Polarization-Discriminated RSOA–EAM for Colorless Transmitter in WDM–PON

: The integrated reﬂective semiconductor optical ampliﬁer (RSOA) and electro-absorption modulator (EAM) is viewed as an appealing solution to the colorless transmitter on the optical network unit (ONU) side of wavelength-division multiplexed (WDM) passive optical networks (PONs), for its broad modulation bandwidth and high optical gain. However, the conventional RSOA–EAM usually exhibits a poor upstream signal eye-diagram because it can hardly simultaneously saturate the downstream signal and boost the upstream signal as required. By exploiting the polarization-depended RSOA gain, we propose a polarization-discriminated RSOA–EAM to improve the quality of the upstream signal eye-diagram. In this device, the transverse electric polarized downstream signal is saturated by the high gain in the RSOA active region made of compressively strained multiple quantum wells, whereas the upstream signal is linearly ampliﬁed after polarization rotation. We ﬁnd that, as the quality of the upstream signal eye-diagram improves with an increased polarization rotation angle, its power drops, which indicates that there exists an optimized rotation angle to reach a compromise between the upstream signal integrity and power. Simulation results show that the dynamic extinction ratio and output power of the upstream signal can reach 8.3 dB and 11 dBm, respectively, through the proposed device with its rotation angle set at an optimum value (80 ◦ ), which exceeds the speciﬁcation (6 dB and 4 dBm) of the upstream transmitter as required by the next-generation PON stage two. The quality of the upstream signal eye-diagram measured in Q-factor is improved by 10 dB compared to the conventional RSOA–EAM design without polarization rotation introduced.


Introduction
With the increasing demand for bandwidth from the subscriber end, it is unlikely that a traditional time-division multiplexed passive optical network (TDM-PON) will satisfy the market's future requirements [1,2]. As an alternative technology, the wavelength-division multiplexed passive optical network (WDM-PON), which supports a higher bandwidth, better security, and easier upgradability, is promising for future broadband access networks [2][3][4]. However, large-scale deployment of the WDM-PON is rare due to the drastically increased cost on specific wavelength source in optical network units (ONUs) [3,4]. Therefore, the key to reducing the cost of the WDM-PON is to make the ONU colorless, i.e., all ONUs are made identical and interchangeable [5,6]. To this end, many colorless transmitter solutions have been proposed based on the reflective semiconductor optical amplifier (RSOA) or RSOA integrated with an electro-absorption modulator (RSOA-EAM), such as the spectrum-sliced RSOA [7], the RSOA fiber-cavity laser (FCL) [8][9][10][11], the externally seeded RSOA [12][13][14][15], and the The proposed device structure is schematically shown in Figure 1a. It is functionally composed of three sections: the SOA, the EAM, and the FR [28,29], all on III-V compound semiconductors with InP as the common substrate. The active region of the SOA and the EAM both contain MQW structure made by the AlGaInAs materials. The SOA quantum wells are compressively strained to offer a pure TE mode gain, whereas the EAM quantum wells are slightly tensile, strained for polarization independent absorption [30]. Both the SOA and EAM are made of ridge waveguide with a length of 1200 µm and 100 µm, respectively. Their electrodes are separated by an isolation trench typically in 10 µm. The FR is made by Fe-doped InGaAsP/InP material with a bulk core region [29]. The reported Verdet coefficient is up to 33 • /mm/T in the FR structure [28]. g the Verdet coefficient [29]) will be able to offer a 90 • round-trip Faraday rotation. Hence, a section length of 1 mm under an external magnetic field of 1.37 T [31,32] or less (by increasinIt is worth mentioning that the proposed device shown in Figure 1a needs to be fabricated by the butt-joint regrowth technique due to the inhomogeneity of the material system as well as the layer stack structure in each section. To fabricate the ridge waveguide structure for light guiding and confinement, one may need to exploit different etching depth and/or define different ridge width, in order to achieve a smooth coupling from section to section with negligible reflection and to obtain a strong light confinement, particularly in the FR section for efficiently utilizing the Faraday effect [29]. Appl. Sci. 2020, 10, x FOR PEER REVIEW 3 of 12 structure for light guiding and confinement, one may need to exploit different etching depth and/or define different ridge width, in order to achieve a smooth coupling from section to section with negligible reflection and to obtain a strong light confinement, particularly in the FR section for efficiently utilizing the Faraday effect [29].  In this device, the polarization state of the downstream signal ( DS θ ) is chosen as TE, which can be converted from the random polarized light through the polarization diversified circuits [33][34][35].
