## 5 Design of Flattened Dispersion TA-MCFs with Low Bending Loss  
Based on the analyses given above, a nearly zero dispersion flattened six-core TA-MCF was designed with \(\Lambda=2.195\) um, \(d_{1}/\Lambda=0.822\), \(n_{1}=1.4648\), \(d_{2}/\Lambda=0.628\), and \(n_{2}=1.4346\). Using these parameters, the calculated cut-off wavelength was 1197 nm, and single-mode operation could be guaranteed after that wavelength. Figure 7a shows that the flattened dispersion of the fundamental supermode varied from \(-1.03\) to \(0.75\) ps/(nm\(\cdot\)km) in the wavelength range of 1.52 to 2.01 um, which completely covers the C(1530-1565 nm) + L(1565-1625 nm) + U(1625-1675 nm)communication band. In Figure 7b, the optical intensity distribution \(IR\) and effective mode area \(A_{\text{eff}}\) were investigated as a function of wavelength. The numerical results showed that \(IR\) reached 0.92 and \(A_{\text{eff}}\) was 48.41 um\({}^{2}\) at 1550 nm. The effective mode area of the TA-MCF proposed herein is larger than most air-silica flattened dispersion MSFs reported. Furthermore, compared to Gaussian distribution, the flat-topped distribution is less susceptible to nonlinear effects. Loss is another important parameter for optical fibers. For the six-core TA-MCF, the numerical simulated confinement loss was as low as \(3\times 10^{-7}\) dB/km at 1550 nm. A weakly guiding fiber is more susceptible to bending. In Figure 8, the bending losses were calculated with different bending radii at 1550 nm. For comparison, the low0 index trench was removed and the bending loss of the six-core MCF without the trench was also calculated and presented in Figure 8. From Figure 8, we can see that the introduction of the low-index trench deteriorated the bending loss. This can be explained by the introduction of trench leading to the reduction of the mode effective index stated in Section 3, which inevitably makes the TA-MCF more sensitive to bending. Moreover, for the six-core fiber, the refractive index of the central region was equal to that of the matrix, and this type of equivalent refractive index profile makes the fiber more sensitive to bending. However, the numerical results showed that the bending loss of our proposed TA-MCF was still less than 4.9 \(\times\) 10\({}^{-4}\) and 0.1 dB/km at 55- and 45-mm bending radius, which is sufficiently low for practical applications. Figure 7: (**a**) The nearly zero flattened dispersion, and (**b**) the \(IR\) value (left axis) and the effective mode area (right axis) of the designed six-core TA-MCF as a function of wavelength. To further reduce the bending loss, an extra germanium up-doped rod with a refractive index \(n_{3}\) and diameter \(d_{3}\) was added in the fiber center to fill the central index valley, and a seven-core TA-MCF was proposed in Figure 9. After parameter optimization, flattened dispersion fluctuating from \(-0.46\) to \(1.35\) ps/(nm\(\cdot\)km) in the wavelength range \(1.50\) to \(2.04\) um was obtained under the parameters of \(\Lambda=2.1\) um, \(d_{1}/\Lambda=0.853\), \(n_{1}=1.4648\), \(d_{2}/\Lambda=0.657\), \(n_{2}=1.4351\), \(d_{3}/\Lambda=0.657\), and \(n_{3}=1.4545\), as shown in Figure 10. In Figure 11, the bending loss of the seven-core TA-MCF was studied. The bending losses of the seven-core MCF without trench and the bending loss of the six-core TA-MCF by removing the central germanium-doped rod are also presented in Figure 11 for ease of comparison. From Figure 11, conclusions can be drawn that the MCF without the trench always has the lowest bending loss of the three. However, the bending loss can be reduced greatly by adding a germanium up-doped rod in the center of the fiber. For the six-core TA-MCF proposed herein, the bending loss was reduced from \(2.95\) dB/km for the six-core TA-MCF to less than \(0.085\)dB/km at \(1550\) nm with \(35\)-mm bending radius. Figure 8: Bending losses of the six-core TA-MCF and six-core MCF at \(1550\) nm with different bending radii.