## 4 Results and Discussions
Similarly, the values of the parameters for Mixture 1825 LC were found to be \(\sim\)1.56, \(\sim\)1.96, and \(\sim\)0.4, respectively, in the frequency range of 0.4-1.2 THz. In this case, we achieved a slightly higher \(\Delta\)n of approximately 0.4 as compared with the reported value of 0.387 at 1 THz by [PERSON] et al. [28], which may be attributed to the different batch production and a more accurate analysis. The \(\Delta n\) values indicate that the thickness of the LC phase shifter could be reduced to a half with the use of Mixture 1825 instead of MDA-00-3461 to achieve the same phase shift. The THz absorption coefficients for both ordinary (\(\alpha_{\mathrm{o}}\)) and extraordinary (\(\alpha_{\mathrm{e}}\)) rays for MDA-00-3461 and Mixture 1825 LC are shown in Figure 4c. The coefficients \(\alpha_{\mathrm{o}}\) and \(\alpha_{\mathrm{e}}\) of MDA-00-3461 LC are estimated to be \(\sim\)1 cm\({}^{-1}\) and \(\sim\)6.6 cm\({}^{-1}\), respectively, at 1.2 THz. In contrast, \(\alpha_{\mathrm{o}}\) and \(\alpha_{\mathrm{e}}\) of Mixture 1825 LC are higher and estimated to be \(\sim\)9.7 cm\({}^{-1}\) and \(\sim\)11.2 cm\({}^{-1}\), respectively, at 1.2 THz. We also evaluated the THz frequency-dependent extinction coefficients (\(\kappa\)) for ordinary (\(\kappa_{\mathrm{o}}\)) and extraordinary (\(\kappa_{\mathrm{e}}\)) rays of both LCs as shown in Figure 4d. In comparison with MDA-00-3461, Mixture 1825 exhibits larger absorption or extinction coefficients and a slightly frequency-dependent nonlinear behavior. Our demonstration of an MDA-250 TN-LC phase shifter confirms the reliability of high-transmittance pristine PEDOT: PSS as TCEs. We plotted the phase shift as a function of frequency at four different voltages in Figure 5a. The experimental data can be well fitted by linear lines. The slopes of these fitting curves gradually increase with increasing applied voltages. For the phase shifter based on MDA-250, the slope of the linear fitting curves varies from 6.38/\(\mathrm{THz}\) to 42.1/\(\mathrm{THz}\) as the applied voltage is ramped from 0.7 to 70.7 V\({}_{\mathrm{RMS}}\). We plotted the phase shift as a function of applied voltage at four different THz frequencies in Figure 5b. Theoretical curves according to Equation (1) are also shown. The results indicate that theoretical predictions of phase shifts fit the experimental data well for applied voltages from 0 to 70 V\({}_{\mathrm{RMS}}\). A phase shift of 45\({}^{\circ}\) at 1.2 THz can be achieved with a driving voltage (V\({}_{\mathrm{D}}\)) as low as 5.2 V\({}_{\mathrm{RMS}}\). The threshold voltage (V\({}_{\mathrm{TN}}\)) determined from the experimental data is approximately 0.5 V\({}_{\mathrm{RMS}}\). Figure 4: THz optical constants \(\mathrm{n_{e}}\), \(\mathrm{n_{o}}\), and \(\Delta\)n for (**a**) MDA-00-3461 and (**b**) Mixture 1825 LC. The (**c**) absorption (\(\alpha\)) and (**d**) extinction (\(\kappa\)) coefficients represent both types of LC molecules. Next, we investigated MDA-550 TN-LC phase shifters in order to evaluate the performances of such devices to achieve a 90\({}^{\circ}\) phase shift at \(\sim\)1.2 THz using pristine PEDOT: PSS as TCEs layers. The phase shift as a function of the THz frequency at four different voltages is shown in Figure 6a. In addition, we present the phase shift as a function of the applied voltage at four different THz frequencies as shown in Figure 6b. For the phase shifter based on MDA-550, the slope for linear fit varies from 5.02/THz to 79.6/THz as the applied voltage is ramped from 1.4 to 70.7 V\({}_{\text{RMS}}\). We can achieve a 90\({}^{\circ}\) phase shift at 1.2 THz with a V\({}_{\text{D}}\) of approximately 7.9 V\({}_{\text{RMS}}\). The experimentally determined V\({}_{\text{TN}}\) is 0.7 V\({}_{\text{RMS}}\). The slightly higher V\({}_{\text{D}}\) and V\({}_{\text{TN}}\) for the MDA-550 device in comparison with the MDA-250 TN-LC phase shifter is ascribed to the increase in misalignment of LC molecules and the decrease in the electric field strength with the increasing thickness of the cell.