# Dynamic and Active THz Graphene Metamaterial Devices
## 1 Introduction  
Terahertz radiation (0.1 THz-10 THz) is situated between microwave and infrared light, possessing the properties of photonics and electronics [1]. The past 20 years have seen a tremendous growth in terahertz science and technology, including diverse research on high-rate wireless communications, high-resolution environment sensing, and imaging research for medical applications [2, 3, 4, 5, 6]. Terahertz technology requires significant advances in the overlapping areas of materials and device design, making terahertz components for efficient operation, detection, and generation compact and economical commercially viable in the future. A wide variety of active materials have been used for terahertz applications, including traditional bulk semiconductor materials, two-dimensional materials, phase-change materials, and liquid crystal materials, which are easily modulated when the carrier concentration is under externally applied electrical or optical stimulus. Graphene stands out due to its easy integration and its unique properties over a broad spectrum, especially in the terahertz band. [7, 8, 9, 10]. It introduces a universal absorption for visible and near-infrared frequencies due to the generation of electron-hole pairs caused by interband transitions [11, 12]. A Drude-like conductivity is observed at far-infrared and terahertz frequencies, corresponding to the absorption of intraband carriers [13, 14]. Furthermore, graphene shows an exceptional nonlinear optical response due to the absence of bandgap and linear energy-momentum dispersion [15, 16]. The graphene nonlinearities have been demonstrated at infrared and visible frequencies, originating from interband electron dynamics, including saturable absorption [17], higher-harmonic generation [18, 19, 20, 21, 22], and four-wave mixing [23, 24]. Nevertheless, in the technologically important terahertz region, the up to seventh-harmonic generation was confirmed experimentally until 2018 [25]. The strong intraband nonlinearity of graphene is related to the collective thermal responseof its background Dirac electrons under terahertz fields, and the controllable saturable absorption effect and third-harmonic generation have been demonstrated successfully in doped graphene [26; 27]. Exploring the THz linear and nonlinear properties of graphene is impressive for developing high-speed optoelectronic devices such as graphene-based transistors, photodetectors, and laser mode-locking. Metamaterials is a rapidly developing direction that has been extensively boosted to metasurfaces and meta-atom structures [28; 29; 30; 31; 32]. Actively-tunable metamaterials can significantly reduce the size of optical devices and enhance light-matter interaction by field localization, which contributes to improving the light modulation capability of graphene, limited by the ultra-thin thickness of only 0.34 nm [33]. Graphene metamaterial comprises graphene with conventional artificial metamaterial structures or alternatively stacked graphene and dielectric layers [34; 35]. Thanks to the carefully-designed geometric shapes, graphene metamaterial offers an ambitious platform for beam transformation, leading to extensive applications, such as modulators, light emitters, detectors, and terahertz lenses. In addition, multilayer graphene hyperbolic metamaterial with strong light absorption is proposed, where graphene-based grating consists of alternating graphene layers separated by lossless dielectric [36]. Furthermore, transmission lines (TL) based on graphene metamaterials have also been extensively studied, which can control the phase constant and the characteristic impedance of the transmission line [37; 38]. This further controllability of circuit parameters paves the way for designing on-chip structures with more compact dimensions, a higher performance, and novel functionalities.