Tight focusing of radially polarized beams by a devil’s vortex lens

Tight focusing of radially polarized beams with a devil’s vortex lens is numerically investigated. Multiple focal spots can be generated in the geometric focus when a radially polarized beam is focused by a high numerical aperture objective in the presence of a devil’s vortex lens. The position of the major focal spot shifts from the geometric focus when a devil’s vortex lens with S = 1 is employed, and the position of the focal spot can be controlled by the numerical aperture of the objective. The intensity components of the major focal spot are influenced by the vortex phase of the devil’s vortex lens. A strong longitudinal component near the optical axis is produced by a devil’s vortex lens without vortex phase, and a nearly pure transversal field is produced by a devil’s vortex lens with vortex phase.