## 3 Structural Design and Numerical Analysis
What's more, the distance between the two intersections is much larger, as seen from Figure 6c,d. Thus, it can be seen that \(n_{3}\) and \(d_{3}\) mainly adjust the number of intersection points of the \(K\) values of both the compensated MSF and SMF. The variation of dispersion and \(K\) values with \(\Lambda\) is shown in Figure 3.3 As seen from Figure 7a, when \(\Lambda\) increases, the Re[\(n_{\text{eff}}\)] of the inner and outer core becomes larger, which makes \(\lambda_{\text{p}}\) move to a longer wavelength and the negative dispersion slowly decrease. The two intersections of the \(K\) values of both the compensated MSF and SMF are red-shifted. What's more, the distance of the two intersections is much larger, and the \(K\) value increases gradually at the intersection, which is observed in Figure 7b. It can be seen that \(\Lambda\) mainly roughly adjusts negative dispersion and \(K\) value. Through optimizing MSF structural parameters, an ultra BDC-MSF with compensation bandwidth of up to 190 nm is proposed when the parameters are \(n_{1}\) = 1.467, \(n_{2}\) = 1.382, \(n_{3}\) = 1.326, \(d_{1}\) = 2.15 \(\upmu\)m, \(d_{2}\) = 0.51 \(\upmu\)m, \(d_{3}\) = 0.84 \(\upmu\)m, and \(\Lambda\) = 1.55 \(\upmu\)m. From Figure 8a,b, the variation of dispersion, \(K\) value, and residual dispersion after dispersion compensation by using the designed MSF is known. Figure 3.4 Variation of dispersion (**a**) and \(K\) value (**b**) with \(\Lambda\). The ADCM is 18.45 times, and the change range of \(\rm D_{R}\) is controlled within \(\pm\)0.72 ps/(nm\(\cdot\)km) when the wavelength varies from 1385 nm to 1575 nm. As we know, the confinement loss and bend loss of MSF can be controlled effectively by increasing the layer number, therefore the loss curve is not given. The effective mode area of the designed MSF and splice loss with standard SMF are listed in Figure 3.5  
According to Equation (9), the parameter affecting the splice loss is the radius of mode field of the fiber, and the radius of mode field is decided by the core diameter of the fiber. Different types of commercially available fibers have different core diameters. However, the core diameter is generally controlled in the range of 8-11 \(\upmu\)m. Table 2 shows the splice loss of the designed MSF and commercially available fibers with different core diameters at 1550 nm. From Table 2, there is a low splice loss between the designed MSF and commercially available fibers of different core diameters. Table 3 shows the comparison results for compensation bandwidth, ADCM, and \(\rm D_{R}\) of the proposed and the reported BDC-MSF. From Table 3, the proposed BDC-MSF not only has wider compensation bandwidth and higher compensation multiple, but also has the advantages of low residual dispersion and easy fabrication. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Wavelength (nm)** & **1385** & **1460** & **1530** & **1550** & **1565** & **1575** \\ \hline \(\rm A_{eff}\) (\(\upmu\)m\({}^{2}\)) & 6.66 & 8.15 & 11.56 & 13.40 & 15.21 & 16.68 \\ \(L_{\rm splice}\) (dB) & 4.63 & 3.95 & 2.83 & 2.39 & 2.06 & 1.81 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The effective mode area of designed MSF and splice loss with standard single-mode fiber (SMF). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Ref.** & **Compensation Bandwidth (nm)** & **ADCM** & \(\rm\bf D_{R}\) (ps/(nm\(\cdot\)km)) & **Optical Fiber Structure** \\ \hline
[2] & 170 & 17.6 & \(\pm\)1.6 & air hole-quartz DCC structure \\ \hline
[8] & 200 & Not mentioned & Not mentioned & air hole-quartz DCC structure \\ \hline
[12] & 105 & 15.43 & \(\pm\)0.15 & all-solid DCC structure \\ \hline This work & 190 & 18.45 & \(\pm\)0.72 & all-solid DCC structure \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The splice loss of designed MSF and commercially available SMF with different core diameters at 1550 nm. Figure 8: Dispersion and \(K\) value (**a**) as well as \(\rm D_{R}\) after compensation by using designed microstructure fiber (MSF) (**b**) with wavelength.