Tight focusing of double-ring-shaped radially polarized vortex beam through dielectric interface

Based on the vectorial Debye theory, the tight focusing of double-ring-shaped radially polarized vortex beams (DRS-RPVBs) through a dielectric interface is investigated. The investigation illustrates that when the interception ratio of the aperture radius to the incident beam waist radius is proper, a tiny bottle beam can be obtained in the focal region. The size of the bottle beam is dependent on the numerical aperture of the objective and the refractive index of the medium in the focal region. In addition, the influence of the numerical aperture, interception ratio and probe depth on the focal shift is investigated. And the calculation for the real focus location indicates that, for a proper interception ratio, there exists a jump in the location.