Focusing of linearly polarized helico-conical Lorentz beam with sine-azimuthal variation wavefront

In this article a theoretical research is described into focusing of a linearly polarized helico-conical Lorentz beam with a sine-azimuthal variation wavefront. The simulation results show the vortex charge on the axis, which has an obvious modulation effect on the focal modes of the Lorenz beam under certain beam parameters and phase parameters. Both the phase parameter and the vortex charge are zero, the focal spot appears round. The focal spot is symmetric about y axis when the charge is 0 and the phase parameter is adjusted. And the focal evolution patterns vary remarkably under different beam parameters and the phase parameters. In the process of focus evolution, there appears some novel focal patterns, such as a circle, a “T”, a butterfly, a small running humanoid, a whale tail, a flower of four leaves, a serpentine, a goldfish, a Chinese knot and an octopus, which indicates that the focus mode of the optical vortex Lorentz beam can be altered by changing the phase parameters and vortex charge