Optical gradient force of linearly polarized sine-azimuthal Lorentz beam with one on-axis optical vortex

Optical gradient force of linearly polarized sine-azimuthal Lorentz beam with one on-axis optical vortex was investigated theoretically in this article, and calculation results show that the effect of charge number of optical vortex on optical gradient force pattern is very considerable, and force evolution principle differs for different beam parameter and phase parameter that indicates the sine phase change frequency on increasing azimuthal angle. Some novel gradient force patterns appear, such as, force rings, swallow shape, force ripples, multiple force lines. In addition, the whole force pattern is symmetric about one axis when phase parameter is odd number, while, whole force pattern is symmetric about two orthogonal axes under condition that phase parameter is even number. Introduction of charge number adds one freedom for controlling optical gradient force distribution.