Tight focusing properties of linearly polarized Gaussian beam with a pair of vortices

The properties of a pair of vortices embedded in a Gaussian beam focused by a high numerical-aperture are studied on the basis of vector Debye integral. The vortices move and rotate in the vicinity of the focal plane for a pair of vortices with equal topological charges. For incident beam with a pair of vortices with opposite topological charges, the vortices move toward each other, annihilate and revive in the vicinity of focal plane.

► The properties of a pair of vortices focused by a high numerical-aperture are studied.
► It is shown that the focusing vortices with equal topological charges move toward and rotate.
► It is shown that the focusing vortices with opposite topological charges move toward each other, annihilate and revive.