Equivalence of Gouy and Courant-Snyder phase

TL;DR

This paper demonstrates that the Gouy phase for light beams and the Courant-Snyder phase for charged particle beams are mathematically equivalent, unifying their descriptions across optics and accelerator physics.

Contribution

It adapts Courant-Snyder theory to laser modes, revealing the equivalence of Gouy and Courant-Snyder phases and unifying mode conversion techniques.

Findings

Gouy and Courant-Snyder phases are mathematically equivalent.

Identical mode converters have been developed for light and charged particle beams.

The adaptation of accelerator optics theory to laser modes is demonstrated.

Abstract

The generation of electron vortex beams and the conversion of these beams into beams without angular momentum by means of astigmatic optical systems, or vice versa, has been pursued in the optical and the electron microscopy community, but also in the accelerator community in the past decades. Despite different conceptual approaches similar results have been achieved. By adapting the Courant-Snyder theory, which was originally developed for the description of optical properties of accelerators, to the description of laser modes it is shown, that identical mode converters have been developed for charged particle and for light beams, and that the Courant-Snyder phase and the Gouy phase are equivalent.