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.
Multiple optical trapping with high-order axially symmetric polarized beams（ASPBs） is studied theoretically,and a scheme based on far-field optical trapping with ASPBs is first proposed.The focused fields and the corresponding gradient forces on Rayleigh dielectric particles are calculated for the scheme.The calculated results indicate that multiple ultra-small focused spots can be achieved,and multiple nanometer-sized particles with refractive index higher than the ambient can be trapped simultaneously near these focused spots,which are expected to enhance the capabilities of traditional optical trapping systems and provide a solution for massive multiple optical trapping of nanometer-sized particles.
Tight focusing of axially symmetric polarized vortex beams is studied numerically based on vector diffraction theory. The mathematical expressions for the focused fields are derived. Simulation results show that the focused fields and phase distributions at focus are largely influenced by both the polarization order and topological charge of the incident beams. Moreover, focal spots with flat-topped or tightly-focused patterns can be flexibly achieved by carefully choosing the polar- ization order and the topological charge, which confirms the potential of such beams in wide applications, such as optical tweezers, laser printing, lithography, and material processing.
A stimulated emission depletion （STED） microscopy scheme using axially symmetric polarized vortex beams is pro- posed based on unique focusing properties of such kinds of beams. The concept of axially symmetric polarized vortex beams is first introduced, and the basic principle about the scheme is described. Simulation results for several typical beams are then shown, including radially polarized vortex beams, azimuthally polarized vortex beams, and high-order axi- ally symmetric polarized vortex beams. The results indicate that sharper doughnut spots and thus higher resolutions can be achieved, showing more flexibility than previous schemes based on flexible modulation of both phase and polarization for incident beams.
