Programmable Synthetic Motion at a Time-Varying Interface

Space-time metamaterials that exhibit synthetic motion promise arbitrary control over the momentum, frequency and energy of scattered light, but realising the required space-time modulation in a programmable way remains a challenge. Here we program synthetic motion using a single spatial light modulator in a 4f geometry which imprints a continuously tunable pulse-front tilt onto a high-intensity pump pulse, inducing reflectivity modulations at a sub-wavelength indium tin oxide thin film with synthetic velocities spanning the sub- and superluminal regimes. The angle-resolved spectrum of a scattered probe pulse reveals space-time diffraction patterns whose gradient and bandwidth vary continuously with synthetic velocity, in excellent agreement with theory. Splitting the shaped pump into two independently controlled pulses yields space-time double-slit diffraction with tunable fringe separation and frequency-momentum gradient. This programmable platform opens a path towards non-linear and periodic space-time trajectories for tabletop analogue studies of relativistic phenomena and space-time metasurfaces.