## 4 Results and Discussions
We also constructed a Mixture-250 TN-LC phase shifter with a 250 \(\upmu\)m thickness of mixture 1825 LC layer. The phase shift achieved by the device at four different voltages are shown in Figure 7a. The slope of linear fitting curves varies from 2.02/THz to 81.4/THz as the applied voltage is ramped from 1.4 to 70.7 V\({}_{\text{RMS}}\). The maximum slope achieved is approximately 81.4 at the applied voltage 70 V\({}_{\text{RMS}}\), which is much higher in comparison with those for the MDA-250 and MDA-550 TN-LC phase shifters. This is expected because of the high birefringence of Mixture 250. We also plotted the phase shift as a function of applied voltage at four different THz frequencies as shown in Figure 7b. There occurred a phase shift greater than 90\({}^{\circ}\) at the frequency of 1.2 THz with a V\({}_{\text{D}}\) of approximately 7 V\({}_{\text{RMS}}\). The experimentally determined V\({}_{\text{TN}}\) of this phase shifter is 0.5 V\({}_{\text{RMS}}\). The experimental  
Figure 5: Phase shift properties as a function of (**a**) frequency for several values of applied voltage and (**b**) applied voltage at selected frequencies for an MDA-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. Figure 6: Phase shift properties as a function of (**a**) frequency for several values of applied voltage and (**b**) applied voltage at selected frequencies for an MDA-550 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. data also agree well with theoretical data that have been predicted. In addition, this work is the first to demonstrate TN-LC-based THz phase shifters using such LCs with higher birefringence. Previously, [PERSON] et al. [11] demonstrated a phase shifter with DMSO-doped PEDOT, which exhibited higher conductivities than pristine PEDOT films. However, we found that the electrical conductivity of pristine PEDOT: PSS is suitable enough to operate 90\({}^{\circ}\) THz phase shifters. THz transmittance values of MDA-250, MDA-550, and Mixture-250 TN-LC phase shifters are shown in Figure 8. The average THz transmittance of the MDA-250 device is as high as 80% at 0.2 THz and shows a decreasing trend with frequency, down to \(\sim\)30% at 1.2 THz. The observed behavior can be explained by the frequency-dependence of absorption and the interface reflection of the components of the device, namely, LC, fused silica substrates, PEDOT: PSS, and polyimide alignment layers. The inset in Figure 8 shows the theoretical transmittance curve for the MDA-250 device, which is in good agreement with the experimental data. The transmittance of MDA-550 and Mixture-250 devices show similar trends. The theoretically calculated transmittance values for MDA-550 and Mixture-250 TN-LC THz phase shifters are 64.5% and 62.8%, respectively, at 1 THz. This is very close to our experimental data of Mixture-250 devices at 1 THz (i.e., 62%). The theoretical and experimental transmittance of the MDA-250 device is superior, being \(\sim\)73% at 1 THz. Overall, the loss experienced by our devices compares favorably with THz phase shifters previously reported [8; 9; 10; 11]. Moreover, we can attribute the gradually decreased transmittance in the THz frequency range to the strong frequency-dependent transmittance of fused silica substrates. This has been described in our previous work [8]. By considering the structure described in Figure 1 and combining the complex permittivities (and refractive indices) of pristine PEDOT: PSS, fused silica, and liquid crystals, we can estimate the loss caused by different interfaces.