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.
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