After the downstream signal has its bit stream pattern erased by the saturation amplification in the SOA, it is uploaded with the upstream signal in the EAM. Upon the reflection of the light, the FR rotates its polarization state by an angle (i.e., FR θ in the inlet of Figure 1a, defined in a round-trip).
In the light's returning path, the upstream signal in a differently polarized state ( US θ ) will experience a different gain from the downstream signal in the SOA. By exploiting such a polarization-dependent gain discrimination, we can simultaneously saturate the downstream signal and linearly amplify the upstream signal. Apparently, a small (close to 0°) Faraday rotation angle brings in no significant gain discrimination. We will face the contradictory requirement in dealing with the down-and upstream signals in the same SOA, i.e., we can hardly obtain a satisfactory result in erasing the downstream signal (where the SOA needs to be set in its saturation state) and in amplifying the upstream signal (where the SOA needs to be set in its linear amplification region) simultaneously. On the contrary, a large (close to 90°) Faraday rotation angle is in favor of the downstream signal erasing but offers almost no amplification to the upstream signal, as the SOA provides zero gain to the transverse magnetic (TM) mode. An optimum rotation angle, therefore, must exist in balancing the integrity and power of the upstream signal, as the former depends on the erasing of the downstream signal, whereas the later relies on the linear amplification of the upstream signal. A main task of our followed work is to find this optimum rotation angle with different requirements on the upstream signal.

Simulation Results and Discussion
The proposed device is simulated with a well-established traveling wave model [36,37], which has incorporated the propagation of both the signal and the broadband noise, the propagation of the TE and TM modes, and the evolution of the carrier and photon density along the cavity. For more details of the model and its numerical implementation, please see the Supplementary Material. With In this device, the polarization state of the downstream signal (θ DS ) is chosen as TE, which can be converted from the random polarized light through the polarization diversified circuits [33][34][35]. After the downstream signal has its bit stream pattern erased by the saturation amplification in the SOA, it is uploaded with the upstream signal in the EAM. Upon the reflection of the light, the FR rotates its polarization state by an angle (i.e., θ FR in the inlet of Figure 1a, defined in a round-trip). In the light's returning path, the upstream signal in a differently polarized state (θ US ) will experience a different gain from the downstream signal in the SOA. By exploiting such a polarization-dependent gain discrimination, we can simultaneously saturate the downstream signal and linearly amplify the upstream signal. Apparently, a small (close to 0 • ) Faraday rotation angle brings in no significant gain discrimination. We will face the contradictory requirement in dealing with the down-and upstream signals in the same SOA, i.e., we can hardly obtain a satisfactory result in erasing the downstream signal (where the SOA needs to be set in its saturation state) and in amplifying the upstream signal (where the SOA needs to be set in its linear amplification region) simultaneously. On the contrary, a large (close to 90 • ) Faraday rotation angle is in favor of the downstream signal erasing but offers almost no amplification to the upstream signal, as the SOA provides zero gain to the transverse magnetic (TM) mode. An optimum rotation angle, therefore, must exist in balancing the integrity and power of the upstream signal, as the former depends on the erasing of the downstream signal, whereas the later relies on the linear amplification of the upstream signal. A main task of our followed work is to find this optimum rotation angle with different requirements on the upstream signal.

