Analysis of the relationship between numerical and analytical approaches for the complex point source expansion of electromagnetic fields

Complex point source beam expansions are a useful means for the efficient analysis of electromagnetic interactions. In this work, different expansion algorithms proposed in the literature are considered for the case of a spherical expansion surface and their characteristics in terms of compactness of the resulting expansion and computational burden of coefficient calculation are discussed. Then, a strict connection between the analytic expansion based on the spherical wave expansion of the field and the numerical approach based on field matching is revealed.