Encoding orbital angular momentum of light in space with optical catastrophes.

Light beams carrying orbital angular momentum (OAM) possess an unbounded set of orthogonal modes, offering significant potential for optical communication and security. However, exploiting OAM beams in space has been hindered by the lack of a versatile design toolkit. Here, we demonstrate a strategy to tailor OAM across multiple transverse planes by shaping optical caustics leveraging on catastrophe theory. With 3D-printed metasurfaces fabricated using two-photon polymerization lithography, we construct these caustics to steer Poynting vectors and achieve arbitrary shapes of OAM beams. Interestingly, we further realize "hidden" OAM along the propagation trajectory, where the intensity of the beam is spread out thus avoiding detection. By exploiting this intrinsic nature of OAM, we demonstrate the detection of encoded information in optical encryption. Our approach provides a unique framework for dynamic control of OAM in space, with promising applications in optical trapping and sensing, high-capacity data storage, and optical information security.