Dynamically Realizing Arbitrary Multi-Bit Programmable Phases Using a 2-Bit Time-Domain Coding Metasurface

Recently, digital coding metasurfaces have attracted significant attention due to their capability to dynamically control electromagnetic waves in programmable ways. When the digital bit of a metasurface is higher, its controlling capability will be stronger. However, it is extremely difficult to realize 3-bit and higher digital coding metasurfaces since an $n$ -bit digital element will require many active devices (e.g., p-i-n diodes) to achieve $2^{n}$ digital states. Here, we propose to realize arbitrary multi-bit programmable phases using 2-bit time-domain digital coding metasurface at the central frequency or harmonic frequencies. We introduce the method of vector synthesis to design the phase coverages, from which 4-bit and arbitrarily higher-bit coding phases are synthesized by a physical coding metasurface with only 2-bit phases, simply by manipulating the time-coding sequences. A prototype controlled by a field-programmable gate array is used to validate this methodology. The experimental results are in good agreement with the theoretical analysis, which demonstrate good performance of the proposed method in dynamically realizing arbitrary multi-bit programmable phases. This time-varying coding strategy provides a new way to design higher bit programmable metasurface and simplify the structural design and control system, which will find many potential applications such as high-resolution imaging and high-capacity wireless communications.