## 5 Analysis of Physical Mechanism  
In order to clarify the basic properties and internal physical mechanism of the thermal controlled Fano resonance in detail, we simulated the surface current and electric field distributions at the corresponding resonant frequency for the low (45 \({}^{\circ}\)C) and high (70 \({}^{\circ}\)C) temperatures, as shown in Figure 5. The surface current in the asymmetric VO\({}_{2}\)-implanted MM structures can be decomposed into a series of current oscillation units, which is equivalent to the electromagnetic waves radiated from the electric dipole to the far field. The physical mechanism of resonance can be well explained by the theory of electromagnetic scattering and dipole radiation [40]. For eigen resonance mode of 0.700 THz at low temperature shown in Figure 5a, the surface current and electric field intensity are mainly concentrated in the relatively small C-shaped structure on the right side and the induced current direction is the same as the incident THz electric field along the \(y\) axis. The electromagnetic field radiated by the corresponding electric dipole produces constructive interference, which results in high radiation loss, and creates the dipole resonance with a low Q-factor. For the three resonance modes excited at high temperature, the corresponding surface current and electric field distributions are shown in Figure 5b-d. The eigen resonance (0.685 THz) shown in Figure 5b displays the same characteristic of the dipole resonance, except for a slight increase in structure coupled electric field energy. For the Fano 1 induced by the high temperature metal phase  
Figure 5: Surface current and electric filed distributions of the proposed VO\({}_{2}\)-implanted MM structures at the frequencies of Fano resonances for the low and high temperatures. (**a**) Eigen resonance (0.700 THz) at 45 \({}^{\circ}\)C. (**b**) Eigen resonance (0.685 THz), (**c**) Fano 1 (0.515 THz), and (**d**)_Fano 2 (1.160 THz) at 70 \({}^{\circ}\)C.  
VO\({}_{2}\) shown in Figure 5c, the surface electric field and current are mainly concentrated in the relatively large C-shaped structure on left side. The current in the \(x\) direction always anti-phase oscillates (i.e., pointing in the opposite direction). Therefore, the equivalent dipole moment produced by the oscillating current along the \(x\) direction can almost cancel each other, which greatly reduce the radiation damping of the MM structures and promote the formation of a high Q-factor resonance. For the extremely sharp Fano 2 in Figure 5d, it is clear that there are multiple current and electric field oscillation nodes in the MM structures. The phase of current oscillation is both opposite in the \(x\) and \(y\) directions, resulting in the cancellation of the electric dipole moment. So, the radiation loss is significantly suppressed. More importantly, the diffraction coupling effect plays an indispensable role in the creation of a high Q-factor Fano resonance [39]. The simulated surface electric field distributions corresponding to Fano 2 clearly show that the ultra-strong local current and electric field are coupled in the asymmetry VO\({}_{2}\)-implanted MM structures. The coupled electric field energy of Fano 2 is two orders of magnitude higher than that of the eigen resonance shown in Figure 5b. According to the theory of diffraction coupling [41], the resonant frequency of lattice surface mode is \(f_{LSM}=c\sqrt{i^{2}+\beta^{2}}/\eta p\), where \(c\) represents the speed of light in vacuum and \(n\) is the refractive index of substrate, \(p\) is the lattice constant of the MM array (the period length), and \(i,j\) is the order of lattice mode. The calculated resonant frequency of the first-order lattice surface mode corresponding to the asymmetry VO\({}_{2}\)-implanted MM structures at high temperature is 1.112 THz, which is very close to the response frequency of Fano 2.