# Optical catastrophes of the swallowtail and butterfly beams

## TL;DR

This paper experimentally demonstrates higher-order optical caustic structures, specifically swallowtail and butterfly beams, revealing complex caustic hypersurfaces and their analytical descriptions in light fields.

## Contribution

It introduces the experimental realization and analysis of higher-order optical caustic structures, expanding the understanding of complex light field caustics.

## Key findings

- Successful generation of swallowtail and butterfly beams
- Analytical descriptions of their caustic structures
- Experimental observation of field distributions in real and Fourier space

## Abstract

We experimentally realize higher-order catastrophic structures in light fields to access the rich class of caustic swallowtail and butterfly beams. These beams present solutions of paraxial diffraction catastrophe integrals that are determined by potential functions, whose singular mapping manifests as caustic hypersurfaces in control parameter space. We systematically analyze the swallowtail and butterfly beams' caustics analytically and observe their field distributions experimentally in real and Fourier space. Their spectra can be described by polynomials or expressions with rational exponents capable to form a cusp.