this review article we compare two different mathematical descriptions of electromagnetic radiation. Namely one describing the fields in terms of plane-waves, and the other using spherical-waves. We analyse the different approaches in terms of the multipole expansion, and weigh-up advantages and disadvantages of the two approaches. The focus is within the context of a non-relativistic quantum electrodynamical formulation, and we consider processes related to light-matter interactions, such as electronic energy transfer. We also include an analysis of symmetry and group theoretical considerations. Significant numerical details are provided in the appendices that may be useful to readers who want to apply the theory to applications.

The plane- and spherical-wave descriptions of electromagnetic radiation: a comparison and discussion of their relative merits