## 4 Results and Discussions
The loss is mainly contributed by fused silica substrates and the LC itself [8]. Figure 8: THz transmittance of three types of TN-LC phase shifters at 0 V\({}_{\text{RMS}}\). The experimental data (symbol) are verified by theoretical calculation (solid line), as shown in the inset. Figure 7: Phase shift properties as a function of (**a**) frequency for several values of applied voltage and (**b**) applied voltage at selected frequencies for a Mixture-250 TN-LC-based THz phase shifter. The slope of the linear line fitting experimental data is denoted by m. The circles, squares, diamonds, and triangles are experimental data. The solid line, dash line, dot line, and dash–dot line are (**a**) linear fit and (**b**) theoretical curves. Previously, several THz phase shifters which incorporated electrodes based on graphene, ITO-NW, and metal/porous graphene combination have been demonstrated [9; 11; 29]. Most of the works were carried out with a homogeneously aligned LC cell. The experimentally determined threshold voltages for LC THz phase shifters with monolayer graphene, bilayer graphene, and ITO-NW as TCEs were 1.3, 1.25 and 1.7 V\({}_{\text{RMS}}\), respectively. These are much higher than that of the present TN-LC phase shifter (approximately 0.5 V\({}_{\text{RMS}}\)). In addition, most of the THz phase shifters reported have shown much higher THz transmittance loss, for example, the transmittance was in the range of 55 to 20% for devices with nanostructured TCEs at THz frequencies, even though low-absorption-type LCs such as E7 or MDA-00-3461 have been used. This indicates that TCE layers play a vital role in determining THz transmittance loss experienced by the phase shifters. Moreover, many of these TCEs have some disadvantages (e.g., requiring complex processing steps and/or costly fabrication processes). In contrast, PEDOT: PSS can be fabricated by a simple spin coating method, which can significantly reduce the processing time and cost. Previously, [PERSON] et al. [11] demonstrated a homogeneously aligned LC-based THz phase shifter using DMSO-doped PEDOT: PSS as a TCE layer and achieved a 90\({}^{\circ}\) phase shift with a V\({}_{\text{D}}\) of \(\sim\)2.5 V\({}_{\text{RMS}}\). This is much lower than for our Mixture-250 TN-LC device (7 V\({}_{\text{RMS}}\)). However, their proposed phase shifter exhibited a higher threshold voltage of approximately 1.4 V\({}_{\text{RMS}}\) in comparison with that for our Mixture-250 TN-LC device (0.5 V\({}_{\text{RMS}}\)). Additionally, the DMSO-doped PEDOT: PSS phase shifter exhibited transmittance loss of nearly 95%, substantially higher than those of devices reported in this work. Note that there is a difference in frequency ranges for Figures 3-8 for devices using the two LCs. This arises from the relatively high absorption of the Mixture 1825 liquid crystal at low THz frequencies. From 0.2 to 0.4 THz, the absorption of Mixture 1825 is very high. As a result, the signal-to-noise ratio of the THz spectroscopic data is not very good. Therefore, authors are not able to get a reliable value for the THz optical constants of Mixture 1825 and accurately evaluate phase shifting properties for devices using Mixture 1825 in this band. For discussing the performance of all types of TN-LC phase shifters, particularly previously reported homogeneously aligned LC phase shifters, we introduce a figure of merit (FOM) defined by the following:  
\[\text{FOM}=\Delta\Phi_{\text{max}}/(\text{L}_{\text{dB}}\times\text{V}_{ \text{D-FOM}}), \tag{5}\]  
where \(\Delta\Phi_{\text{max}}\) is the maximum phase shift with corresponding driving voltage (V\({}_{\text{D-FOM}}\)) and L\({}_{\text{dB}}\) is the transmittance loss of the phase shifter without the bias voltage at 1 THz. The calculated values of the FOM for several devices are summarized in Table 2.  
The highest FOM value of approximately 6.65 degree-dB\({}^{-1}\cdot\)V\({}^{-1}\) is associated with the Mixture-250 TN-LC-based THz phase shifter.