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

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. (review)