Propagation of a pair of vortices through a tilted lens

The propagation of a pair of vortices nested in a Gaussian beam through a tilted lens is studied. It is shown that after passing through the tilted lens, the relation between the transverse position of vortices and the tilt coefficient is linear in the propagation for isopolar vortex pair and vortex dipole, and in the three-dimensional (3D) case the vortex trajectories are sometimes like U or X shapes. With increasing the orientation angle of the vortex pair, the trajectories of vortices are circles for the both cases. The overlap of vortices may take place for the isopolar vortex pair, while the annihilation and revival of vortices occur for the vortex dipole in the propagation.