## 3 Analysis of Moire THz Printed FSS  
To study the Moire interference effect, the simulation was performed while stacking two identical BPFs made from printed FSSs, with the orientation of the second one being changed relative to the first, with a rotation angle ranging from 0\({}^{\circ}\) to 90\({}^{\circ}\), with a 10\({}^{\circ}\) step. It can clearly be seen that as the superposition angle increases, the number of smaller groups with new periodic patterns also increases because of the geometric design of the hexagonal air-hole array. Thus, two identical THz FSS are being used to form reconfigurable THz FSS. From Figure 3, it is obvious that the patterns for the 40\({}^{\circ}\), 50\({}^{\circ}\), and 60\({}^{\circ}\) rotations look like those for the 20\({}^{\circ}\), 10\({}^{\circ}\), and 0\({}^{\circ}\) rotations, respectively. Similarly, the Moire patterns for the \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **PE-Based THz FSS** & **3D-Printed THz FSS** \\ \hline Lattice type & Triangular & Triangular \\ Fabrication method & R2R flexography & Powder bed fusion-selective \\  & & laser melting system \\ Material & Ink: Ag & Aluminum foil \\  & Substrate: PET & \\ Thickness & Ink: 352 nm & 100 \\  & Substrate: 125 μm & 2.50 \(\times\) 10\({}^{7}\) S/m \\ Conductivity & 4.40 \(\times\) 10\({}^{6}\) S/m & 2.50 \(\times\) 10\({}^{7}\) S/m \\ Peak resonance frequency & 0.235 THz & 0.365 THz \\ (experimental) & 250 GHz & 180 GHz \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison between PE-based and 3D-printed THz FSS. \(70^{\circ}\), \(80^{\circ}\), and \(90^{\circ}\) rotations are symmetrical with the \(10^{\circ}\), \(20^{\circ}\), and \(30^{\circ}\) rotations, respectively. Clearly, beyond the \(30^{\circ}\) rotation angle, the Moire patterns repeat symmetrically, which is why we evaluated the azimuthal response of the THz transmission from a \(0^{\circ}\) to a \(30^{\circ}\) rotation angle, with a \(10^{\circ}\) step. PET was taken into consideration as a substrate of the analyzed FSS. Figure 4a-d shows the corresponding electric field distribution in the near-field for different rotation angles. The 2D simulated electric field distribution was obtained by placing the frequency domain field and power monitor in the near-field for different rotation angles. It is noteworthy that as the rotation angle was changed from \(0^{\circ}\) to \(30^{\circ}\), unique Moire patterns were observed with distinct field distributions, i.e., the spatiotemporal electromagnetic responses. Additionally, to evaluate the performances of the proposed THz amplitude modulator, the modulation depth needed to be calculated for various rotation angles at one fixed frequency, which was determined as the operating frequency where the maximum transmissions occur when the two samples are rotated with a \(0^{\circ}\) angle. The modulation depth (_MD_) is defined as follows:  
\[MD(\%)=\frac{T_{0}(\omega)-T_{x}(\omega)}{T_{0}(\omega)}\times 100\% \tag{6}\]  
where \(T_{0}(\omega)\) and \(T_{x}(\omega)\) are the normalized transmission of the \(0^{\circ}\) and \(x^{\circ}\) rotation, respectively, at the operating frequency (\(\omega\)). Figure 5a shows the simulated normalized transmission at various rotation angles. As can be seen in the figure, the peak normalized transmission gradually decreases when the second sample is rotated from \(0^{\circ}\) to \(20^{\circ}\), and for a \(30^{\circ}\) rotation angle, the normalized transmission is again increased with respect to the \(20^{\circ}\) rotation. It is also worth noting that the maximum expected transmission peak for the \(0^{\circ}\), \(10^{\circ}\), \(20^{\circ}\), and \(30^{\circ}\) rotation angles are \(97\%\), \(70\%\), \(48\%\), and \(58\%\), respectively. The maximum transmission peak was obtained for a \(0^{\circ}\) rotation at \(0.25\) THz, which is hereafter called the operating frequency to calculate the modulation depth for different rotation angles.