Optimizing Light in Space and Time: Inverse Design of Spacetime‐Modulated Metasurfaces via Discontinuous Galerkin Time‐Domain Method

The transition from static to dynamic metasurface systems represents a frontier in our ability to control light. Yet unlocking the full potential of spacetime‐modulated metasurfaces requires a departure from conventional design modeling strategies. Here we present a rigorous inverse design methodology based on the discontinuous Galerkin time‐domain (DGTD) method and an advanced Bayesian optimization algorithm to handle arbitrary temporal variations in material properties and treat time as a true design degree of freedom. From one hand, our novel DGTD approach enables accurate simulation of spacetime‐modulated metasurfaces with high modulation frequencies and with arbitrary complex geometries. On the other hand, our DGTD method is coupled with a global advanced statistical learning optimization strategy to optimize a realistic spacetime‐modulated silicon‐based metasurface that achieves nearly frequency‐conversion efficiency. Meanwhile, by pushing the optimization into higher modulation frequency regimes, we explored exotic functionalities such as asymmetric frequency mixing, highlighting the method's versatility for the design of spacetime‐modulated metasurfaces and paving the way for a new generation of spacetime reconfigurable metasurfaces.