Generation of a family of Pearcey beams based on Fresnel diffraction catastrophes

Based on the theory of differential geometry and Fresnel diffraction catastrophes, we theoretically prove that the cusped caustic of Pearcey beams are the evolute of a parabola and thus identify the key factor determining the optical structure of Pearcey beams. We numerically simulate and experimentally generate a family of Pearcey beams with various optical topological structures using different parabolas. We then investigate their optical structures and propagation properties.