Theory and Experimental Observation of Scattering by a Space-Time Corner

The corner problem is a century-old canonical scattering problem describing wave diffraction at a quarter-plane spatial discontinuity. Here, we study its space-time analog: wave scattering at a corner in space-time, arising at a time-switched spatial interface. We highlight and resolve an inconsistency between spatial and temporal boundary conditions arising in this problem, and analytically demonstrate the emergence of shock waves launched by the scattering process. After numerically verifying our theory, we realize and experimentally probe the scattering at a space-time corner arising at the edge of a time-switched waveguide. Our results unveil and efficiently model the unusual phenomena arising at the spatial interface between time-modulated and static media, of great relevance for the growing field of spatiotemporal metamaterials.