Metaserfaces, optically thin layers composed of two-dimensional arrays of subwavelength scatterers, have attracted much attention due to their powerful and flexible wave manipulation capabilities [1], [2], [3], [4]. Many useful applications of these structures have been demonstrated, such as perfect absorbers [5], [6], planar-lens focusing [7], anomalous refraction/reflection [8], [9], vortex beam generation [10], and optical holograms [11].

In general, materials used in the scatterers largely determine the strength of the interaction with the incident wave, which is why various dielectric and metallic materials are used in metasurfaces [12]. Graphene has proven to be an outstanding structural material for metasurfaces [13], [14], [15], [16], [17]. With high carrier mobility, graphene can generate localized surface plasmons in the wide wavelength band from terahertz to mid-infrared [18], [19]. More importantly, graphene plasmons exhibit strong field confinement and relatively low loss compared to plasmons produced in traditional noble metals [20]. In addition, it can use external electrical gating or chemical doping to dynamically control the plasmon resonances [21], [22]. Graphene-based metasurfaces are thus used to realize high-efficiency and tunable functional devices, such as absorbers [23], [24], filters [25], and polarizers [26]. On the other hand, graphene metasurfaces can transform the incident wavefront into the desired wavefront by designing the shape and dimension of these scatterers [27]. The design of these metasurfaces requires an accurate analysis of the spectral response of the surface plasmon to achieve optimal performance, so analytical solutions for the electromagnetic behavior of various graphene nanostructures have been studied [28], [29], [30], [31], [32]. Among them, disk configuration receives particular attention due to its two-dimensional isotropic responses on the array plane. However, there is no a fully analytical model that can predict the optical response of the metasurfaces with good accuracy, which is crucial for better understanding their properties and designing new devices based on them.

In this paper, we present a fully analytical model to describe the fundamental plasmon mode of a metasurface consisting of graphene disks based on an equivalent circuit method. By using the Floquet expansion and proper boundary conditions, we shall first analyze the scattering of a normally-incident TM polarized wave by a metasurface. It turns out that the metasurface can be modeled by an equivalent admittance. The equivalent admittance is then associated with the induced surface current, and the expression of the admittance is obtained by solving the integral equation governing the surface current. Finally, by inspecting the surface current density distribution on the graphene disks, new analytical formulas for the metasurface is derived by suitably modifying the known impedance expressions for a single disk and squared patches. The validity of the proposed model is further verified by comparison with the full-wave numerical results obtained from the commercial electromagnetic simulator COMSOL Multiphysics. As a proof of concept, we demonstrate the use of the proposed model in various graphene metasurface applications, namely tunable transmission resonances and broadband absorbers.