Isolating the Gouy phase shift in a full physical-optics solution to the propagation problem

Abstract

The Gouy phase shift has remained an object of fascination since its discovery by the eponymous scientist at the end of the nineteenth century. The reason behind this uninterrupted interest resides, at least in part, in the fact that the Gouy effect is to be found in the borderland between geometrical optics and diffractive behavior. Using purely mathematical arguments in a full electromagnetic solution to the propagation problem, it is possible to derive a formula where all the physical effects that we know must appear are laid bare, including the Gouy phase. Additionally, by discarding the field information, this formula retrieves the ray-tracing result, and in doing so vindicates the predictions that geometrical optics can make, of the ray mapping and optical path length accretion. The resulting analysis helps overcome the geometrical-physical optics dichotomy in our understanding of the Gouy phenomenon.