Spherical-wave and plane-wave propagators

This paper explores the equivalence between spherical-wave and plane-wave propagators. Spherical-wave propagators are intimately part of diffraction and boundary scattering theory. They consequently are used almost exclusively in introductory presentations of electromagnetic theory. However, equivalent representations can be constructed from superpositions of propagating plane waves. This leads to two different approaches to diffraction theory. Spherical-wave computations are initiated by induced point sources. Plane-wave computations are initiated by an equivalent-aperture plane field. Subsequent propagation can be computed with Fourier transformations. Sampling requirements ultimately limit the utility of Fourier-domain computations. Examples are presented.