Parametric characterization of vortex higher-order cosine-hyperbolic-Gaussian beams in free space

Based on the Collins formula and the moment’s method, the analytical expressions for the beam field propagation through an ABCD system, the beam propagation factor (M 2 -factor) and the kurtosis factor of a vortex higher-order cosine-hyperbolic-Gaussian beam (vHOChGB) are derived. It is shown that the propagation characteristics are determined by the beam structure parameters, such as the decentered parameter b, the cosh order N and the topological charge m. The kurtosis parameter is dependent, besides the structure beam parameters, on the propagation distance. Numerical examples are presented to discuss the influence of the parameters b, N and m on the propagation characteristics of vHOChGB in free space. This research may be beneficial to the applications involving vortex beams in optical communications, beam splitting, and micromanipulation of particles.