By extending the coding of digital metasurfaces from the spatial domain to the temporal domain, it has become possible to control the spatial distribution of the frequency spectrum of reflected electromagnetic waves through the adjustment of time-dependent coding sequences. In this approach, the constituent parameters of digital metasurfaces, such as the reflection phase, are simultaneously encoded in both the spatial and temporal domains, enabling the simultaneous manipulation of electromagnetic waves in the spatial and frequency domains.

In this paper, a time-varying method based on a 2-bit digital metasurface with temporal coding is proposed to achieve multibit and even quasi-continuous phase modulation at the central frequency. To this end, a vector synthesis method is introduced, and the analytical and simulation results demonstrate that 16 distinct phase states, equivalent to full 360° phase coverage, can be generated using a single physical 2-bit cell. For the proposed temporal coding sequences, the amplitude of the fundamental harmonic exceeds 0.7 in all cases, while the amplitudes of the other harmonics remain below 0.3. Furthermore, the average phase error of the proposed sequences is calculated to be 6.3°, and the average total harmonic distortion (THD) is 0.285.

The proposed method provides a simple and efficient technique for designing programmable digital metasurfaces with arbitrary multibit phase resolution, without requiring complex structures or sophisticated control systems. These features offer considerable potential for applications in high-performance antennas, high-resolution imaging systems, high-capacity wireless communications, and advanced radar systems.