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The propagation properties of a double-half inverse Gaussian hollow beam with vortex through free space

A double-half inverse Gaussian hollow beam with vortex (VDHIGHB) is introduced. As a generalization of the doublehalf inverse Gaussian hollow beam (DHIGHB), such novel beams can be easily realized in the laboratory using spiral phase plates or computer-generated holograms. Based on the Huygens-Fresnel integral and the complex Gaussian function expansion of hard aperture function, analytical formulae for the propagation of the VDHIGHBs through free space is derived theoretically. Their intensity distribution and phase distribution properties are numerically examined. It is found that such beams can exhibit the self-focusing properties with their energy being redistributed. Moreover, a comparative study between the VDHIGHB and DHIGHB demonstrates that the existence of the vortex can greatly affect the evolution behavior of the beams during the propagation in free space.