## 3 VO\({}_{2}\)-Implanted THz Metamaterials  
Figure 2 presents the graphical representation of the VO\({}_{2}\)-implanted THz asymmetric double C-shaped MM sample under the thermal pump and THz pulse irradiation. The detailed geometry dimensions of the unit cell are shown in the upper right inset. The yellow area is symmetrical double C-shaped resonance structure composed of gold, which can be used to generate a dipole resonance. To excite the high Q-factor Fano resonance and realize the active tunable function, we introduce a phase-change VO\({}_{2}\) rectangular array (purple area) into the MMs, breaking the symmetry of the original structure. Asymmetric parameter (offset length \(a\)) is used to describe the extent of structural asymmetry, which refers to the distance between the center of the MM unit structure \(l_{x}\) and the center of the gap \(d\), as shown in the red dotted line. The thickness of gold and VO\({}_{2}\) is 1 \(\upmu\)m. To eliminate the interference of the substrate to the THz spectrum, the polyimide with high THz wave transmittance is selected as the substrate material and the thickness is set to 20 \(\upmu\)m. We preliminarily predict that VO\({}_{2}\) in the insulating phase at room temperature is transparent to incident THz wave and the designed metadevice behaves as a dipole resonance. However, when the metadevice is excited by external heat, the VO\({}_{2}\) film embedded in the MMs plays a quasi metallic role, the symmetry of the structure is broken, and then it will show the Fano resonance characteristic. Thus, using the external thermal excitation, it is easy to realize the mutual conversion of different resonance modes and active switching of the Fano resonance. The Fano resonance mode switching behavior of the proposed VO\({}_{2}\)-implanted THz asymmetric MM can be characterized by using three-dimensional full wave electromagnetic simulation software COMSOL Multiphysics based on the finite element method. The periodic boundary conditions are set in the \(x\) and \(y\) direction and the perfect matched layers are assigned along the \(z\) direction. The incident THz pulse propagates perpendicularly to the \(x\)-\(y\) plane and the electric field component is along the \(y\)-axis direction. Because the linewidth of the Fano resonance excited by designed MM structure is very narrow, in order to improve the frequency resolution of THz spectrum, the simulated frequency step is set to 0.005 THz, and the ultra-fine grid is adopted. The dielectric constant of polyimide substrate is  
Figure 1: Conductivity of VO\({}_{2}\) during phase transition. The heating and cooling processes agree well with experimental data [23]. 2.25 and the dielectric dispersion of gold material is formulated by Drude model, \(\varepsilon(\omega)=1-\omega_{p}^{2}/(\omega^{2}+i\gamma\omega)\), where the resonance frequency of plasma is \(\omega_{p}=1.37\times 10^{16}\) rad/s, the damping coefficient is \(\gamma=4.08\times 10^{13}\) rad/s [36]. In addition, considering the asymmetric line shape of Fano resonance, to fully characterize the resonance characteristics of the metadevice, we define the modulation depth as \(M_{d}=[(T_{max}-T_{min})/T_{max}\times 100\%]\), where \(T_{max}\) and \(T_{min}\) represent the maximum and minimum transmittances at the resonance frequency, respectively. From the energy point of view, the Q-factor is defined as \(Q=2\pi f_{0}\times P_{S}/P_{L}=f_{0}/\Delta f\), where \(f_{0}\) is the central frequency of the resonance, \(P_{S}\) and \(P_{L}\) represent the stored and dissipated energy, respectively, and \(\Delta f\) is the full width at half maximum (FWHM) of resonance. In order to verify the experimental feasibility of the proposed active switching of extremely high Q-factor Fano resonances, the fabrication process and characterization method of the device are described in detail. VO\({}_{2}\) films can be successfully prepared by pulsed laser deposition (PLD), sputtering or sol-gel method (SGM).