Tight focusing of partially coherent and radiallly polarized vortex beams

We investigate the tight focusing properties of partially coherent and radially polarized vortex beams by use of vectorial Debye theory. It is found that the intensity profiles and the degree of coherence in the focal region are strongly dependent on the numerical aperture (NA) of the focusing objective, the parameters of the binary diffractive optical element (DOE) with several concentric zones, the topological charge, and the coherence property of incident vortex beams. Some interesting beam patterns, including a three dimensions (3D) maximally homogenized field with a very strong longitudinal component, a subwavelength optical bubble, and a hollow optical needle with quite long focal depth, can be generated by appropriately adjusting the above parameters. These beams are useful in microscopy techniques such as particle acceleration, laser processing, etc.