Based on the vectorial Debye theory, the tight focusing properties of partially coherent and circularly polarized vortex beams are investigated. The focused characteristics of right-circular and left-circular polarized partially coherent vortex beams in the focal region are presented and compared by some numerical calculation results. Furthermore, the influences of the source coherence and the numerical aperture of the focusing objective on the tight focusing properties are studied in great detail. It is shown that the coherence and polarization properties of the focused left-circular polarized beam is less influenced by the source coherence and the numerical aperture of the focusing objective than that of the focused right-circular polarized beam. By selecting certain parameters, the widely used flat top beam can be obtained.

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This paper studies the propagation properties of Gauss-Bessel beams in a turbulent atmosphere. Based on the extended Huygens-Fresnel principle, it derives the intensity distribution expression for such beams propagating in a turbulent atmosphere. Then the influence of turbulence and source beam parameters on the beam propagation is studied in great detail. It finds that the intensity distribution of Gauss-Bessel beams will change into Gaussian profile in a turbulent atmosphere, and that stronger turbulence and smaller topological charges will lead to a faster changing.

We study the focusing properties of elliptically polarized vortex beams. Based on vectorial Debye theory, some numerical calculations are given to illustrate the intensity and phase distribution properties of tightly focused vortex beams. It is found that the spin angular momentum of the elliptically polarized vortex beam will convert to orbital angular momentum by the focusing. The influence of corresponding parameters on focusing properties is also investigated in great detail. It is shown that elliptical light spots can be obtained in the focal plane. Moreover the elliptical spot may rotate and the spot shape may change with the change of certain parameters. These properties are quite important for application of this kind of elliptically polarized vortex beam.

We investigate the focusing properties of a femtosecond vortex light pulse focused by a high numerical aperture objective. By using the Richards-Wolf vectorial diffraction method, the intensity distribution, the velocity variation and the orbital angular momentum near the focus are studied in great detail. We have discovered that the femtosecond vortex light pulse can travel at various speeds, that is, slower or faster than light with a tight focusing system. Moreover, we have found that the numerical aperture of the focusing objective and the duration of the vortex light pulse will influence the orbital angular momentum distribution in the focused field.

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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.

Based on the vectorial Debye theory, the focusing properties of the Gaussian beam through an annular high numerical aperture are studied numerically, including the intensity, the phase and the orbital angular momentum properties. Then the influence of certain parameters on the focusing properties is also investigated. It is shown that sub-wavelength elliptical light spots can be obtained. And there exists a vortex in the longitudinal component of the focused field even though the incident beam is Gaussian beam, indicating that the spin angular momentum of the elliptically polarized Gaussian beam is converted into the orbital angular momentum by the focusing.