Random Time-Space Coding Metasurfaces for Spatial Control of the Temporal Statistics of Electromagnetic Fields

Conventional methods to control electromagnetic (EM) fields via digital coding metasurfaces are basically focused on generating deterministic EM responses, such as beam forming, holographic imaging, and harmonic modulation, by employing specific coding patterns or sequences. In contrast, controlling random EM fields aims to produce EM fields with target temporal statistical properties, such as spatial mean and variance distributions. Here, we propose a framework to control the spatial distribution of temporal statistical properties of EM fields via random time-space coding metasurfaces (RTCM). We establish a statistical model of RTCM in probability space and reveal that the spatial mean and variance distributions of EM fields are determined by the marginal and pairwise joint distributions of the random codes. Time-varying random EM fields with desired mean and variance distributions are generated by the sampling codes constrained by these distributions. We further show that simultaneously direct transmission and jamming can be achieved via the spatial mean and variance peaks, respectively. This work extends the metasurface paradigm into the probability domain, marking a shift from deterministic response design to probabilistic structuring, and paving the way for new approaches in communication, information security, and EM countermeasures.