Focal shift of focused truncated Lorentz-Gauss beam

Based on the Collins diffraction integral formula and the complex Gaussian expansion of the aperture function, an analytical expression for a Lorentz-Gauss beam focused by an optical system with a thin lens and a circular aperture has been derived. The focal shift of the focused truncated Lorentz-Gauss beam is investigated with numerical examples, and the dependence of the focal shift on the different parameters of the focused truncated Lorentz-Gauss beam is discussed in detail. This research is useful to the applications of highly divergent laser beams.