# Real-Time Spatial-Division Multiplexing Transmission with Commercial 400 Gb/s Transponders
## 3 Real-Time MDM Transmission Using Non-Degenerate LP Modes of the WC-FMF  
The modal field of non-degenerate LP modes in the WC-FMF are invariant under the rotation, so \(4\times 4\) MIMO DSP are not necessary. In this paper, we only employ non-degenerate LP modes in the WC-FMF link. Therefore, the whole system could be compatible with commercial single-mode transponders. Figure 4a shows the designed and fabricated refractive index profile of the proposed weakly coupled FMF and the effective refractive index of the supported LP modes. The fiber has a normalized frequency \(V\) of 4.8 and a relative refractive index difference between the fiber core and cladding (\(\Delta n\)) of 0.6%. The FMF support LP\({}_{01}\), LP\({}_{11}\), LP\({}_{21}\) and LP\({}_{02}\) modes. As is known, the \(n_{\text{eff}}\) of all LP modes of a step-index WC-FMF are between \(n_{\text{eff}}\) of the cladding (\(n_{\text{cl}}\)) and core (\(n_{\text{co}}\)). Given that the core and cladding index difference (\(\Delta\)) remains constant, if the \(n_{\text{eff}}\) of all LP modes distribute equally between \(n_{\text{cl}}\) and \(n_{\text{co}}\), the \(\min\mid\Delta n_{\text{eff}}\mid\) could achieve its maximum. Therefore, the design principle of WC-FMF is to adjust the \(n_{\text{eff}}\) of all LP modes to approach equal spacing as much as possible under a certain \(\Delta\). If we introduce a small perturbed refractive index ring area in the fiber core, the \(n_{\text{eff}}\) of the guided LP mode can be adjusted. Since different LP modes have different power spatial distributions, only one ring structure cannot satisfy the \(n_{\text{eff}}\) adjustment for all modes. Therefore, multiple-ring-core structure, considering the power distributions of all LP modes, can be utilized to achieve a large \(\min\mid\Delta n_{\text{eff}}\mid\) and the inter-LP-mode crosstalk can be effectively suppressed. In this paper, three perturbed rings areas are adopted in the core to adjust the \(n_{\text{eff}}\) of four LP modes to maximize the \(\min\mid\Delta n_{\text{eff}}\mid\) as much as possible. In order to reduce the bending sensitivity of high-order LP modes, a depressed-index fluorine-doped trench is applied in the cladding. The \(\min\mid\Delta n_{\text{eff}}\mid\) of the  
Figure 3: (**a**) OSNR and (**b**) BER curves versus input power of core 1, 2 and 4 in single-roll and 20-roll cases. fabricated FMF is 1.89 \(\times\) 10\({}^{-3}\) lying between LP\({}_{21}\) and LP\({}_{02}\) modes, which can effectively suppress the modal crosstalk between them. The attenuations of the four LP modes are all lower than 0.227 dB/km thanks to the depressed-index trench. The mode MUX/MDEMUX in this work are consisted of side-polished all-fiber mode-selective couplers (MSC), the structure of which is shown in Figure 4b. MSC is a directional fiber coupler providing exclusive mode-coupling between the fundamental mode of the SMF and a specific higher order mode of the FMF when the propagation constants of the two modes are identical. Phase mismatch will increase the insertion loss and decrease the modal selectivity. In this paper, the mode MUX is made up by cascading LP\({}_{01}\) and LP\({}_{02}\) MSCs whose FMF is the same as the transmission fiber. On one hand, identical fibers can reduce the insertion loss induced by mode field mismatch at the connection point between the MSC and the transmission FMF. On the other hand, since the transmission FMF has been finely designed to enlarge the \(\min\left|\Delta n_{\text{eff}}\right|,\) it could effectively decrease the modal crosstalk. The insertion loss for a pair of LP\({}_{01}\) MSCs are about 2 dB, while it is 6 dB for a pair of LP\({}_{02}\) MSCs. Similar to the two links in MCF transmission, we also constructed single-roll 60 km and 20-roll 3 km FMF links to simulate real deployment of the fiber cable. Besides, 5-roll (60 + 25 + 25 + 25 + 15 = 150 km) FMFs are constructed to test the long-haul real-time MDM transmission performance.