The Generation And Singularity Splitting Of Tight Focusing Of Vortex Beam

Vortex beams has so many characteristics, this kind of special laser beam has been applied in many fields including optical micromanipulation, free space optical communication, photon calculation and the biomedical sciences. In this paper, based on the paraxial light beam transmission theory and vector diffraction integral Debye theory, we studied the generation and singularity splitting of tight focusing of vortex beam.Firstly, based on the modulation characteristics of Spiral Phase Plate(SPP) and the paraxial light beam transmission theory, we get the complex amplitude distribution function of vortex beam that produced by Gaussian beams through SPP. Analysis of intensity distribution and phase distribution of vortex beam, the numerical simulation results illustrate that phase singularities of the orbital angular momentum beams produced by high order SPP may split in a small scale, the singularity divided area is expanding with transmission distance increased. On the other hand, the number of the singularity split is equal to the topological charge. The experimental results indicate that when high order orbit angular momentum beams through aperture stop filtering out background bright, the dark nuclear area appears windows around the center, next to each window appears one dark. It shows that phase singularities splitting. Accordingly, the experimental results are consistent with theoretical simulation.Secondly, based on modulation characteristics of SPP and the paraxial light beam transmission theory, the complex amplitude of vortex beam that produced by elliptical Gaussian beams through SPP are investigated during propagation. It is shown that a elliptical ring spot with relatively uniform intensity distribution obtained when the elliptical Gaussian beam through SPP, and the original intensity distribution in the process of transmission lost the elliptical characteristics with increase of propagation distance. The light spot of high-order elliptical vortex beam appeared on a certain amount of deflection, the deflection direction is associated with the symbol of the topological charge. On the other hand, different from the fist-order elliptical vortex beam, high-order elliptical vortex beam will split in the dark nuclear area, the number of singularities is equal to the topological charge of the original beam.Finally, the properties of off-center Gaussian vortex beams focused by a high numerical aperture are investigated on the basis of vector Debye integral. The complex amplitude of off-center Gaussian vortex beams through a high numerical aperture objective is derived and numerical calculation by Mathcad software is performed to analyze the intensity and phase distributions of the beams in the focal plane. It is shown that the intensity and phase distributions change significantly with variance of off axial distance, the intensity distribution in the focal plane is different in the direction of y axis aggravates with the increase of off axial distances; the sign of off axial distance determines the direction where the intensity concentrates. On the other hand, different from 1st order off axial vortex beam, high-order off axial vortex will split in the tightly focused field. Multiple phase singularities appear and the number of singularities is equal to the topological charge of the original beam. Besides, the split singularities are symmetric, obviously. It is found that the splitting of high order vortex is due to the tight focusing.The research results have contributed to intensively understanding the generation of vortex beams and the light evolution and phase structure change in the process of free space transmission, and singularity splitting of tight focusing of vortex beam, have some guidance for vortex beams experimental that generated through SPP.