Simulation Results and Discussion
The proposed device is simulated with a well-established traveling wave model [36,37], which has incorporated the propagation of both the signal and the broadband noise, the propagation of the TE and TM modes, and the evolution of the carrier and photon density along the cavity. For more details of the model and its numerical implementation, please see the Supplementary Material. With the material and structural parameters listed in Table 1, the separated SOA and EAM sections are first characterized by the simulation model, respectively. The gain and the saturation input power [38] of the separated SOA section at different polarizations are plotted in Supplementary Figure S2a, and the EAM single-pass transmission curve is plotted in Supplementary Figure S2b. As shown in Supplementary Figure S2a, the gain discrimination between the TE and TM modes is around 40 dB for a bias current of 100 mA, and is enhanced with an increased SOA bias. The saturation input power of the SOA is raised with an increased polarization angle from 0 • to 90 • . Since the linear and nonlinear response regimes depend on the saturation input power [38], and considering a nonlinear response is required to erase the downstream signal while a linear response is required by the upstream signal, the down-and upstream polarizations should therefore be aligned at 0 • (maximize the nonlinear regime) and close to 90 • (maximize the linear regime), respectively. The single-pass insertion loss in the EAM section is about 1.5 dB and doubles for a round-trip. The static single/double-pass extinction ratio is around 10/20 dB with an EAM bias voltage of −1 V plus a peak-peak voltage (V pp ) of 2 V (see Supplementary Figure S2b).

Downstream Signal Suppression
Figure 1b depicts the schematic operation diagram of the proposed device. In this subsection, the downstream signal suppression is studied during its first pass in the SOA, taking into account the gain affected by the contribution of the reflected light. The EAM section is biased at 0 V without modulation (i.e., V pp = 0), and the suppressed downstream signal is extracted before entering the EAM. The SOA section is biased at a constant current of 150 mA. Figure 2a plots the static gain saturation curves of the 1550 nm downstream signal when θ FR varies from 0 • to 90 • (with θ DS fixed at 0 • ). The corresponding relationships between the downstream signal output and input powers are shown in Figure 2b, where the erased 10 Gbps eye-diagrams at a downstream signal input power (P in ) of −15 dBm are inserted to show the erasing effects. It is apparent that, as the Faraday rotation angle increases from 0 • to 90 • , the downstream signal saturation is more pronounced as evidenced by the deeper slope of the gain saturation curve. Consequently, a cleaner seed DC light is obtainable, as shown by the drastically reduced ER in the eye-diagram at θ FR = 90 • as compared to θ FR = 0 • (see Figure 2b). These results indicate that a large (close to 90 • ) Faraday rotation angle is in favor of the downstream signal erasing.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 5 of 12 eye-diagram at FR θ = 90° as compared to FR θ = 0° (see Figure 2b). These results indicate that a large (close to 90°) Faraday rotation angle is in favor of the downstream signal erasing. To understand the results in Figure 2, one should keep in mind that a higher SOA gain leads to more severe SOA saturation [40], hence one should keep the gain as high as possible during the first pass to suppress the downstream signal. Since the material gain is related to the carrier density (N) by 0 ln( / ) tr g N N [37,41] (with 0 g and tr N indicating the gain coefficient and transparent carrier density, respectively), we should preserve more carriers for the downstream signal. As indicated in Figure 3a, the averaged carrier density inside the active region of the SOA increases with an increased Faraday rotation angle (this is attributed to the decreased carrier consumption of the upstream light, since the upstream light TE mode power decreases with the Faraday rotation angle following Equation (S9a) in Supplementary Material, whereas the upstream light TM mode does not consume carriers at all [37,42]). Therefore, the increased carrier density in turn provides increased gain to the downstream signal, as shown in Figure 3b, through which the saturation is enhanced, hence the cleaner erasing of the downstream signal is obtained. The ER of the suppressed downstream signal is plotted in Figure 3c as a function of the Faraday rotation angle. Compared to the situation without any rotation (0°), the suppression of the downstream signal is further improved by more than 2 dB in addition to the normal 3 dB suppression, when the Faraday rotation angle is 90°.  To understand the results in Figure 2, one should keep in mind that a higher SOA gain leads to more severe SOA saturation [40], hence one should keep the gain as high as possible during the first pass to suppress the downstream signal. Since the material gain is related to the carrier density (N) by g 0 ln(N/N tr ) [37,41] (with g 0 and N tr indicating the gain coefficient and transparent carrier density, respectively), we should preserve more carriers for the downstream signal. As indicated in Figure 3a, the averaged carrier density inside the active region of the SOA increases with an increased Faraday rotation angle (this is attributed to the decreased carrier consumption of the upstream light, since the upstream light TE mode power decreases with the Faraday rotation angle following Equation (S9a) in Supplementary Material, whereas the upstream light TM mode does not consume carriers at all [37,42]). Therefore, the increased carrier density in turn provides increased gain to the downstream signal, as shown in Figure 3b, through which the saturation is enhanced, hence the cleaner erasing of the downstream signal is obtained.
