Physical foundations of vector beams and applications in micro-nano optics: A review

In view of the fast development of vector beams and their broad application prospects, the systematical review about the characterizations, generation methods, propagation mechanisms and diverse micro-nano optical applications of various vector beams are provided. Four mathematical characterizations of vector beams are generalized and the relation of different characterization methods is uncovered. The direct and indirect generation methods including some innovation techniques are summarized. The propagation fields of vector beams in different circumstances are analyzed and the related phenomena are explained. The diverse applications in various fields are enumerated. The detailed description of vector beams provides a theoretical basis for deeply understanding of the polarization properties of vector beams. The comparison of several generation methods brings the researchers the purposeful choices in practice works. The analysis about propagation mechanisms of vector beam lays the foundation for predicting the unique phenomena and utilizing reasonably vector beams. The presented applications confirm the significance of vector beams in many fields. We expect this review will bring more help for the deep studies about foundational and applications of vector beams.