Spatiotemporal Co-reflection with Spacetime Discontinuities at Moving Interfaces

The control of reflection and refraction at interfaces using engineered media is central to numerous optical technologies, with negative refraction and the suppression of backscattering representing two prominent research frontiers. In this work, we demonstrate that an effective negative refraction accompanied by an absence of backscattering can be realized at a moving spatiotemporal interface when temporal and spatial reflections occur concurrently. While such spatiotemporal co-reflection is prohibited in one-dimensional linear dispersive media, we show that it becomes permissible under oblique incidence within a specific range of traveling-wave modulation velocities. Leveraging this mechanism, we propose a spatiotemporal flat lens capable of nonreciprocal electromagnetic wave focusing. These findings provide a framework for developing advanced spatiotemporal metamaterials and time-varying metasurfaces.