eye-diagram at FR θ = 90° as compared to FR θ = 0° (see Figure 2b). These results indicate that a large (close to 90°) Faraday rotation angle is in favor of the downstream signal erasing. To understand the results in Figure 2, one should keep in mind that a higher SOA gain leads to more severe SOA saturation [40], hence one should keep the gain as high as possible during the first pass to suppress the downstream signal. Since the material gain is related to the carrier density (N) by 0 ln( / ) tr g N N [37,41] (with 0 g and tr N indicating the gain coefficient and transparent carrier density, respectively), we should preserve more carriers for the downstream signal. As indicated in Figure 3a, the averaged carrier density inside the active region of the SOA increases with an increased Faraday rotation angle (this is attributed to the decreased carrier consumption of the upstream light, since the upstream light TE mode power decreases with the Faraday rotation angle following Equation (S9a) in Supplementary Material, whereas the upstream light TM mode does not consume carriers at all [37,42]). Therefore, the increased carrier density in turn provides increased gain to the downstream signal, as shown in Figure 3b, through which the saturation is enhanced, hence the cleaner erasing of the downstream signal is obtained. The ER of the suppressed downstream signal is plotted in Figure 3c as a function of the Faraday rotation angle. Compared to the situation without any rotation (0°), the suppression of the downstream signal is further improved by more than 2 dB in addition to the normal 3 dB suppression, when the Faraday rotation angle is 90°.  The ER of the suppressed downstream signal is plotted in Figure 3c as a function of the Faraday rotation angle. Compared to the situation without any rotation (0 • ), the suppression of the downstream signal is further improved by more than 2 dB in addition to the normal 3 dB suppression, when the Faraday rotation angle is 90 • .
Appl. Sci. 2020, 10, 9049 6 of 12 The device's colorless working ability is also characterized and shown in Figure S3 in the Supplementary Material. The ER of the incident downstream signal is 6 dB and the rotation angle is 90 • . It is seen that the colorless working range is significantly broadened as the downstream signal input power increases from −25 dBm to −5 dBm. Nonetheless, the suppressed downstream signal ER can be kept below 2 dB for a broad wavelength span from 1505 nm to around 1560 nm, when the input power is not less than −25 dBm.

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 • 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 • 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 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 • 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 • and 75-90 • , respectively. Therefore, a Faraday rotation angle within 75 • and 88 • will simultaneously satisfy the upstream signal power and the dynamic ER as required by NG-PON2.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 6 of 12 The device's colorless working ability is also characterized and shown in Figure S3 in the Supplementary Material. The ER of the incident downstream signal is 6 dB and the rotation angle is 90°. It is seen that the colorless working range is significantly broadened as the downstream signal input power increases from −25 dBm to −5 dBm. Nonetheless, the suppressed downstream signal ER can be kept below 2 dB for a broad wavelength span from 1505 nm to around 1560 nm, when the input power is not less than −25 dBm.

