# An \(N\)-Port Universal Multimode Optical Router Supporting Mode-Division Multiplexing
## 3 Results  
In this section, based on the replacement scheme of Figure 1, we use multimode waveguide to replace the traditional single-mode waveguide, multimode bending to replace the single-mode bending, multimode waveguide crossing to replace the single-mode waveguide crossing, and multimode switching element to replace the \(1\times 2\) CSE. Finally, the five-port MDM-OR, which supports MDM, is shown in Figure 9b. The optical router shown in Figure 9a is a five-port optical router, which is the single-mode optical router before replacement. In addition, the five-port MDM-OR is a general \(5\times 5\) all-pass optical router, that is, the mode can be transferred from one port to any other port. Different from a traditional single-mode optical router, MDM-OR can not only transmit TE\({}_{0}\) mode but also transmit other modes at the same time. The five-port MDM-OR is just a concrete implementation of our method. Based on this replacement scheme, we can build \(N\)-port MDM-ORs. We utilize the calculation models of insertion loss, crosstalk noise, OSNR, and BER in the previous section and use MATLAB to obtain the transmission loss, crosstalk noise, OSNR, and BER between different port pairs of this five-port MDM-OR in the input 1550 nm TE\({}_{0}\), TE\({}_{1}\), and TE\({}_{2}\) mode. Additionally, in the simulation example, the input power is 0 dBm and other parameters used are shown in Tables 1 and 2. Figure 8: \(N\)-port MDM-OR. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Value** & **Reference** \\ \hline \(L_{sb}\) & \(-0.005\) dB/90\({}^{\circ}\) & [31] \\ \(L_{sc}\) & \(-0.04\) dB & [32] \\ \(L_{sc2}\) & \(-0.5\) dB & [33] \\ \(L_{sp1}\) & \(-0.005\) dB & [33] \\ \(L_{mb0}\) & \(-0.4\) dB & [21] \\ \(L_{mb1}\) & \(-0.7\) dB & [21] \\ \(L_{mb2}\) & \(-0.84\) dB & [21] \\ \(L_{dmx0}\) & \(-0.17\) dB & [34] \\ \(L_{dmx1}\) & \(-0.27\) dB & [34] \\ \(L_{dmx2}\) & \(-0.13\) dB & [34] \\ \(L_{mx0}\) & \(-0.17\) dB & [34] \\ \(L_{mx1}\) & \(-0.13\) dB & [34] \\ \(L_{mx2}\) & \(-0.09\) dB & [34] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Loss cofficients. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Value** & **Reference** \\ \hline \(K_{c}\) & \(-40\) dB & [31] \\ \(C_{pse,eff}\) & \(-20\) dB & [32] \\ \(C_{pse,on}\) & \(-25\) dB & [33] \\ \(C_{01 mx}\) & \(-35\) dB & [34] \\ \(C_{02 mx}\) & \(-48.8\) dB & [34] \\ \(C_{10 mx}\) & \(-43\) dB & [34] \\ \(C_{12 mx}\) & \(-37.3\) dB & [34] \\ \(C_{20 mx}\) & \(-25.4\) dB & [34] \\ \(C_{21 mx}\) & \(-39.9\) dB & [34] \\ \(Cmb_{01}\) & \(-20\) dB & [21] \\ \(Cmb_{02}\) & \(-25\) dB & [21] \\ \(Cmb_{10}\) & \(-25\) dB & [21] \\ \(Cmb_{12}\) & \(-25\) dB & [21] \\ \(Cmb_{20}\) & \(-32\) dB & [21] \\ \(Cmb_{21}\) & \(-22\) dB & [21] \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Crosstalk coefficients. Figure 9: (a) The five-port single-mode optical router. (b) The five-port MDM-OR that supports MDM. According to the insertion loss models of different multimode optical devices in the previous section, the transmission loss between different port pairs of the five-port MDM-OR is calculated. Figure 10 shows the transmission loss between different port pairs of this router when the TE\({}_{0}\), TE\({}_{1}\), and TE\({}_{2}\) mode is input, where 12 in the abscissa represents the TE\({}_{0}\) mode being transmitted from Port 1 to Port 2. It can be seen from Figure 10 that when the optical router transmits the TE\({}_{0}\) mode, the transmission loss between the different port pairs of the MDM-OR is in the range of (\(-9.31\), \(-0.84\)) dB. According to the same method, we can obtain the transmission loss between different port pairs when this router inputs TE\({}_{1}\) mode. We can find that the maximum transmission loss between different port pairs is \(-10.64\) dB, and the minimum is \(-1.58\) dB. When the TE\({}_{2}\) mode is input, its transmission loss range is from \(-9.98\) dB to \(-2.07\) dB.