Electrically tunable metasurface design for phase delay at 470  nm with an analytical analysis

Metasurface research is essential given its revolutionary potential in enabling unprecedented electromagnetic wave manipulation. The design of the unit cell, which is the fundamental building block of metasurfaces, is crucial as it precisely determines the overall electromagnetic properties and functionalities through tailored geometric, material, and structural parameters. This study focuses on the design and analysis of an electrically controlled metasurface. An analytical equation for the rough prediction of the height of the functional layer of an electrically controlled metasurface unit cell is proposed. This equation takes into account the material properties and the voltage range. To validate the analytical equation, numerical simulations are employed at a wavelength of 470 nm. The simulation results, including the spatial distribution of the incident beam under different bias voltages, the phase delay characteristics, and the transmission efficiency, are analyzed. The phase delay predicted by the analytical equation is compared with the numerical simulation results, and it is found that the equation can effectively provide a preliminary estimation of the electronic sensitivity functional layer height. Meanwhile, the influence of voltage changes on the field distribution and the transmitted phase delay is investigated, which is crucial for understanding the electro-optical response mechanism of the metasurface. The results show that our analytical equation has certain guiding significance for the design of electrically controlled metasurfaces, and the numerical simulation at 470 nm can well verify the effectiveness of the equation.