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° 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° 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 (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° 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° and 75-90°, respectively. Therefore, a Faraday rotation angle within 75° and 88° 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° and 88°, the Q-factor drops significantly. As such, the eye-diagram at a Faraday rotation angle of 88° is worse than that at 81°, as shown in the inlets of Figure 4b, although the dynamic ER in the former case with a higher rotation angle is almost 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 • and 88 • , the Q-factor drops significantly. As such, the eye-diagram at a Faraday rotation angle of 88 • is worse than that at 81 • , as shown in the 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 • 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 • in Figure 4b). At a Faraday rotation angle close to but not exactly at 90 • , 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.
To be able to find an optimum rotation angle that makes a compromise between the upstream signal integrity and power, we introduce the following dimensionless figure of merit (FOM): The dependence of the total gain (P us /P in ) and Q 2 are plotted in Figure 5a, and the FOM is plotted in Figure 5b, respectively, both as a function of the Faraday rotation angle. As a FOM peak appears at 80 • , we know that the device will offer an overall best performance at this optimum Faraday rotation angle. At this angle (80 • ), the output power and dynamic ER of the upstream signal are 11 dBm and 8.3 dB, respectively, exceeding the minimum required value at 4 dBm and 6 dB, respectively, as specified by NG-PON2. To further clarify the effectiveness of the device, in Figure 5c we plot the one-way static gain for signals going downstream (at 0 • or TE mode, from left to right) and upstream (at 80 • , from right to left), respectively, when only the down-or upstream signal is inside the cavity (i.e., without XGS) and when they both exist inside the cavity (i.e., with XGS). For the case without XGS, we find that the SOA is well-saturated for an input power higher than −30 dBm along the downstream path, whereas the SOA is in its linear amplification region for an input power lower than −20 dBm along the upstream path, which indicates that the proposed PD RSOA-EAM can indeed erase the downstream signal and linearly amplify the upstream signal simultaneously. The device's fairly wide working range (from −30 dBm to −20 dBm, i.e., where the saturation discrimination can be achieved) facilitates the power management in operation, hence is superior to the conventional design without utilizing the polarization dimension, not only in terms of the gain discrimination scale, but also in terms of the power operation range. When both the down-and upstream signals exist inside the cavity, the XGS will bring in extra saturation compared to that without XGS, as shown by the lower output powers in Figure 5c. By utilization of polarization discrimination, however, even under XGS we still manage to have the downstream signal saturated and the upstream signal linearly amplified. Although the saturation of the downstream signal is not as good and the linear gain of the upstream signal is lower, the gain difference between the down-and upstream signals brought in by the polarization discrimination still exists nonetheless, which is not achievable in a straight SOA design without using the polarization dimension [22]. Figure 6 gives a comparison of the FOM calculated from the proposed device (when the rotation angle is set at 0 • and 84 • , respectively) and measured with the horn-waveguide RSOA-EAM [22] as referred to in the introduction. The inlets are the corresponding upstream signal eye-diagrams at output. The downstream input signal power is −14 dBm, and the EAM is modulated at 5 Gbps as performed in [22] for a fair comparison. In addition, note that the rotation angle is changed to 84 • instead of 80 • because the optimum rotation angle varies with the input power, as will be discussed later. The ER of the downstream input signal is increased from 0 dB (i.e., downstream CW) to 5 dB. It is seen from Figure 6 that both the horn structure and the polarization rotation design can improve the FOM, while the polarization rotation design is more advantageous. It is also observed that the two schemes can both improve the quality of the upstream signal eye-diagram. Measured in Q-factor, the improvements are 3.7 dB and 10 dB, respectively, for the horn RSOA-EAM and the PD RSOA-EAM with θ FR set at 84 • . Meanwhile, for high ERs (e.g., 5 dB) of the downstream input signal, the PD RSOA-EAM (at 84 • ) can significantly reduce the XGS effect when compared to the horn-waveguide RSOA-EAM, as evidenced by its much thinner "1" level.
