## 3 Simulation and Discussion  
The proposed fiber is designed using COMSOL software, and the finer mesh is used in all regions to obtain more accurate results. The electric field distributions of the fundamental mode with water at 280 K and without water at 0.45 THz are shown in Figure 3. The electric field of the fundamental mode with water leaks less to the cladding than without water. Meanwhile, the fiber filled with water has most of the power guided in the core region, which leads to a lower loss. Thanks to the strong absorption characteristic of liquid water in the THz frequency region, this contributes to the stronger transverse resonant coupling between core modes and water defect modes. The effective mode area indicates the actual area covered by the propagating THz wave. The effective mode area of the proposed THz fiber can be calculated by [31]  
\[A_{eff}=\frac{\left[\iint{\left|E(x,y)\right|}^{2}dxdy\right]^{2}}{\iint{\left|E( x,y)\right|}^{4}dxdy} \tag{8}\]  
Figure 3: (**a**) The electric field distributions of the fundamental mode with water at 280 K (**b**) and without water at 0.45 THz. where \(E(x,y)\) is the electric field density distribution obtained by the eigenvalue for solving Maxwell's equations. Figure 4 shows the effective mode area with water at different temperatures. The effective mode area takes on two dips at about 0.38 THz and 0.62 THz, respectively. Dip1 and the peak of the effective modal area are formed by the transverse resonant coupling between core modes and defect modes. Dip2 is formed by the Bragg resonant. The more leakage of the THz wave into the cladding region produces a larger effective mode area. With the temperature of water rising from 280 K to 340 K, the dip1 of the effective mode area decreases from 280 K to 340 K; in contrast, the peak from 280 K to 340 K.  
The effective RI of the fundamental mode in the proposed fiber is shown in Figure 5. The real part of the effective RI of the proposed fiber is almost the same, from 280 K to 340 K. As shown in Figure 5b, in the range of the lower frequency, the imaginary part of effective RI decreases with increased frequency. The inset of Figure 5b shows that, with the frequency range of 0.4 THz to 0.5 THz, it displays a temperature effect. Among few limits in the fiber, the major loss is effective material loss (EML). EML arises from the background material. The hollow core can reduce the amount of the THz  
Figure 4: Effective mode area of the fundamental mode with water at different temperatures. Figure 5: (**a**) Real part and (**b**) imaginary part of the effective refractive index (RI) with water at different temperatures. The inset: detailed information of (**b**) ranging from 0.4 THz to 0.5 THz. wave absorbed by the background material in the core region, which may help reduce the EML. This loss of the proposed PCF can be expressed as [32]  
\[\alpha_{eff}=\sqrt{\frac{\varepsilon_{0}}{\mu_{0}}}\Bigg{(}\frac{\int_{mat}n_{ mat}|E|^{2}\alpha_{mat}dA}{\big{|}\int_{all}S_{z}dA\big{|}}\Bigg{)} \tag{9}\]  
where \(\varepsilon_{0}\) and \(\mu_{0}\) are the permittivity and permeability on the free space, respectively, \(n_{mat}\) is the RI of the photosensitive resin, \(\alpha_{mat}\) is the photosensitive resin absorption loss, \(E\) is the modal electric field component, and \(S_{z}\) is the \(z\) component of the Poynting vector \(S_{z}=0.5\cdot(E\times H^{*})\cdot z\) where \(H^{*}\) is a complex conjugate of the magnetic field component. Figure 6a indicates that EML is proportional to the operating frequency. It shows that the electric field is more strongly confined within the hollow core at the low-frequency region. Moreover, it has a temperature-insensitive EML. The core power fraction indicates the amount of power that propagates through the core region of a fiber. A higher core power fraction is desired in efficient THz wave transmission application.