## 3 Simulation and Discussion
The core power fraction can be expressed by [33]  
\[\eta=\frac{\int_{i}S_{z}dA}{\int_{all}S_{z}dA} \tag{10}\]  
where \(\eta\) is the mode core power fraction, and the \(z\) component of the Poynting vector of the numerator is integrated over the hollow-core region, but the integral range of the denominator is integrated over the entire cross-section region. As shown in Figure 6b, the core power fraction is greater than 98%. It represents that more than 98% of power propagates through the core region over the whole range of the frequency. As shown in the inset of Figure 6b, the core power fraction increases with the temperature rising within the range of 0.4 THz to 0.5 THz because a stronger interaction is induced between the THz wave and the liquid water. The confinement loss indicates how much the THz wave leaks from the core region to the cladding when the THz wave propagates through a fiber. The rise of the core and the number of layers lying in the cladding may lead to the leakage of the THz wave. According to the imaginary of the complex RI, the confinement loss can be quantified using the following expression [6]  
\[\alpha_{CL}=8.686\times\frac{2\pi f}{c}\text{Im}\Big{(}n_{eff}\Big{)} \tag{11}\]  
Figure 6: (a) EML; (b) core power fraction with water at different temperatures. The inset: zoomed-in core power fraction. where Im\(\left(n_{eff}\right)\) is the imaginary of the effective RI. The confinement loss is shown in \[A_{eff}=\frac{\left[\iint{\left|E(x,y)\right|}^{2}dxdy\right]^{2}}{\iint{\left|E( x,y)\right|}^{4}dxdy} \tag{8}\]0 It can be observed that a lower confinement loss can be obtained at a frequency of more than 0.4 THz. The inset of Figure 7 shows that the frequency range of 0.4 THz to 0.5 THz exhibits an obvious temperature dependence. The THz wave tends to propagate through materials with a higher RI, and water at high temperatures has a high RI, which causes the lower confinement loss. With an increase in the temperature of liquid water, the change trends of the confinement loss at the dip and at 0.45 THz frequency are shown in Figure 8, respectively. The symbols are the simulated data, and the dotted lines are the linear fitting curves. It is apparent that the confinement loss at the dip and at 0.45 THz are both in linear inverse proportion to the temperature. The temperature sensitivity is obtained at 0.09614 dB\(\cdot\)m\({}^{-1}\)/K at 0.45 THz, and the coefficient of determination reaches 0.99465. The proposed THz fiber can be fabricated by the 3D printing stereolithography (SLA) technique with the advantages of flexible design, fast fabrication, low cost, and convenient applications [14, 15]. Liquid water is circulated flowing in the defect layer in the fiber cladding to maintain the same temperature. \[A_{eff}=\frac{\left[\iint{\left|E(x,y)\right|}^{2}dxdy\right]^{2}}{\iint{\left|E( x,y)\right|}^{4}dxdy} \tag{8}\]1 Temperature dependence of the confinement loss at the dip and at 0.45 THz. \[A_{eff}=\frac{\left[\iint{\left|E(x,y)\right|}^{2}dxdy\right]^{2}}{\iint{\left|E( x,y)\right|}^{4}dxdy} \tag{8}\]2 Confinement loss with water for various temperatures. The inset: the detailed information of the confinement loss ranging from 0.4 THz to 0.5 THz.