## 2 Modeling, Fabrication, and Experimental Characterization of THz FSSs  
The FSS pattern designed in this work is similar to that reported recently in the GHz frequency range [39], but with dimensions of the air hole diameter and the distance between two holes much smaller to be suitable for THz applications. Real and microscopic images of the FSS based on PE and 3D printing are shown in Figure 1a,b, respectively. For the PE sample, they were printed on a flexible substrate using silver (Ag) nanoparticle ink (PFI-600, NovaCentrix, Austin, TX, USA) using an industrial roll-to-roll (R2R) continuous press with flexography printing units (OMET Varyflex, Lecco, Italy). With the R2R printer, a variety of plastic substrates are available, including polyethylene terephthalate (PET),polyethylene naphthalene (PEN), and polyimide (PI). The processing temperatures for PET, PEN, and PI are 150 \({}^{\circ}\)C (heat stabilized), 200 \({}^{\circ}\)C, and 360-400 \({}^{\circ}\)C, respectively [40]. PEN and PI can be more expensive when compared to the PET substrate. Since the printed FSSs were dried inline with hot air at a maximum temperature of 100 \({}^{\circ}\)C, this allows us to choose PET as the printing substrate, which is the cheapest available and most widely used substrate. The thicknesses of the FSS pattern and PET substrate were 352 nm and 125 \(\upmu\)m respectively, while the conductivity of the printed sample was 4.40 \(\times\) 10\({}^{6}\) S/m. The diameter of the sample's air hole was \(\sim\)600 \(\upmu\)m with a distance between the centers of the two air holes (the pitch) of \(\sim\)800 \(\upmu\)m, all covering an area of 40 \(\times\) 40 mm\({}^{2}\). A second FSS structure with the same air hole diameter and pitch size was fabricated using the 3D printing technique (printer model: MPL-1 from Nanogrande company). The main difference between the two types of fabrication is the presence of the PET substrate in the PE method while the 3D printing sample has no substrate. This one has simply a thickness of 100 \(\upmu\)m obtained by the selective fusion by laser on metal powder bed obtaining a conductivity of approximately 2.50 \(\times\) 10\({}^{7}\) S/m. To investigate the features of the fabricated FSSs, we employed a commercial continuous wave (CW) THz spectroscopy system (TERASCAN 1550 from TOPTICA photonics). The experimental setup is illustrated in Figure 1c. The terahertz emitter and receiver are based on an InGaAs photodiode and InGaAs photomixer, respectively. The radiated THz waves were collimated and refocused onto the detector by a pair of 2-inch diameter and 3-inch focal length off-axis parabolic mirrors. Note that in our experiment, we used a resolution of 50 MHz to resolve the characteristics of our analyzed BPF. To extract the normalized transmission characteristics of the PE-based and 3D-printed THz BPF, the following equation was applied:  
\[NT(\omega)=\left|\frac{T_{sample}(\omega)}{T_{ref}(\omega)}\right| \tag{1}\]  
where \(T_{sample}(\omega)\) and \(T_{ref}(\omega)\) are the transmission of the sample and reference, respectively. The experimental results of PE-based and 3D-printed FSS, accordingly, are shown with  
Figure 1: THz FSS (**a**) based on printable electronics using silver (Ag) ink and PET as a substrate; (**b**) based on 3D printing made from aluminum foil. (**c**) Experimental setup of CW THz spectroscopy. Here Tx, Rx, and OAP stand for transmitter, receiver, and off-axis parabolic mirror, respectively. a solid blue line in Figure 2a,b. It was observed from experimental measurements that PE-based filters offered a larger bandwidth covering from 130 to 380 GHz, as compared to the 3D-printed filter, which came in at 250 to 430 GHz (i.e., at FWHM). To confirm our experimental observation, we performed finite difference time domain (FDTD) simulations on both FSSs using Ansys Lumerical software to characterize the properties of the investigated FSSs.