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中文摘要：
基于德拜矢量衍射积分理论,对离轴高斯涡旋光束经过大数值孔径透镜后聚焦场的特性进行了研究,获得了离轴高斯涡旋光束深聚焦后复振幅分布函数,在此基础上对离轴高斯涡旋光束深聚焦场的光强和相位分别进行了分析.数值模拟结果表明：离轴距离的改变对高斯涡旋光束在焦平面上的光强分布和相位分布会产生影响,离轴距离的增加会加剧聚焦场光强在y轴方向上分布的差异,而离轴距离的符号决定了光强集中区域的方向.另一方面,与一阶离轴涡旋光束不同,高阶离轴涡旋光束经过深聚焦后会发生暗核分裂现象,出现多个相位奇点,奇点个数等于原始光束对应的拓扑荷数,且分裂后的奇点具有明显的对称性.研究表明,这种暗核分裂现象由大数值孔径透镜深聚焦引起.
英文摘要：
The properties of off-center Gaussian vortex beams focused by a high numerical aperture are investigated on the basis of vector Debye integral. A complex amplitude of off-center Gaussian vortex beams through a high numerical aperture objective is derived and numerical calculation 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 the variation of off-axial distance; the intensity distribution in the focal plane is different in the direction of y-axis which is enhanced with the increase of off-axial distances; the sign of off-axial distance determines the direction in which the intensity is concentrated. On the other hand, different from the 1^storder off-axial vortex beam, high-order off-axial vortex will split in the tightly focused field. Multiple phase singularities will 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.
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