## 3 Results and Discussion
### THz Imaging of LCP  
We demonstrated the THz polarization imaging of the LCP by using the THz DFG source. Since the THz emission from the THz DFG source was ultrabroadband, it was necessary to confirm the frequency dependency of the polarization properties of the THz beam from the DFG source. We obtained the frequency-dependency of the polarization properties by using frequency band pass filters with three different center frequencies. Figure 3 shows the polarization properties of the THz beam from the DFG source at each frequency (2.0 THz, 2.5 THz, and 3.0 THz, respectively). There was no noticeable difference in the polarization properties at each frequency. Considering the frequency-independency of the polarization properties of the THz beam and the constant birefringence across the frequency range, we could demonstrate polarization imaging without frequency filtering. We demonstrated imaging of LCP test objects having different liquid crystal orientations (\(\varphi=0^{\circ}\), \(45^{\circ}\) and \(90^{\circ}\)). Figure 4a shows a photograph of the test object and Figure 4b is a schematic illustration of the test object showing the direction of the liquid crystal orientation. As shown in Figure 4a, we could not find any difference in the liquid crystal orientation with visible light. Figure 5a shows a THz image obtained in the open-Nicol configuration. We found that the sample with the molecular long axis parallel, or the sample orthogonal to the polarizer axis (namely, \(\varphi=0^{\circ}\) and \(90^{\circ}\), respectively), had a relatively high transmission intensity, whereas the sample with the molecular long axis at an angle of \(45^{\circ}\), with respect to the polarizer axis (namely, \(\varphi=45^{\circ}\)), had a low transmission intensity. For \(\varphi=45^{\circ}\), the THz beam was attenuated by the analyzer because of the elliptical polarization induced by the birefringence of the LCP sample. In contrast, for \(\varphi=0^{\circ}\) and \(90^{\circ}\), the THz transmission intensity was not attenuated by the analyzer because the THz beam was linearly polarized parallel to the transmission axis of the analyzer. Figure 2: (**a**) Refractive index and (**b**) absorption coefficient of liquid crystal polymer sample. Figure 5b shows the THz image obtained in the cross-Nicol configuration. We found that the transmission image of the sample rotated by 45\({}^{\circ}\) (\(\varphi\) = 45\({}^{\circ}\)) and was detectable, whereas the transmission images of the sample for 0\({}^{\circ}\) and 90\({}^{\circ}\) (\(\varphi\) = 0\({}^{\circ}\) and 90\({}^{\circ}\), respectively) vanished. For \(\varphi\) = 45\({}^{\circ}\), the THz beam could pass through the analyzer because of the elliptical polarization induced by the birefringence of the LCP sample. In contrast, for  
Figure 4: (**a**) Photograph of test object. (**b**) Schematic illustration of test object showing direction of liquid crystal orientation. Figure 5: (**a**) THz image obtained in open-Nicol configuration. (**b**) THz image obtained in cross-Nicol configuration. Figure 3: Terahertz polarization properties at each frequency, obtained using 2.0 THz, 2.5 THz, and 3.0 THz bandpass filters (FB19M150, FB19M120 and FB19M100, respectively, Thorlabs, Inc., Newton, MA, USA). \(\varphi\) = 0\({}^{\circ}\) and 90\({}^{\circ}\), the THz wave could not pass through the analyzer because the THz beam had a linear polarization orthogonal to the transmission axis of the analyzer. The observed transmission intensity of the birefringent material is explained by its phase shift and rotation angle. The phase shift \(\delta\) is written as:  
\[\delta=\frac{2\pi}{\lambda}\cdot\Delta n\cdot h \tag{1}\]  
where \(h\) is the thickness of sample, \(\lambda\) is the wavelength of light, and \(\triangle n\) is the birefringence.