# Electrically Tunable Propagation Properties of the Liquid Crystal-Filled Terahertz Fiber
## 3 Results and Discussion
### Guided-Mode Properties of the Designed THz LC-MOF  
Although position of the PBGs and the maximum transmission bandwidth (\(\Delta\)F = F\({}_{\rm H}\) \(-\) F\({}_{\rm L}\)) can be estimated from the bandgap diagram of the infinitely cladding structure, 3 dB bandwidth of the bandgap-guiding MOF is narrower than \(\Delta\)F. It is necessary to study guided mode properties of the designed THz LC-MOF. Lower panels in Figure 3 show mode profiles and transverse electric-field distributions (arrow diagram) of the fundamental modes. Figure 3i, ii is the mode profile of HE\({}_{\rm 11x}\) at the central frequency of the first and second x-polarization PBGs, respectively. It can be seen that the second PBG provides better confinement for the guided mode than the first PBG. Figure 3 iii, iv is the mode profile of HE\({}_{\rm 11y}\) at the central frequency and high-frequency edge of the first y-polarization PBG, respectively. It can be found that the bandgap effects confined most energy of the guided mode in the fiber core around the central frequency of the bandgap, but the fundamental mode is diffused in cladding region with the guided frequency approaching the bandgap edge, which leads to increasing transmission loss, as explained blow.  
Figure 4 shows the fraction of core (with radius of \(\Lambda/\sqrt{3}\)) confined energy for the HE\({}_{\rm 11x}\) within the first and second x-polarization PBGs (solid red lines), and HE\({}_{\rm 11y}\) within the first y-polarization PBG (dashed blue line). Comparing Figures 3 and 4, it can be found that the maximum (more than 60%) of the core confined energy fraction is near the central frequency of the relevant bandgaps. The core confined energy fraction decreases rapidly as the guided frequency approaches the bandgap edges. The power spreads to the cladding (especially to the first ring of LC inclusions, which has much higher material loss than Topas [11; 17], as shown in Figure 3 iv) and escapes from the entire structure when it disappears from the core. This leads to high absorption loss and confinement loss (see Section 3.4). So, the fraction of core confined energy of the fundamental mode against frequency could provide a qualitative estimation of the fiber's transmission spectrum.  
The guided mode is considered to be cut off when the core confined energy is reduced to half of its maximum value. There are two distinct frequency regions where single-mode single-polarization guidance occurred, as the shaded regions show in Figure 4. Between the first and second x-polarization PBGs, the x-polarized fundamental mode also had a minimum of the core confined energy around the normalized frequency F = 2.2. The experimental results of [PERSON] et al. [20] and [PERSON] et al. [36] show that the spectral dip (corresponding to the resonant frequency of the individual high-index inclusion) is consistent with the frequency region between two adjacent bangaps. So, the minimum of the core confined energy between the first and second x-polarization PBGs would give rise to a spectral dip of the x-polarized fundamental mode for the designed THz LC-MOF. This spectral dip can be utilized for making tunable optical filters [37; 38].