without XGS, as shown by the lower output powers in Figure 5c. By utilization of polarization discrimination, however, even under XGS we still manage to have the downstream signal saturated and the upstream signal linearly amplified. Although the saturation of the downstream signal is not as good and the linear gain of the upstream signal is lower, the gain difference between the downand upstream signals brought in by the polarization discrimination still exists nonetheless, which is not achievable in a straight SOA design without using the polarization dimension [22].  Appl. Sci. 2020, 10, x FOR PEER REVIEW 8 of 12 Figure 6 gives a comparison of the FOM calculated from the proposed device (when the rotation angle is set at 0° and 84°, respectively) and measured with the horn-waveguide RSOA-EAM [22] as referred to in the introduction. The inlets are the corresponding upstream signal eye-diagrams at output. The downstream input signal power is −14 dBm, and the EAM is modulated at 5 Gbps as performed in [22] for a fair comparison. In addition, note that the rotation angle is changed to 84° instead of 80° because the optimum rotation angle varies with the input power, as will be discussed later. The ER of the downstream input signal is increased from 0 dB (i.e., downstream CW) to 5 dB. It is seen from Figure 6 that both the horn structure and the polarization rotation design can improve the FOM, while the polarization rotation design is more advantageous. It is also observed that the two schemes can both improve the quality of the upstream signal eye-diagram. Measured in Q-factor, the improvements are 3.7 dB and 10 dB, respectively, for the horn RSOA-EAM and the PD RSOA-EAM with FR θ set at 84°. Meanwhile, for high ERs (e.g., 5 dB) of the downstream input signal, the PD RSOA-EAM (at 84°) can significantly reduce the XGS effect when compared to the hornwaveguide RSOA-EAM, as evidenced by its much thinner "1" level.  [22], and of the proposed PD RSOA-EAM at a rotation angle of 0° and 84°. The inlets are the upstream signal eye-diagrams (data rates of the down-and upstream signals: 10 Gbps and 5 Gbps, respectively).
In practical applications, the downstream signal input power may vary among different ONUs at different locations in the WDM-PON. Its impact on the optimum rotation angle therefore needs to be studied. Figure 7a plots the normalized FOM as a function of the rotation angle at different downstream signal input powers. As the downstream signal input power increases from −25 dBm to −5 dBm, the optimum rotation angle decreases from 88° to 73° correspondingly, which is further plotted in Figure 7b. This effect indicates that for an ONU placed closer to the remote node (RN), the rotation angle of the proposed device should be set at a smaller value for achieving its best performance (we define it as "adaptive FR θ "). Figure 7a also indicates that the full width at halfmaximum (FWHM) of the FOM can be broadened with an increased input power, which means that higher input powers are beneficial to relax the fabrication requirements as the optimum rotation angle is easier to hit. In practical applications, the downstream signal input power may vary among different ONUs at different locations in the WDM-PON. Its impact on the optimum rotation angle therefore needs to be studied. Figure 7a plots the normalized FOM as a function of the rotation angle at different downstream signal input powers. As the downstream signal input power increases from −25 dBm to −5 dBm, the optimum rotation angle decreases from 88 • to 73 • correspondingly, which is further plotted in Figure 7b. This effect indicates that for an ONU placed closer to the remote node (RN), the rotation angle of the proposed device should be set at a smaller value for achieving its best performance (we define it as "adaptive θ FR "). Figure 7a also indicates that the full width at half-maximum (FWHM) of the FOM can be broadened with an increased input power, which means that higher input powers are beneficial to relax the fabrication requirements as the optimum rotation angle is easier to hit.
