## 4 Results and Discussions  
The frequency-dependent transmittance of pristine PEDOT: PSS layers with three different thicknesses in the THz frequency band are shown in Figure 3a. It can be seen that the best THztransmittance is achieved for a pristine PEDOT: PSS layer spin-coated at a speed of 3000 rpm, with a thickness of approximately 1 \(\upmu\)m, confirmed by a cross-sectional image obtained by field emission scanning electron microscope (FESEM) (see Figure 3b). This sample exhibited an average THz transmittance as high as 92% and a relative flat response across a wide frequency range of 0.2-1.2 THz. The FESEM cross-sectional images of films spin-coated at 2000 and 4000 rpm are similar to those shown in Figure 3b. The apparent fluctuation in THz transmittance for thinner (<1 \(\upmu\)m) pristine PEDOT: PSS layers as shown in Figure 3a is possibly caused by the scattering effect at the interface of the film and the substrate, especially at the higher THz frequency [26]. Although we cannot provide a quantitative analysis on this conjecture, scattering could arise from a variation in the surface morphology of the thinner films. On the other hand, a pristine PEDOT: PSS layer with a thickness greater than 1 \(\upmu\)m (>1 \(\upmu\)m) showed a somewhat lower average transmittance of approximately 85% at the frequency range of 0.2-0.7 THz. The transmittance gradually decreased to less than 60% for f >0.7 THz. This is tentatively attributed to the slow-varying broad-band frequency-dependent absorption of the pristine PEDOT: PSS layer, which becomes significant for thicker films. Based on the observations above, we chose the 1 \(\upmu\)m thick pristine PEDOT: PSS layer for THz phase shifter applications as TCEs. We note that the present 1 \(\upmu\)m thick pristine PEDOT: PSS layer exhibits a much higher THz transmittance as compared with published reports [14; 15]. It is possible that different manufactured batches of pristine PEDOT could have subtle differences in the THz optical properties. Further analysis is needed to ascertain the observed phenomena. In addition, the THz transmittance achieved is much higher than those for DMSO- and EG-doped PEDOT: PSS thin layers, where their thicknesses are only approximately 31 and 34 nm, respectively [14; 15]. In this study, we chose two LCs: MDA-00-3461 from Merck and Mixture 1825 proposed by [PERSON] et al. [27; 28]. The former is readily available and affordable. The latter exhibits birefringence almost twice as high as the former. As it is well known, LCs with high birefringence offer possibilities for greater tenability and more functionalities. However, other issues, such as transparency in the THz frequency range and dynamic responses, must be considered. Therefore, we constructed LC THz phase shifters using both types of LCs for a comparative study. Figures of merit for LC THz phase shifters, defined in a later section, were used to facilitate the selection of LCs for THz device applications. As we shall see, higher-birefringence LCs do not offer decisive advantages over LCs with somewhat lower ones. The THz optical constants \(n_{\text{o}}\), \(n_{\text{e}}\), and \(\Delta n\) of MDA-00-3461 and Mixture 1825 LC are shown in Figure 4a,b, respectively. We determined that the \(n_{\text{o}}\), \(n_{\text{e}}\), and \(\Delta n\) for MDA-00-3461 LC were \(\sim\)1.53, \(\sim\)1.73, and \(\sim\)0.2, respectively, and were relatively frequency-independent in the frequency range of 0.2-1.2 THz. Such results are in agreement with those obtained in our previous work (\(n_{\text{o}}\sim\)1.54, \(n_{\text{e}}\sim\)1.74,  
Figure 3: (**a**) THz transmittance of pristine PEDOT: PSS layers with three different thicknesses controlled by the rotation speed of the spin coater and (**b**) FESEM cross-sectional image of the 1 \(\upmu\)m thick pristine PEDOT: PSS layer deposited on clean substrate by spin coating with a rotation speed of 3000 rpm for 30 s.  
and \(\Delta n\) \(\sim\)0.2 in the frequency range of 0.3-1.4 THz) [27].