“…12,13 In particular, the azimuthally polarized vector field (another typical vector field) carrying a vortex phase can realize a sharper far-field focal spot of 0.15λ 2 . 14 Based on the design of the SOP distribution, the engineered vector fields can achieve the focus shaping, 15 the light needle of longitudinally polarized field, 16 the optical cage, 17,18 the optical chain, 19 and so on. The vector fields have many important applications such as particle acceleration, 20 single molecule imaging, 21 near-field optics, 22 nonlinear optics, 23 and optical trapping and manipulation of particles.…”