## 3 Structural Design and Numerical Analysis
Figure 1: Cross-section and equivalent Re[\(n_{\text{eff}}\)] profile of all-solid dual-concentric-core microstructure fiber (DCC-MSF). What's more, if either the distance of the two intersections or the difference of the \(K\) values is large, it is difficult to realize BDC. Therefore, in order to realize the BDC, regulating the dispersion and \(K\) value is necessary. When the Re[n\({}_{\text{eff}}\)] of the two modes is much closer, coupling can occur more easily. According to the mode coupling theory, this indicates that complete coupling occurs, and the coupling strength is much stronger. The effect of MSF structural parameters on \(\lambda_{\text{p}}\), dispersion, and the \(K\) value was studied, as shown from Figures 4-7. Figure 4: Variation of dispersion with \(n_{1}\) (**a**) and \(d_{1}\) (**b**). Figure 3: Variation of \(K\) value with wavelength. Figure 2: Variation of Re(n\({}_{\text{eff}}\)) (**a**) and dispersion (**b**) with wavelength, the illustration is the mode field distribution of the fundamental and second-order supermode at different wavelengths. Figure 5: Variation of dispersion (**a**), (**b**) and \(K\) value (**c**), (**d**) with \(n_{2}\) and \(d_{2}\), respectively. Figure 6: Variation of dispersion (**a**), (**b**) and \(K\) value (**c**), (**d**) with \(n_{3}\) and \(d_{3}\), respectively. The variation of dispersion with \(n_{1}\) and \(d_{1}\) is shown in Figure 3.0 With \(n_{1}\) increasing, the Re[\(n_{\text{eff}}\)] difference between the inner and outer core increases, and \(\lambda_{\text{p}}\) shifts to a longer wavelength. Meanwhile, the negative dispersion value decreases gradually, as observed from Figure 4a. As \(d_{1}\) becomes bigger, \(\lambda_{\text{p}}\) moves to a longer wavelength. At the same time, the negative dispersion value also decreases gradually, as shown in Figure 4b. Because the variation of \(n_{1}\) and \(d_{1}\) has an important impact on \(\lambda_{\text{p}}\) and the negative dispersion value, the \(K\) value changes greatly if the calculation formula of the \(K\) value is adopted under these conditions. This will mean that the condition of BDC is not met, so the variation of the \(K\) value with \(n_{1}\) and \(d_{1}\) is not given. In order to obtain a better \(K\) value, the appropriate \(n_{1}\) and \(d_{1}\) are chosen first during parameter selection process. The variations in dispersion and \(K\) values with \(n_{2}\) and \(d_{2}\) are shown in Figure 3.1 As seen from Figure 5a,b, with increasing \(n_{2}\), the Re[\(n_{\text{eff}}\)] difference between the inner and outer core increases, and \(\lambda_{\text{p}}\) shifts to a longer wavelength. At the same time, the negative dispersion value decreases slowly. The increase of \(d_{2}\) makes \(\lambda_{\text{p}}\) shift to a longer wavelength and the negative dispersion value also decreases gradually. Under the two conditions, the intersection of the \(K\) value of both the compensated MSF and SMF shifts to a longer wavelength, and the \(K\) value increases gradually, as seen in Figure 5c,d. It can be seen that \(n_{2}\) and \(d_{2}\) mainly fine-tune negative dispersion and the \(K\) value. The variation of dispersion and \(K\) value with \(n_{3}\) and \(d_{3}\) is shown in Figure 3.2 When \(n_{3}\) decreases, the Re[\(n_{\text{eff}}\)] between the inner and outer core decreases simultaneously, which causes \(\lambda_{\text{p}}\) to have a slight change, and the negative dispersion value to become obviously large, as seen in Figure 6a,b. The increase of \(d_{3}\) also causes \(\lambda_{\text{p}}\) to have a slight change, and the negative dispersion value to distinctly increase. Under the two conditions, the number of intersections between the \(K\) value curves of both the compensated MSF and SMF varies from zero to two. The intersection is blue-shifted and the \(K\) value gradually decreases at short wavelengths. However, the intersection is red-shifted and the \(K\) value gradually increases at long wavelengths.