Characterization of vortex Hermite cosine-hyperbolic-Gaussian beams based on the beam propagation factor

In this paper, the beam propagation factor (M²-factor) of the so-called vortex Hermite-cosh-Gaussian beams (vHChGB) is investigated by using the second-order intensity moments. The analytical expression of the M²-factor of the vHChGB is derived in detail, and several numerical illustrative examples are given to discuss the influence of the field structure parameters, such as the beam order n, the decentered b, and the topological charge index m, on the M²-factor. The results obtained represent a more general analysis because the considered beam has a variable shape, and it can be reduced under appropriate conditions to well-known vortex beams, such as hollow vortex-Gaussian beams, cosh vortex-Gaussian beams, and vortex Hermite beams. Our work will be useful for practical applications of vortex beams in free-space optical communications, atomic optics, and microparticle manipulation.