# Polarization-Discriminated RSOA-EAM for Colorless Transmitter in WDM-PON
## 3 Simulation Results and Discussion
### Upstream Signal Integrity and Power  
In addition to erasing the downstream signal, the device also needs to linearly amplify the upstream signal in its returning path to provide sufficient upstream launch power. Apparently a 90\({}^{\circ}\) Faraday rotation angle will fail to achieve any signal amplification as the SOA provides zero gain to the TM mode (see Supplementary Figure S2a). We therefore need to reduce the Faraday rotation angle from 90\({}^{\circ}\) on the premise of maintaining the upstream signal integrity. In this subsection, the EAM is biased at \(-\)1 V and driven by an upstream signal bit stream (10 Gbps NRZ-OOK) with a peak-peak voltage of 2 V. The upstream output signal is extracted at the \"upstream output\" point in Figure 1b. The SOA is biased at a constant current of 150 mA. The input power and ER of the downstream signal are \(-\)10 dBm and 6 dB, respectively. Figure 4 presents the simulated Faraday rotation angle dependence of the output power (\(P_{\text{us}}\)) (Figure 4a), dynamic ER (Figure 4a), and Q-factor (Figure 4b) of the upstream signal, where the Q-factor is a measure of the eye-diagram quality [(43)]. The inlets in Figure 4b are the 10 Gbps upstream signal eye-diagrams at different Faraday rotation angles. As can be seen in Figure 4a, the upstream signal dynamic ER increases, but its output power drops monotonically with an increased Faraday rotation angle. The Q-factor, however, has a maximum and a minimum in the close neighborhood of the 90\({}^{\circ}\) Faraday rotation angle. The reduced output power and increased dynamic ER of the upstream signal are caused by the reduced upstream signal gain and decreased gain saturation, respectively, with an increase of the Faraday rotation angle. Following the specification of the next-generation PON stage two (NG-PON2) on the upstream signal launch power (\(>\)4 dBm) and dynamic ER (\(>\)6 dB) [(44)], the Faraday rotation angle should be set in the range of 0-88\({}^{\circ}\) and 75-90\({}^{\circ}\), respectively. Therefore, a Faraday rotation angle within 75\({}^{\circ}\) and 88\({}^{\circ}\) will simultaneously satisfy the upstream signal power and the dynamic ER as required by NG-PON2. Attention should be paid that a high dynamic ER does not necessarily mean a high quality of the eye-diagram, as the Q-factor also reflects the level of crosstalk, whereas the ER does not. As shown in Figure 4b, if the Faraday rotation angle falls between 81\({}^{\circ}\) and 88\({}^{\circ}\), the Q-factor drops significantly. As such, the eye-diagram at a Faraday rotation angle of 88\({}^{\circ}\) is worse than that at 81\({}^{\circ}\), as shown in the  
Figure 4: Faraday rotation angle dependence of the (**a**) upstream signal power and dynamic ER, and (**b**) Q-factor. Inlets are the 10 Gbps upstream signal eye-diagrams at different Faraday rotation angles. (downstream signal power at input: \(-\)10 dBm, ER: 6 dB, wavelength: 1550 nm; SOA DC bias current: 150 mA; EAM bias voltage: \(-\)1 V, EAM peak-peak voltage: 2 V). inlets of Figure 4b, although the dynamic ER in the former case with a higher rotation angle is almost 9 dB higher. The Q-factor valley in the vicinity of 88\({}^{\circ}\) is caused by the pronounced crosstalk due to the XGS between the down- and upstream signals (see the stratified \"1\" level in the eye-diagram at 88\({}^{\circ}\) in Figure 4b). At a Faraday rotation angle close to but not exactly at 90\({}^{\circ}\), the upstream signal has a none-zero TE component according to Equation (S9a). Since the SOA is in deep saturation, the XGS effect transfers the downstream signal pattern onto the upstream signal, as the latter's nonvanishing TE mode power fluctuates anticorrelatedly with the former's (TE mode) power.