Cylindrical vector beams: from mathematical concepts to applications

An overview of the recent developments in the field of cylindrical vector beams is provided. As one class of spatially variant polarization, cylindrical vector beams are the axially symmetric beam solution to the full vector electromagnetic wave equation. These beams can be generated via different active and passive methods. Techniques for manipulating these beams while maintaining the polarization symmetry have also been developed. Their special polarization symmetry gives rise to unique high-numerical-aperture focusing properties that find important applications in nanoscale optical imaging and manipulation. The prospects for cylindrical vector beams and their applications in other fields are also briefly discussed.