Programmable Space-Time Diffraction

Diffraction is a fundamental wave phenomenon that describes the spreading of waves when they encounter an obstacle or aperture comparable to their wavelength. Beyond the conventional spatial diffraction, waves can also exhibit diffraction-like behavior in temporal and spatiotemporal domains. In microwave regime, the diffraction plays a crucial role in shaping electromagnetic fields; however, its time and space-time counterparts with reprogrammable characteristics remain largely unexplored. Here, we investigate the time and space-time diffraction in the microwave band using a transmission-reflection-integrated programmable metasurface (TRPM). The physical feasibility of time and space-time diffraction is first established by theoretical analyses and numerical simulations. To enable experimental realization, a 1 bit amplitude-programmable element capable of switching between the reflection and transmission modes is presented, from which a TRPM prototype is fabricated and measured. Experimental results demonstrate that distinct time diffraction phenomena are observed in the frequency domain, while space-time diffraction effects emerge in the momentum-frequency domain by appropriately reconfiguring the time and space-time coding matrices of TRPM. The good agreement between experimental and numerical results illustrates the feasibility and flexibility of the proposed TRPM in realizing the programmable space-time diffraction, highlighting its potential as a versatile platform to explore fundamental physics and exotic functions in space-time metamaterials and metasurfaces.