Propagation properties of vortex Hermite cosine-hyperbolic-Gaussian beams in uniaxial crystals orthogonal to the optical axis

The evolution properties of a vortex Hermite cosine-hyperbolic-Gaussian beam (vHChGB) in uniaxial crystals are investigated. Based on the Huygens–Fresnel diffraction integral, the propagation equation for a vHChGB passing through a uniaxial crystal orthogonal to the optical axis is derived in detail. The propagation features of the intensity and phase distributions of the beam in the uniaxial crystal are analyzed with numerical illustrative examples. It is demonstrated that upon propagation, the anisotropy of the uniaxial crystal influences strongly the beam properties. The output beam is astigmatic, and its intensity and phase distributions are strongly related to the ratio of refractive indices of the crystal and the initial beam structure parameters. This study may provide a convenient way to generate astigmatic vortex hollow beams.