A super-length optical needle (~14λ) of strong transversally polarized field with homogeneous intensity along the optical axis and subdiffraction beam size (~0.9λ) can be generated by focusing a hybridly polarized vector beam through a dielectric interface with an annular high-NA lens. Moreover, it is found that the polarization of the cross section near the focal plane is radial variant. Such a nondiffracting optical needle may have applications in atom-optical experiments, such as with atom trap and atom switches.

We theoretically investigate the tight focusing properties of hybridly polarized vector beams. Some numerical results are obtained to illustrate the intensity, phase, and polarization of tightly focused hybridly polarized vector beams. It is shown that the shape of the focal pattern may change from an elliptical beam to a ring focus with increasing radial index. The phase distribution around the tightly focused ring is shown to be the helical phase profile, indicating that the radial-variant spin angular momentum of hybridly polarized vector beams can be converted into the radial-variant orbital angular momentum.

The propagation and focusing properties of partially coherent vector beams including radially polarized and azimuthally polarized (AP) beams are theoretically and experimentally investigated. The beam profile of a partially coherent radially or AP beam can be shaped by adjusting the initial spatial coherence length. The dark hollow, flat-topped, and Gaussian beam spots can be obtained, which will be useful in trapping particles. The experimental observations are consistent with the theoretical results.

Based on the cross-spectral density function of Gaussian Shell-Model and Huygens integral, the expression of partially coherent Airy beam was derived. The non-diffraction and acceleration characteristics of partially coherent Airy beam were theoretically studied and experimentally observed. The experimental observation was consistent with the theoretical prediction. Furthermore, the non-diffraction distance and the transversal acceleration decrease with decreasing coherent length.