Facilitated by ultrafast dynamic modulations, spatiotemporal metasurfaces have been identified as a pivotal platform for manipulating electromagnetic waves and creating exotic physical phenomena, such as dispersion cancellation, Lorentz reciprocity breakage, and Doppler illusions. Motivated by emerging information-oriented technologies, we hereby probe the information transition mechanisms induced by spatiotemporal variations and present a general model to characterize the information processing capabilities of the spatiotemporal metasurface. Group theory and abstract number theory are adopted through this investigation, by which the group extension and independent controls of multiple harmonics are proposed and demonstrated as two major tools for information transitions from the spatiotemporal domain to the spectra-wavevector domain. By incorporating Shannon’s entropy theory into the proposed model, we further discover the corresponding information transition efficiencies and the upper bound of the channel capacity of the spatiotemporal metasurface. The results of harmonic information transitions show great potential in achieving high-capacity versatile information processing systems with spatiotemporal metasurfaces.

在超快动态调制的推动下，时空超表面已被认为是操纵电磁波和创造奇异物理现象（例如色散抵消、洛伦兹互易破坏和多普勒错觉）的关键平台。在新兴信息导向技术的推动下，我们探讨了时空变化引起的信息转换机制，并提出了一个表征时空超表面信息处理能力的通用模型。本研究采用群论和抽象数论，提出并论证了群扩展和多次谐波的独立控制作为从时空域到谱波矢域信息转换的两个主要工具。通过将香农的熵理论融入到所提出的模型中，我们进一步发现了相应的信息传输效率和时空超表面的通道容量上限。谐波信息转换的结果显示出在实现具有时空超表面的高容量多功能信息处理系统方面的巨大潜力。