# Design of Tunable Broadband Graphene-Based Metasurface with Amplitude-Phase Modulation
## 1 Introduction  
As the evolution of mobile communication technology has progressed from 1G to 5G, a multitude of wireless communication methods have emerged, encroaching upon scarce spectrum resources. In order to expand communication capacity, i.e., obtain wider bandwidth, future wireless networks will be compelled to venture into higher frequency bands, including millimeter wave and terahertz bands, which hold promise for the advancement of sixth-generation communication technologies (6G communication). Against this background, beam-reconfigurable antennas are increasingly being employed in personal communication devices, wireless local area networks, the Internet of Things, and 5G communication technologies. Traditional beam-reconfigurable antennas include phased array antennas [1], reflector antennas [2], and beam former antennas [3]. In recent years, with the rapid development of microstrip and metamaterials, beam reconfiguration can also be achieved through microstrip parasitic antennas [4] and metasurface antennas [5]. As a two-dimensional representation of metamaterials, metasurfaces, which are periodically arranged by artificial composite structures, have exceptional electromagnetic properties and have been widely adopted in the design of beam reconfigurable antennas. Generally, depending on whether controllable elements or materials are added, the metasurface can be divided into active and passive types [6]. Once a passive metasurface is designed and fabricated, its electromagnetic characteristics cannot be changed. By loadingactive tunable elements or materials into the passive static metasurface unit, the electromagnetic beam can be dynamically modulated in real time. Active tunable components or materials include PIN diodes [7], varactor diodes [8], RF MEMS switches [9], liquid crystals [10], graphene [11], etc. PIN diodes and varactor diodes are diminutive in size and economical, thereby resolving the challenge of sluggish control velocity of electronic control machinery. This attribute is beneficial for devising multi-functional reconfigurable metasurface antennas with uninterrupted adjustment. Nevertheless, a significant impediment is that PIN diodes or varactor diodes demonstrate high losses and inadequate stability in high frequency applications. RF MEMS switches exhibit the merits of low power consumption, low insertion loss, high isolation, and excellent high frequency performance. However, they have the disadvantages of long switching time, high voltage drive, and high cost. The material of liquid crystal possesses low losses and anisotropic dielectric constants, which is an outstanding material for controllable media. Nonetheless, the extent of control of liquid crystal dielectric constants is narrow, thus restricting the overall regulation range of the system. Graphene exhibit a high degree of freedom in electrical modulation efficacy and also display singular and outstanding characteristics in optics, thermodynamics, and mechanics. Therefore, graphene is an excellent candidate for controllable metasurface in the high frequency band. Initially, graphene has gained significant popularity in the optical and terahertz frequency bands owing to outstanding optical characteristics and the pliable and manageable surface conductivity over an extensive range of high frequencies. [PERSON] et al. demonstrated a broadband terahertz amplitude regulator based on complementary stacking of multilayer metamaterials, which shows a bandwidth of 0.5 THz centered at 1.25 THz, corresponding to a relative bandwidth of 40% [12]. [PERSON] et al. discovered dynamically tunable Faraday rotation in the terahertz band using a graphene metasurface [13]. [PERSON] et al. proposed and realized a new phase regulation metamaterial based on graphene-metal composite metamaterials [14], and achieved a maximum dynamic phase adjustment of 243\({}^{\circ}\) at 0.48 THz for the first time.