The theoretical and experimental results of tightly focused radially polarized vortex beams are demonstrated. An auto-focus technology is introduced into the measurement system in order to enhance the measurement precision, and the radially polarized vortex beams are generated by a liquid-crystal polarization converter and a vortex phase plate. The focused fields of radially polarized vortex beams with different topological charges at numerical apertures （NAs） of 0.65 and 0.85 are measured respectively, and the results indicate that the total intensity distribution at focus is dependent not only on the NA of the focusing objective lens and polarization pattern of the beam but also on the topological charge l of the beam. Some unique focusing properties of radially polarized vortex beams with fractional topological charges are presented based on numerical calculations. The experimental verification paves the way for some practical applications of radially polarized vortex beams, such as in optical trapping, near-field microscopy, and material processing.
We numerically study the surface plasmon interference formed by tightly focused higher polarization order axially symmetric polarized beams （ASPBs） based on the vectorial diffraction theory. The definition of ASPBs is stated, and the optical setup for surface plasmon polariton （SPP） excitation and mathematical expressions for interfering SPP fields are proposed. The simulation results show that the interfering SPP fields present a multi-focal spot pattern. In addition, the number of spots is related to the polarization order of the incident beams P as 2×（P-1）, indicating potential utilization in near-field multiple optical trapping and near-field imaging and sensing. The unique interfering phenomenon is also explained.
