Broadband complex-amplitude metasurfaces for arbitrary engineering of spatial caustics

We present a broadband complex-amplitude metasurface for generating optical spatial caustics with arbitrary trajectories and transverse profiles. The required field at the metasurface plane is calculated from the target caustic geometry using a Fourier-space interference model that incorporates light-cone, Nyquist, phase-sampling, and aperture constraints. Its performance is evaluated by scalar angular-spectrum propagation and validated through finite-difference time-domain simulations of the full metasurface. Both shape-preserving and morphing caustics follow a prescribed parabolic trajectory. Designed at 1064 nm with a 420 nm period, the metasurface preserves recognizable crescent profiles from 920 to 1060 nm without redesign, offering a compact platform for broadband three-dimensional caustic engineering.