## 2 Device Structure  
The configuration of the proposed THz modulation structure is shown in Figure 1a. The hybrid structure is supported by a low loss plastic substrate, on which the first layer deposited is the metallic metamaterial, composed of a periodic structure with the unit cell shown in the schematic drawing of Figure 1a. In the unit cell, the square slit ring with width marked g, period P, and inside length L are also marked. When THz wave impinges onto the square slit ring, resonance will be excited and the local field confined in gap of the square slit ring will be enhanced. The second layer is a dielectric with the thickness of t acting as a spacer to avoid direct contact of the graphene and the metallic structure. The graphene film on top of the dielectric layer acts as the active layer. In the electrical modulation process, the metallic metamaterial also plays the role of bottom electrode to apply modulation voltage. With the separation of the dielectric spacer, the applied modulation electrical field is formed between the graphene and the metamaterial. And the conductivity of the graphene is tuned with the applied modulation voltage. It leads to the resonant change in the metamaterial and the transmitted THz wave is modulated. The modulation depth of the transmitted amplitude is defined as:  
\[MD=\frac{|T(V_{1})-T(V_{2})|}{max\{T(V_{1}),T(V_{2})\}}\times 100\% \tag{1}\]  
where the \(T(V_{1})\), \(T(V_{2})\) are the transmission at the different modulation voltages. To demonstrate the modulation enhancement in the hybrid structure, the transmitted THz spectrum is simulated with the finite element method (FEM). A polyethylene terephthalate (PET) film of thickness 30 \(\upmu\)m is taken as the low loss plastic substrate. Aluminum is chosen as the material of the metamaterial with \(P\)= 150 \(\upmu\)m, \(g\) = 12.5 \(\upmu\)m, and \(L\) = 90 \(\upmu\)m.The dielectric material is polymethyl methacrylate (PMMA) with the thickness \(t\) = 0.5 \(\upmu\)m as the spacer between the graphene and the  
Figure 1: (**a**) The schematic drawing of the terahertz (THz) modulation structure based on hybrid graphene and metamaterial. (**b**) The simulated spectrum of the structures with and without the metamaterial in the cases of different Fermi levels. metallic structure. The thickness of graphene is set as 1 nm and the conductivity is calculated with the Drude mode [24]. In this mode, the oscillation frequency \(\gamma\) = 2 THz. The transmission spectrum of the hybrid structure at different Fermi level is shown in Figure 1b. The pink curve is for the pure metallic structure on the substrate, which shows a transmission peak at the frequency of \(f_{res}\) = 0.51 THz, which indicates that the resonant is excited by the metallic square slit ring. When the graphene layer is added, the black curve for the \(Ef\) = 0.1 eV shows that the resonant frequency is blue shifted to \(f_{res}\) = 0.6 THz. When the Fermi level of graphene is changed to \(Ef\) = 0.3 eV, the transmission is the red curve. It shows that the transmission peak is blue shifted to \(f_{res}\) = 0.79 THz and the value of the peak is lower. The resonant frequency shift reveals that the dielectric condition is changed when the Fermi level of the graphene is tuned. It leads to a remarkable change of the transmission near the resonant frequency. In comparison, a control sample without the metallic metamaterial is simulated under the same condition. The blue and the green curves are corresponding to the different Fermi level of 0.1 eV and 0.3 eV respectively. The flat transmission lines indicate that there is no resonance in the control structures. And the transmission difference between the two lines is much lower than that of the hybrid structures. When calculating the modulation depth with Formula (1), there is a maximum \(MD\) = 67.3% at the frequency of f = 0.52 THz for the hybrid structure, while the value of the \(MD\) is only 3.3% for the control structure without the metallic square slit ring.