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Programmable calculus operations in electromagnetic space using space-time-coding metasurface

With the rapid advancement of metasurfaces and the increasing demand for programmable metasurfaces to simplify information systems, wave-based computation using metasurfaces has emerged as an attractive research topic. To facilitate the mathematical operations in electromagnetic (EM) space, here we propose a space-time coding metasurface (STCM) system capable of directly performing calculus operations on the spatial energy distributions of EM waves. By exploiting harmonic characteristics induced by time-varying coding, the responses of meta-atoms at specific harmonics can be flexibly controlled, which enables the metasurface system to address more complex tasks. Owing to its programmability, the STCM can dynamically switch functions in real time to accommodate different calculus tasks. To fully leverage the capability of STCM, we not only present the space-time coding sequences for differentiation and integration of EM waves, but also develop and numerically simulate the space-time coding sequences that can independently and simultaneously implement different calculus operations on the same incident EM waves. To experimentally validate the feasibility of the EM calculus operations, proof-of-concept experiments are conducted using a programmable 2-bit STCM. Good agreements among the theory, numerical simulations, and experiments confirm the feasibility of performing calculus operations in the EM space and demonstrate the broad application prospects of STCM in EM wave manipulations, wireless communications, and signal processing.