Abstract
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.
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