## 2 Design and Method  
Figure 1a,b shows the schematic drawings of the proposed RTM device configured with four SRR meta-atoms and the geometrical denotations of the RTM unit cell, respectively. The thickness of the SRR meta-atoms is 300 nm on silicon on insulator (SOI) substrate. The permittivities of Au and Si materials are assumed as constants in this study. They are \(10^{4}\) for Au layer and 10 for Si substrate, respectively [37]. For a convenient description, we denote these four SRR meta-atoms as SRR-1, SRR-2, SRR-3 and SRR-4. The line width of each SRR meta-atom is 6 \(\upmu\)m and the period of SRR array is \(100\times 100\)\(\upmu\)m\({}^{2}\) (\(P_{x}\times P_{y}\)). The length (\(L\)) and width (\(W\)) of each SRR meta-atom are 30 \(\upmu\)m. The distance between the SRR meta-atoms (\(G\)) is 2 \(\upmu\)m. The coordinates of the incident electromagnetic wave in transverse electric (TE) and transverse magnetic (TM) modes are also illustrated in Figure 1a, where \(E\), \(H\) and \(k\) are the electric field, magnetic field and wave vector of the incident electromagnetic wave, respectively. In this study, each SRR meta-atom is designed to move along the \(x\)- or \(y\)-axis direction and to investigate the corresponding electromagnetic responses. We define each SRR meta-atom that has its own reference position denoted as (\(x_{i}\), \(y_{i}\)), where \(i\) is each SRR meta-atom, i.e., \(i=1\), 2, 3 and 4, as shown in Figure 1b. The center points of SRR meta-atoms are the initial reference positions whose variations represent the movement of each SRR meta-atom. The initial reference positions are (\(x_{1}\), \(y_{1}\)) = (-16, 16), (\(x_{2}\), \(y_{2}\)) = (16, 16), (\(x_{3}\), \(y_{3}\)) = (-16, -16) and (\(x_{4}\), \(y_{4}\)) = (16, -16), respectively. The electromagnetic characteristics of SRR array will be investigated by moving SRR meta-atoms to six different (\(x_{2}\), \(x_{4}\)), (\(y_{1}\), \(y_{2}\)), (\(y_{2}\), \(y_{4}\)), \(x_{2}\), (\(x_{2}\), \(x_{3}\)) and (\(y_{2}\), \(y_{3}\)) positions.  
In simulations, the incident electromagnetic wave is a plane wave, whose propagation direction is perpendicular to the \(x\)-\(y\) plane. The boundary conditions are set periodic for \(x\)-\(y\) plane and perfectly matched for the \(z\) plane. The electromagnetic filed monitor is set on the bottom of the substrate to  
Figure 1: **(a)** Schematic drawing of the proposed reconfigurable terahertz (THz) metamaterial (RTM) device with four split-ring resonator (SRR) meta-atoms; **(b)** The geometric parameters of four SRR meta-atoms. The geometric dimensions are: \(W=30\)\(\upmu\)m, \(L=30\)\(\upmu\)m, \(G=2\)\(\upmu\)m and \(P_{x}=P_{y}=100\)\(\upmu\)m. The reference points are (\(x_{1}\), \(y_{1}\)) = (-16, 16), (\(x_{2}\), \(y_{2}\)) = (16, 16), (\(x_{3}\), \(y_{3}\)) = (-16, -16) and (\(x_{4}\), \(y_{4}\)) = (16, -16).  
calculate the transmission of the incident THz wave. The resonances of the engineered SRR meta-atoms can be expressed by [13]  
\[f_{LC}=\left(\frac{c_{0}}{2\pi P\sqrt{\varepsilon_{s}}}\right)\sqrt{\frac{G}{W}} \tag{1}\]  
where \(c_{0}\) represents the velocity of light in a vacuum, \(P\) is the period of SRR array (\(Px\) and \(Py\) in this study), \(\varepsilon_{s}\) is the relative permittivity of the materials in the SRR array, \(G\) is the gap width and \(W\) is the width of the SRR meta-atom.