## 4 Structural Parameter Influence on the Dispersion  
To obtain the six-core TA-MCF with wideband nearly zero flattened dispersion, the structural parameter influence on the dispersion of the fundamental supermode were studied, as shown in in Figure 6. The TA-MCF with \(n_{0}=1.45\), \(n_{1}=1.465\), \(n_{2}=1.435\), \(\Lambda=2.2\) um, \(d_{1}/\Lambda=0.80\). and \(d_{2}/\Lambda=0.60\), which is the same as that described in Section 3, was initial chosen. To avoid unrealistic doping concentrations, the index differences between the germanium up-doped inclusions and the pure silica matrix were limited to no greater than 0.017, and the index differences between the fluorine down-doped inclusions and the pure silica matrix were set to no less than \(-0.016\). In Figure 6a,b, the germanium up-doped inclusions' impacts on the dispersion were investigated by changing \(n_{1}\) and \(d_{1}/\Lambda\), respectively. From the analysis of Section 3, we know that the fundamental supermode has a flat-topped field distributed over the entire core in the communication bands, and that the core region can be treated as a whole when analyzing the relationship between its dispersion and structural parameters. Because larger \(n_{1}\) and \(d_{1}/\Lambda\) means a larger average index of the fiber core, from Figure 6a,b, we can conclude that the dispersion value increased monotonously with the increment of wavelength in the range of 1.4 to 2.0 um if the equivalent core index is large. However, this monotonicity is not favorable in the respect of flattened dispersion TA-MCF designing. With the decrement of \(n_{1}\) and reduction of \(d_{1}/\Lambda\), the equivalent index of the fiber core was reduced and the monotonicity of dispersion curve could be broken. A dispersion curve with a local maximum at short wavelength and  
Figure 5: The optical intensity distribution of the fundamental supermode of (**a–c**) the six-core TA-MCF, and (**d–f**) the six-core MCF at 1.0 μm, 1.55 μm, and 2.0 μm, respectively; (**g**) the intensity ratio (\(IR\)) value of the six-core TA-MCF and six-core MCF.  
a local minimum at long wavelength was obtained. Meanwhile, almost the entire dispersion curve dropped as a whole with the decrement of core index. Next, the low-index trench's influences on the dispersion of the fundamental supermode were investigated in Figure 6c,d. Because the trench was composed of twelve fluorine down-doped inclusions, the decrement of \(n_{2}\) and enlargement of \(d_{2}/\Lambda\) both led to the reduction of average index in the trench region. As can be seen from Figure 6c,d, it was found that the relationship between trench index and dispersion was analogous to the relationship between core index and dispersion shown in Figure 6a,b. A trench with high index meant a monotonously increasing dispersion curve, while the monotonicity was lost and the entire dispersion curve dropped by decreasing the trench index. At last, the inclusion-to-inclusion space \(\Lambda\) was changed from 2.0 to 2.3 \(\upmu\)m at a step of 0.1 \(\upmu\)m in Figure 6e. The numerical results revealed that, with the enlargement of \(\Lambda\), the dispersion curves rose as a whole and the flatness of the dispersion curves was weakly changed.  
Figure 6: The influences of structural parameters on the dispersion (**a**) \(n_{1}\) from 1.464 to 1.467; (**b**) \(d_{1}/\Lambda\) from 0.75 to 0.90; (**c**) \(n_{2}\) from 1.434 to 1.437; (**d**) \(d_{2}/\Lambda\) from 0.55 to 0.7; (**e**) \(\Lambda\) from 2.0 to 2.3 \(\upmu\)m.  
Taking all the effects mentioned above into consideration, conclusions can be drawn that the low index difference between the core and matrix and the high index difference between the matrix and trench are essential to break the monotonicity and further manage the slope of the dispersion curve. Meanwhile, the amplitude of the curve can be adjusted by tuning the inclusion-to-inclusion space \(\Lambda\) when designing the flattened dispersion TA-MCF.