Properties of Axial Caustic under Autofocusing of Airy-like and Chirped Beams

In this report, a method of quantitative analysis of the axial caustic properties is proposed. Previously, the radial caustic was considered, but for it, due to mathematical difficulties, it is possible to obtain only an equation that determines the shape of the surface. If we do not take into account the absolute value of the intensity and consider only the characteristics of the position, then a beam created by a generalized lens can replace an arbitrary Airy-like beam. Within this framework, analytical formulas are derived for the characteristic positions of the focal line - the point of maximum intensity, the shadow boundary, and the longitudinal boundaries of the focal line. In the report, two variants of the generalized lens - a full lens and a displaced lens are considered. The results of the numerical simulation are in good agreement with the theoretical estimates.