The intensity distribution of hollow Gaussian beams focused by a lens with spherical aberration

We developed an expression that describes the hollow Gaussian beams (HGBs) passing through a spherically aberrated lens by using the Collins formula. The radial intensity distribution in both spherical aberration SA free lens, lens that exhibits relatively large in both positive spherical aberration PSA, and negative spherical aberration NSA is calculated. Numerical calculations are made and the results show that the PSA and NSA have a strong influence on the intensity distribution especially at the focus. The study showed remarkable results for which there is no hollow Gaussian beam at a large NSA along the optical axis at the focus. In addition, we found that the DSS, and w_r of focused hollow Gaussian beams in the focal region depend not only on the beam radius, and beam order; but also on the spherical aberration.