为了获得多种类型的波长量级聚焦光斑，研究了一种新型涡旋光束，高次方涡旋光束经过大数值孔径透镜的聚焦。基于矢量德拜积分公式，理论上研究了线偏振的高次方涡旋光束经过大数值孔径透镜的聚焦特性。研究了涡旋光束的拓扑荷数和幂次方数对聚焦平面光强和电场x分量的相位分布的影响。研究结果表明，通过控制涡旋光束的拓扑荷数和幂次方数可以产生不同类型的聚焦光强分布，例如尺寸约为2个波长大小的实心和空心型聚焦光斑。此外，与普通的涡旋光束聚焦不同，高次方涡旋光束聚焦后的奇点并不在焦点处。这些特殊的聚焦光斑有望在微粒的操控等领域中得到应用。

Based on vectorial Debye theory, the focusing properties of linearly polarized power-exponent-phase vortex beam focused by a high numerical aperture objective is studied. The influence of the topological charge and power index on the focal intensity and the phase of x-component is investigated in detail. The result shows that different types of focal intensity distribution, such as dark-core shape focal beam with beam size of 2 wavelength, can be generated by controlling the topological charge and power index. In particular, it is found that the phase singularity of power-exponent phase vortex beam has a deviation from the geometrical focus. The potential applications of this study may include particle manipulation.