We propose a method for generating focal beams with special intensity distributions using radially polarized vortex beams in a 4Pi configuration. A spherical dark-hollow beam and hollow beam array can be obtained by vortex beams with topological charge of $m=1$. A dark channel can be generated using vortex beams with topological charge of $m=2$. The length of the well-defined hollow beam array and the dark channel is about $30\lambda$. These interesting beams are useful in optical trapping and manipulation.

Unconventional systems that adopt the concept of ghost schemes have led to advancements in some imaging applications. However, their application in quantitative phase imaging remains a challenge. Here, we introduce a basis for quantitative phase imaging with ghost diffraction and demonstrate ghost diffraction holographic microscopy for complex-valued imaging. We achieve this by introducing an off-axis holography approach in the modified ghost diffraction system. We also realize a correlation hologram in the cross-correlation of intensities from two detectors in the modified ghost diffraction setup and digitally process the correlation hologram to image complex-valued objects. To generate experiment results, we use a modified interferometer setup and exploit the spatial statistics of the scattered field from a time-frozen pseudothermal light source. Finally, we evaluate the efficacy of the approach by simulation and follow that with experiments that demonstrate imaging of pure phase objects, planar transparencies, and resolution test targets, among others.

A partially coherent vortex beam propagating in a turbulent atmosphere is investigated by using extended Huygens-Fresnel diffraction integral. The influence of the turbulence, the spatial coherence, and the topological charges of the incident beam on the propagation characteristics of the beam is studied in great detail. It is shown that the spreading of the partially coherent vortex beam is less influenced by atmospheric turbulence than that of a partially coherent nonvortex beam, and that a partially coherent vortex beam of lower coherence is less influenced than one of higher coherence.

A super-length optical needle ($\sim 14\lambda$) of strong transversally polarized field with homogeneous intensity along the optical axis and subdiffraction beam size ($\sim 0.9\lambda$) 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.