Fig. 1: Space-time diffraction from a synthetically moving modulation.

a Separable modulations of the dielectric permittivity ε can only induce transformations of the optical spectrum parallel to either the frequency or momentum axes. b Meanwhile, the general non-separable modulations of ε(x, t), demonstrated here, can perform arbitrary momentum-frequency transformations that are unobtainable with static metasurfaces. c The synthetic motion of permittivity modulations, Δε(x, t), can describe arbitrary trajectories in space-time (solid blue line), even moving at superluminal velocities outside the light cone.