## 3 Transmission Characteristics of Ultra-Bend-Resistant 4-Core SXC
### XT between Adjacent Cores  
In this section, we will investigate the \(XT\) between adjacent cores due to the cabling and bending dependence of \(XT\). For the weakly coupled multicore fiber, the \(XT\) between adjacent cores accumulated along fiber length \(L\) can be evaluated by [1; 16]  
\[XT\approx h\cdot L \tag{3}\]  
where \(h\) is the power-coupling coefficient between adjacent cores, which can be approximately expressed as [1; 16]  
\[h\approx\kappa^{2}\frac{\lambda R_{b}}{\pi n_{b}\lambda_{km}} \tag{4}\]  
where \(\kappa\) and \(\lambda\) are the mode-coupling coefficient and transmission wavelength, respectively. \(n_{b}\) is the average equivalent refractive index of the bent core. \(\Lambda_{km}\) is the distance between adjacent core \(m\) and core \(k\).  
As shown in Equation (4), the \(XT\) level will be directly affected by the bending radius \(R_{b}\). Thus, the \(XT\) between adjacent cores under bending conditions was measured and the experimental setup is shown in Figure 6a. The laser source is a 1310 nm single-wavelength fiber laser. Its output power is \(-7\) dBm and the power fluctuation is less than 0.01 dB. The optical power meter (OPM) with four channels can be used to monitor the output power from the 4-core fiber and SXC. In order to investigate the bending dependence of \(XT\) sufficiently, 10 loops with a minimal bending radius of 6 mm were imposed on the 4-core SXC. Figure 6b shows the \(XT\) characteristics of the 4-core fiber, 4-core SXC and 4-core SXC under bending conditions, respectively. It can be calculated that the average value of the \(XT\) between adjacent cores of this trapezoid-index 4-core fiber is \(-68.12\) dB/km, which is 1.12 dB/km lower than that of the step-index core [3; 17]. In our experiment, the core pitch (\(\Lambda_{km}\)) of the prepared 4-core fiber is 41.2 \(\upmu\)m. Based on Equations (3) and (4), we can increase the core pitch up to 43 \(\upmu\)m, and thus further suppress the intrinsic \(XT\) of the 4-core SXC to or below \(-70\) dB/km. In this case, the width and depth of the refractive index trench should be wider and deeper so as to suppress the coating-leakage loss in the O-band due to a shorter core to coating distance (the minimum distance from one center to the coating) [1]. As shown in Figure 6b, the average \(XT\) between adjacent cores of the 4-core SXC and 4-core SXC with a minimal bending radius can be calculated as \(-61.95\) dB/km and \(-61.39\) dB/km, respectively. The \(XT\) changes from the non-cabled 4-core fiber originate from the micro-bend-affected crosstalk induced by the actual cabling processes and winding on the bobbin with the radius of 15.4 cm as well as the longitudinal structural fluctuation [1; 16], especially the 3\(\#\) and 4\(\#\) cores which are, respectively, the first and second nearest neighbors to the marker core. It can be found that the maximum value and average value of the \(XT\) degradation induced by the bending are only 1.17 dB/km and 0.56 dB/km, respectively. These measured results indicate that the prepared 4-core SXC with an excellent bending resistance will have a considerable application prospect on SDM optical transmission in narrow space.  
\begin{table}
\begin{tabular}{c c c c c} \hline \multirow{2}{*}{**Bending Radius**} & \multicolumn{4}{c}{**Macro-Bending Loss (dB/10 Turns)**} \\ \cline{2-5}  & **1\(\#\)** & **2\(\#\)** & **3\(\#\)** & **4\(\#\)** \\ \hline \(R_{b}=6.0\) mm & 0.37 & 0.22 & 0.37 & 0.21 \\ \(R_{b}=8.2\) mm & \textless{}0.10 & \textless{}0.10 & \textless{}0.10 & \textless{}0.10 \\ \(R_{b}=10.0\) mm & \textless{}0.04 & \textless{}0.04 & \textless{}0.04 & \textless{}0.04 \\ \(R_{b}=18.3\) mm & \textless{}0.02 & \textless{}0.02 & \textless{}0.02 & \textless{}0.02 \\ \hline \end{tabular}
\end{table}
Table 1: Measured macro-bending loss at different bending radii.