Nature holds situations in which sudden changes are caused by smooth alterations. The famous Airy and Pearcey beams represent diffraction patterns of corresponding fold and cusp bifurcations, respectively. When classified in a hierarchical order, they are subsequently followed by swallowtail and butterfly beams. These beams are generally characterized as cuspoid beams, accelerated on bent trajectories. They lead to various applications, among them the realization of curved waveguides. Their umbilic counterparts, however, characterized by even more complex diffraction patterns, have up to now only been characterized, but not yet been utilized as functional fabrication templates for applications in photonics.
In this contribution, we present our results on embedding higher-order cuspoid and umbilic catastrophes in tailored light. These light structures show versatile curved strands of high intensity during propagation. The elliptic umbilic beam even morphs from a hexagonal transverse intensity pattern to a beam with a single central hot spot to become again the original hexagonal pattern. We thus exploit the dynamics of these caustics to optically induce corresponding photonic lattices in nonlinear media and demonstrate light propagation in elliptic umbilic lattices.
Our approach enables fabricating continuously transforming lattices with varying band structure, paving the way for advanced topological photonics.