Introduction of the vortex Hermite-Cosh-Gaussian beam and the analysis of its intensity pattern upon propagation

In this paper, a vortex-Hermite-cosh-Gaussian beam (vHChGB) is introduced as a general form of the vortex cosh-Gaussian and vortex Hermite-Gaussian beams. Based on the Huygens-Fresnel diffraction integral, a propagation formula of the vHChGB passing through a paraxial optical system is derived. The evolution of the intensity pattern of the propagated vHChGB as a function of the beam order, decentered parameter (b parameter) and topological vortex charge is discussed with numerical results. It is shown that the vHChGB shape in the source plane depends crucially on the decentered parameter. In far-field, the multi-lobe profile obtained for small b evolves into a four-petal-like beam. Whereas the initial four-lobe profile for large b, morphs into a multi-lobes pattern. The vHChGB shows specific intensity patterns depending on the beam order and the vortex charge. This study may be beneficial for applications involving beam shaping of hollow vortex beam, beam splitting techniques and optical communications.