Design of tunable terahertz metalenses with single and multifocus capabilities

<strong>Objetive:</strong> To meet the demands for integration, miniaturization, and tunability in optoelectronic devices, we designed a tunable metalens structure with a width of 940&mu;m, the designed metalens structure consists of an antenna array formed by graphene ribbons on the top layer, a SO₂ middle dielectric layer, and a reflective gold film layer. This design leverages the miniaturization and focusing capabilities of metalenses along with the electrically tunable properties of graphene. By investigating the reflected optical field of x- and y-polarized light, we demonstrate flexible dynamic focusing within the terahertz (THz) frequency range. <strong>Method:</strong> First, using the Finite-Difference Time-domain method, a voltage ranging from 0 to 1 eV was applied to graphene strips. Terahertz plane waves with frequencies polarized along the x-axes and y-axes were then incident on the graphene strips and scanned with high precision, achieving near-complete phase compensation from 0 to 2&pi;. <strong>Result:</strong> By precisely tuning the Fermi level of the graphene strips, we achieved single-focus imaging at different positions for x- and y-polarized light, as well as dual-focus imaging in both transverse and longitudinal directions. When we design the focal position at z=300&mu;m, the actual focal position for x-polarized light is at z=290&mu;m, and the actual focal position for y-polarized light is at z=292&mu;m. The focal length accuracy reached 96.7% for x-polarized light and 97.3% for y-polarized light compared to the design values. Furthermore, when designing transverse dual-focus imaging for x-polarized light and longitudinal dual-focus imaging for y-polarized light, the focusing performance remained highly effective. <strong>Conclusion:</strong> This design enables multifunctional control of the metalens simply by fine-tuning the Fermi level of graphene, demonstrating high flexibility and reliability in optical modulation. These findings provide valuable guidance for the design and optimization of multifunctional metasurface metalenses.