L. Stoyanov, A. Stefanov, A. Dreischuh, and G. G.
Paulus
Abstract.
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.