## 3 Experiment, Results and Discussion
Table 1 shows the applied bias voltage, measured current drawn, and calculated resistance, as well as power consumption by the switch. The calculated resistances of the thermo-optic phase shifter are similar when the applied bias voltage increases from 5 V to 20 V, and the calculated resistance is about 1.3 k\(\Omega\). We also measure that a bias voltage of 12 V is needed to change the state of the switch from bar to cross, which requires 0.1 W electrical power. Figure 6a,b show the experimentally measured normalized crosstalk observed at different output ports of the 3 \(\times\) 3 switch when inputted at CH1 to CH3, respectively. Here, CH1 is defined as the input port being the TE\({}_{0}\) mode port for MDM and output from the top port of the 3 \(\times\) 3 switch, as shown in Figure 1, CH2 is defined as the input port being the TE\({}_{1}\) mode port for MDM and output from the middle port of the 3 \(\times\) 3 switch, and CH3 is defined as the input port being the TE\({}_{2}\) mode port for MDM and output from the bottom port of the 3 \(\times\) 3 switch. Similar to the measured optical spectra in Figure 5a-c, the optical spectra at the three output ports are normalized with respect to the corresponding input channel, respectively. We can observe that the typical switch crosstalk is low enough, which is \(<\)\(-\)20 dB in most of the 45 nm wavelength windows. Then, we experimentally evaluate the MDM optical power divider. As illustrated in Figure 3a, the MDM power divider can support three operations: \"\(\text{TE}_{0}\rightarrow\text{TE}_{1}\rightarrow\text{2 TE}_{0}\)\", \"\(\text{TE}_{1}\rightarrow\text{TE}_{3}\rightarrow\text{2 TE}_{1}\)\", and \"\(\text{TE}_{2}\rightarrow\text{TE}_{5}\rightarrow\text{2 TE}_{2}\)\". In the experiment, since we cannot measure the output TE\({}_{1}\) and TE\({}_{2}\) modes of the MDM power divider directly, they will be further converted to TE\({}_{0}\) modes via ADCs as also illustrated in Figure 3a. As a result, there are six outputs from the MDM optical power divider. Figure 7a-c show the experimentally measured relative crosstalk of the MDM power divider for power divisions of TE\({}_{0}\), TE\({}_{1}\), TE\({}_{2}\) modes, respectively. We can observe \(\sim\)\(-\)18 dB crosstalk for the TE\({}_{0}\) power division, and \(\sim\)\(-\)15 dB crosstalk for the TE\({}_{1}\) and TE\({}_{2}\) power divisions, respectively. The higher crosstalk in the TE\({}_{1}\) and TE\({}_{2}\) power divisions could be due to more instances of mode conversions as well as fabrication error. The overall loss of the MDM power divider is \(\sim\)5 dB for the TE\({}_{0}\) mode and \(\sim\)10 dB for higher order modes. \begin{table}
\begin{tabular}{c c c c} \hline \multirow{2}{*}{**Bias Voltage (V)**} & **Measured Current** & **Calculated** & **Power Consumption** \\  & **(mA)** & **Resistance (k\(\Omega\))** & **(W)** \\ \hline
5 & 3.754 & 1.332 & 0.019 \\
10 & 7.421 & 1.348 & 0.074 \\
12 & 9.062 & 1.324 & 0.109 \\
15 & 10.99 & 1.365 & 0.165 \\
20 & 14.316 & 1.397 & 0.286 \\ \hline \end{tabular}
\end{table} 
Table 1: Performance of a single 2 \(\times\) 2 switch. Figure 6: Measured normalized crosstalk observed at different output ports of the 3 \(\times\) 3 switch when inputted at (**a**) CH1, (**b**) CH2 and (**c**) CH3. Then, we evaluate the BER performance of the 48 DWDM wavelength channels in C-band. The BER performances of the outputs of the 3 \(\times\) 3 switch are shown in Figure 8a-c, respectively. Here, we evenly chose five wavelength channels for display: 1530.33 nm (ITU-16), 1539.77 nm (ITU-22), 1550.12 nm (ITU-34), 1559.79 nm (ITU-47) and 1564.68 nm (ITU-59). Measurement results show that every wavelength channel can satisfy the pre-HD-FEC threshold. The target of our BER measurement is to achieve the highest possible OFDM transmission data rate while satisfying the HD-FEC threshold. Therefore, wavelength channels with higher Rx sensitivities do not necessarily mean poorer performance, as these channels may carry higher data rates.