# Electrically Tunable Hydrogen-Bonded Liquid Crystal Phase Control Device
## 3 Results and Discussions
The solid line in Figure 6 shows the calculated results of the terahertz transmittance by using the Jones matrix calculation. We set the parameters as follows: \(\Psi_{P}=\Psi_{A}=0^{\circ}\), \(d=800\)\(\upmu\)m. The calculation data showed a good fit with the experimental data when we set \(\Delta n=0.17\), \(n_{e}^{\prime\prime}=0.022\), and \(n_{o}^{\prime\prime}=0.060\). In this study, we took into account the attenuation of the two substrates by setting the absorption coefficient of the quartz substrates at \(\alpha_{s}=0.5\) cm\({}^{-1}\). This value was consistent with the reported value [36], and the transmittance decreased by 95% when the thickness of each substrate was 500 \(\upmu\)m.  
Table 1 shows the birefringence, absorption coefficients, and dielectric anisotropy of LC1. In the case of LC1, which consisted of hydrogen bonding, \(\alpha_{e}\) and \(\alpha_{o}=37\) cm\({}^{-1}\) and \(\Delta n=0.17\) at 2.5 THz. Here we also show the reported values of birefringence, absorption coefficients, and dielectric anisotropy for several LCs from References [8; 12; 22; 32; 33]. The birefringence of LC1 at 2.5 THz was not remarkably high compared to the LCs shown in Table 1. In addition, absorption coefficients of LC1 were slightly high or nearly the same as reported values of 2.5 THz in Table 1. It should be noted that the absorption coefficients \(\alpha_{e}\) and \(\alpha_{o}\) of the hydrogen-bonded LCs were almost of the same value. Since the hydrogen-bonded LC exhibits nondichroism, it is easy to design terahertz control devices the same way as with Si or other nondichroism materials [2; 3; 4; 5; 6; 7]. On the other hand, the dielectric anisotropy of LC1 was 0.6, and this value was smaller than that of common LCs used for other terahertz applications. This result indicates that rise time (the switching time between off-state and on-state) of the LC phase shifter became slow compared to the cases of using the other LCs, as seen  
Figure 6: Experimental and calculation terahertz transmittance of LC1 at 2.5 THz. in Table 1. We did not measure the relaxation time (the switching time between on-state and off-state), but we confirmed that the response of the LC1 phase shifter was almost same as with the case of E44. We believe that introduction of a reflection structure [30], a polymer-stabilized LC [17], and an electrospun nanofiber [31] is effective in improving the relaxation time of the LC1 phase shifter. More detailed measurements are in progress to characterize the broadband terahertz optical properties of the hydrogen-bonded LC. Figure 7 shows the simulation results of the polarization condition of the transmitted terahertz wave calculated by using the Jones matrix method. The transmitted terahertz wave polarization condition just after the LC phase shifter is displayed. We set the parameters as follows: \(\Psi_{p}=45^{\circ}\), \(\Psi_{i}=0^{\circ}\), \(d=800\)\(\mu\)m, and \(\lambda=117.7\)\(\mu\)m. Figure 7 shows the polarization conditions for retardation when \(R=\Delta nd=\lambda\), \(\lambda/2\), and \(\lambda/4\), which correspond to phase shifts of \(360^{\circ}\), \(180^{\circ}\), and \(90^{\circ}\), respectively. Figure 7a shows the calculation results without losses for the ideal case. In this instance, the output terahertz wave was linearly polarized at \(R=\lambda\) and \(R=\lambda/2\) and was circularly polarized at \(R=\lambda/4\). As shown in Figure 7a, the direction of the electric fields corresponded to the input terahertz wave at \(R=\lambda\) and is \(90^{\circ}\) rotated from input terahertz wave at \(R=\lambda/2\). Figure 7b,c shows the calculation results by using LC losses, as shown in Table 1. In the case of LC1, the intensity of the output became lower, but a \(\pm 45^{\circ}\) linearly polarized terahertz wave was obtained at \(R=\lambda\) and \(\lambda/2\). Conversely, since E44 exhibited dichroism at 2.5 THz, the direction of the output linear polarized terahertz wave deviated from \(\pm 45^{\circ}\) at \(R=\lambda\) and \(\lambda/2\), as shown in Figure 7c.