We study the tight focusing properties of partially coherent, partially polarized vortex
beams through a high numerical aperture (NA) objective. The influence of the degree of
polarization, the topological charge, the correlation length of the incident beam, and the
NA of the objective on the intensity in the focal region is investigated in great detail. We
also perform a study on the degree of coherence around the focal plane. We found that the
intensity distribution and the degree of coherence in the focal region will change with the
variation of the degree of polarization and the other parameters of the incident beams.
In the regime of Fresnel diffraction, a novel algorithm is proposed for aperture design for getting expected diffraction patterns. Experiments have verified the feasibility of this method. It may be used in beam transition, optics communication, information encryption, and other related fields.
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