  Caustics occur in diverse physical systems, spanning the nano-scale in
electron microscopy to astronomical-scale in gravitational lensing. As
envelopes of rays, optical caustics result in sharp edges or extended networks.
Caustics in structured light, characterized by complex-amplitude distributions,
have innovated numerous applications including particle manipulation,
high-resolution imaging techniques, and optical communication. However, these
applications have encountered limitations due to a major challenge in
engineering caustic fields with customizable propagation trajectories and
in-plane intensity profiles. Here, we introduce the compensation phase via
3D-printed metasurfaces to shape caustic fields with curved trajectories in
free space. The in-plane caustic patterns can be preserved or morphed from one
structure to another during propagation. Large-scale fabrication of these
metasurfaces is enabled by the fast-prototyping and cost-effective two-photon
polymerization lithography. Our optical elements with the ultra-thin profile
and sub-millimeter extension offer a compact solution to generating caustic
structured light for beam shaping, high-resolution microscopy, and
light-matter-interaction studies.
