## 3 Analysis of Moire THz Printed FSS
Accordingly, the normalized transmission decreased from \(93\%\) to \(39\%\) at \(0.25\) THz when the rotation angle was adjusted from \(0^{\circ}\) to \(20^{\circ}\), resulting in a modulation depth of \(58\%\) (see Figure 5b-left axis). Likewise, the modulation depth was calculated as \(28\%\) and \(46\%\) for the \(10^{\circ}\) and \(30^{\circ}\) rotation angles, respectively (see Figure 5b-right axis). Changes in bandpass filtering bandwidth could also be seen when the second sample was rotated from \(0^{\circ}\) to \(30^{\circ}\). At FWHM, the filtering bandwidth became \(238\), \(175\), \(230\), and \(160\) GHz for \(0^{\circ}\), \(10^{\circ}\), \(20^{\circ}\), and \(30^{\circ}\) rotation angles, respectively. It can also be seen that the peak resonance frequency is also shifted towards the higher frequency range due to the geometry of the Moire pattern for different rotation angles. The corresponding peak resonance frequency becomes 0.241, 0.254, 0.275, and 0.280 THz for the 0\({}^{\circ}\), 10\({}^{\circ}\), 20\({}^{\circ}\), and 30\({}^{\circ}\) rotation angles, respectively. From both the FWHM bandwidth and peak resonance frequency for different rotation angles, it is evident that the rotation angle of 30\({}^{\circ}\) exhibits the highest \(Q\) factor among all the rotation angles, with the FWHM bandwidth dropping to its lowest value (160 GHz). As mentioned earlier, the Moire patterns repeat symmetrically after a 30\({}^{\circ}\) rotation. To validate this, we studied the modulation depths over an azimuthal range up to 120\({}^{\circ}\), as shown in Figure 5c. From this figure, it can easily be estimated that a total of five \"zero\" modulation depths with 60\({}^{\circ}\) intervals will be obtained for a full 360\({}^{\circ}\) rotation, in agreement with the hexagonal array of the designed filters. Finally, the simulation clearly showed that the transmission of the incident THz wave could thus be controlled at the operating frequency by employing only the rotational tuning approach. In order to validate our simulation results, we studied the visual effect of Moire interference patterns using a 633 nm diode mounted on a 2f imaging system and coupled to a CMOS camera (model: DCC3260M). To form a Moire FSS, we employed two identical PE-based FSSs positioned as close as possible to each other. It should be recalled that two PE-based samples were arranged such that the conductive ink parts touched one another, and on the two exterior surfaces are PET substrates. The alignment of the two printed samples was also performed using a 2f imaging system, with one held fixed in one sample holder and the other with a rotatable mount to rotate at some fixed angles. The respective Moire patterns obtained for 10\({}^{\circ}\), 20\({}^{\circ}\), and 30\({}^{\circ}\) angle rotations with the printed samples are shown in Figure 6a-c, respectively. It can be seen that the simulated and experimental images are consistent and quite similar (e.g., see between Figures 4a-d and 6a-c). In the following step, the normalized transmissions for various rotation angles were measured by using two PE-based THz FSSs (shown in Figure 6d). At 0.22 THz, we extracted the normalized transmission for 0\({}^{\circ}\), 10\({}^{\circ}\), 20\({}^{\circ}\), and 30\({}^{\circ}\) rotation angle and obtained 90\(\%\), 66\(\%\), 53\(\%\), and 58\(\%\), respectively. Their respective modulation depths were calculated using Equation (6). Furthermore, from Figure 6d, it can be seen that as the rotation angle changed from 0\({}^{\circ}\) up to 30\({}^{\circ}\), significant variations in the transmission and modulation depths were observed. The lowest transmission of an incident THz wave obtained at 0.22 THz for the 20\({}^{\circ}\) rotation angle was 53\(\%\), corresponding to a maximum modulation depth of 41\(\%\). Additionally, for the 10\({}^{\circ}\) and 30\({}^{\circ}\) rotation angles the modulation depth was calculated as 26\(\%\) and 35\(\%\), respectively. It can be seen that our experimental results show some deviations from the simulation results.