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Analyzing of the off-axis caustic created by the chirp-beams with autofocusing property

We studied the autofocusing properties of chirp beams whose phase has an arbitrary power-law dependence on the radius. Two types of such beams were considered (theoretically and numerically): two-parameter beams corresponding to a generalized lens, and three-parameter beams corresponding to a displaced generalized lens. On the basis of theoretical analysis, the conditions imposed on the parameters of the beams, under which the off-axis caustic is formed, are revealed and the equation of the caustic line is obtained. It is shown how changing the beam parameters affects the autofocusing properties. The results of numerical simulation are consistent with theoretical calculations. Thus, we can form beams with controlled autofocusing properties, which are in demand in various applications of optics and photonics.