Gouy phase of Bessel-Gaussian beams: theory vs. experiment.

It is well-known that the wave of a freely propagating Gaussian beam experiences an additional π phase shift compared to a plane wave. This phase shift, known as the Gouy phase, has significant consequences in, e.g., nonlinear optics, since the nonlinear processes require high peak intensity and phase matching of the focused beams. Hence, determining and controlling the Gouy phase is crucial in many fields of modern optics and photonics. Here, we develop an analytical model for the Gouy phase of long-range Bessel-Gaussian beams obtained by annihilating highly charged optical vortices. The model accounts for the influence of the relevant experimental parameters (topological charge, radius-to-width ratio of the initial ring-shaped beam, and focal length of the Fourier-transforming lens). We find an evolution of the Gouy phase varying nearly linearly with propagation distance and confirm this result experimentally.