异常空心光束通过球差光阑透镜的聚焦和在焦区的位相奇异特性

Focusing of an anomalous hollow beam by a spherically aberrated aperture lens and its phase singularities in the focal region

研究了用德拜公式对异常空心这类新型光束经过光阑透镜后的聚焦特性.结果表明,异常空心光束的形状一般不能保持传输不变性,但选择合适的截断参数和球差异常空心光束在一定位置可保持其初始光强分布近似不变.在焦区位相奇点会出现移动、产生和湮灭,并与截断参数、球差和光阑透镜半角有关.当无球差时,出现鞍点,奇点对的湮灭过程与鞍点对湮灭相伴发生,导致亚波长结构.用计算例对结果做了说明,并与文献中已有工作做了比较.

The focusing properties of a novel type of beam, i.e. an anomalous hollow beam focused by a spherically aberrated aperture lens, are studied by using the Debye formula. It is shown that, the shape of the anomalous hollow beam does not keep unchanged upon propagation. However, the anomalous hollow beam at a certain position can keep its initial profile nearly unchanged by selecting the suitable truncation parameter and spherical aberration. The motion, creation and annihilation of phase singularities occur in the focal region, which depends on the truncation parameter,the spherical aberration and the half angle of the aperture lens. The saddle points may appear, and the annihilation process of a pair of phase singularities is accompanied by the annihilation of a pair of saddle points in the spherical aberration-free case, which leads to the subwavelength structure. The results are illustrated by numerical examples and are compared with the results of previous work.