光场相位奇异特性研究在奇点光学研究领域中具有非常重要的意义。本文运用广义惠更斯-菲涅尔衍射积分公式推导出高斯涡旋光束通过像散透镜后的光场分布表达式, 并研究了它在几何焦平面上的相位奇异特性。结果表明, 高斯涡旋光束通过像散透镜后在几何焦平面上存在相位奇点, 相位奇点受到透镜的像散系数、光束束腰宽度和涡旋离轴量等参数的影响。在一定条件下, 几何焦平面上出现直刃型位错线或光涡旋。当像散系数为0时, 光涡旋出现在y轴上。当像散系数不为0, 而涡旋离轴量为0时, 会出现直刃型位错线或光涡旋, 且各自的位置都非常稳定。当像散系数、涡旋离轴量或束腰宽度改变时, 光涡旋会发生移动。这对光学元器件的设计和涡旋光束相位奇点的控制有一定的参考价值。

The research of phase singularity in light fields is significant in singular optics. Herein, the expressions of field distribution and phase singularity distribution for Gaussian vortex beams through an astigmatic lens were derived based on the generalized Huygens-Fresnel diffraction integral formula, in order to study phase singularities at geometrical focal plane. The results show that the phase singularities that appear at the geometrical focal plane when Gaussian vortex beams pass through an astigmatic lens, are dependent on the astigmatic coefficient, waist width and off-axis distance of vortex. Under certain conditions, a straight edge dislocation or an optical vortex appears at the geometrical focal plane. The optical vortex locates on the y axis when the astigmatic coefficient is zero. Otherwise with the off-axis distance of zero, there is a fixed straight edge dislocation or a stable optical vortex. The optical vortex moves with the variation of astigmatic coefficient, off-axis distance or waist width. Thoes results are proved to be references for the design of optical components and the control of vortex beam phase singularities.