Guiding light in photonic caustic structures

Nonlinear dynamical systems can perform sudden shifts due to perturbations of external control parameters. In optics, modelling the distribution of light according to their nonlinear potentials leads to the formation of caustics as geometrically stable structures whose characteristics are predicted by an analysis in terms of catastrophe theory. Caustics as singularities of intensity may be observed in nature at rainbows or as networks of high intensity at the bottom of shallow waters. However, in recent years the artificial and controlled embedding of the fundamental fold and cusp catastrophes in light fields led to accelerating Airy and Pearcey beams with unique propagation properties. Here, we utilize higher-order cusp and swallowtail catastrophes in paraxial light to inscribe photonic caustic structures in nonlinear media. We demonstrate waveguides with a rich diversity of light guiding paths, along 2D quasi cubic and 3D disposed curved caustic structures as well as their functionality as optical splitters. Finally, taking advantage of the strong auto-focusing of Pearcey beams, we demonstrate the formation of a Pearcey solitary wave in a nonlinear photorefractive crystal.