To show the device performance differences with an adaptive θ FR and a constant θ FR (i.e., θ FR irrespective to the downstream signal input power), their Q-factors are plotted as a function of the downstream signal input power in Figure 7c. It is found that the adaptive θ FR in general gives the highest Q-factors, the constant θ FR of 87 • favors the relatively low input powers (around −20 dBm), and the constant θ FR of 80 • favors the relatively high input powers (around −10 dBm). Nonetheless, they all give higher Q-factors than the constant θ FR of 0 • , i.e., the design without polarization rotation. Nonetheless, they all give higher Q-factors than the constant FR θ of 0°, i.e., the design without polarization rotation. Finally, to verify the colorless operation potential of the proposed device, Figure S4 (see the Supplementary Material) plots the wavelength dependence of the output power and Q-factor of the upstream signal when the downstream signal input power is −15 dBm and the rotation angle is 84°. We can find that the full width half-maximum (FWHM) optical bandwidth of both the integrity (the Q-factor) and the power of the upstream signal are larger than 50 nm, sufficient to cover the 20 nm wideband operation requirement as specified by NG-PON2 [44].

Conclusions
In summary, we have proposed a PD RSOA-EAM to discriminately processes the down-and upstream signals at a different polarization state. Influences of the rotation angle on both the downand upstream signals have been studied. An increased rotation angle enhances the downstream signal erasing, hence improving the dynamic ER of the upstream signal eye-diagram at a cost of the low upstream output signal power. An optimum rotation angle always exists at which the upstream signal output power and integrity are both guaranteed. With the polarization state exploited as an extra dimension, the proposed device can simultaneously saturate the downstream signal and linearly amplify the upstream signal in a fairly wide power operation range. As evidenced by the simulation result, our proposed device can significantly improve the eye-diagram quality and raise the output power of the upstream signal. Hence, the proposed PD RSOA-EAM is promising as a colorless transmitter solution to ONUs in the WDM-PON.
Supplementary Materials: The following are available online at www.mdpi.com/xxx/s1, 1. Theoretical Models for the proposed PD RSOA-EAM. 2. Numerical Implementation. 3. Numerical Simulation Results. Figure S1: Schematic diagram of the simulation setup for polarization-discriminated RSOA-EAM. Figure S2a: Static gain of the single SOA section (at an input power of −25 dBm) and the SOA saturation input power as a function of the input polarization angle. Figure S2b: Static single-pass extinction curve of the EAM section with different powers injected into the EAM section. Figure S3: ER of the suppressed downstream signal as functions of the Finally, to verify the colorless operation potential of the proposed device, Figure S4 (see the Supplementary Material) plots the wavelength dependence of the output power and Q-factor of the upstream signal when the downstream signal input power is −15 dBm and the rotation angle is 84 • . We can find that the full width half-maximum (FWHM) optical bandwidth of both the integrity (the Q-factor) and the power of the upstream signal are larger than 50 nm, sufficient to cover the 20 nm wideband operation requirement as specified by NG-PON2 [44].

Conclusions
In summary, we have proposed a PD RSOA-EAM to discriminately processes the down-and upstream signals at a different polarization state. Influences of the rotation angle on both the downand upstream signals have been studied. An increased rotation angle enhances the downstream signal erasing, hence improving the dynamic ER of the upstream signal eye-diagram at a cost of the low upstream output signal power. An optimum rotation angle always exists at which the upstream signal output power and integrity are both guaranteed. With the polarization state exploited as an extra dimension, the proposed device can simultaneously saturate the downstream signal and linearly amplify the upstream signal in a fairly wide power operation range. As evidenced by the simulation result, our proposed device can significantly improve the eye-diagram quality and raise the output power of the upstream signal. Hence, the proposed PD RSOA-EAM is promising as a colorless transmitter solution to ONUs in the WDM-PON.
Supplementary Materials: The following are available online at http://www.mdpi.com/2076-3417/10/24/9049/s1, 1. Theoretical Models for the proposed PD RSOA-EAM. 2. Numerical Implementation. 3. Numerical Simulation Results. Figure S1: Schematic diagram of the simulation setup for polarization-discriminated RSOA-EAM. Figure S2a: Static gain of the single SOA section (at an input power of −25 dBm) and the SOA saturation input power as a function of the input polarization angle. Figure S2b: Static single-pass extinction curve of the EAM section with different powers injected into the EAM section. Figure S3: ER of the suppressed downstream signal as functions of the downstream signal wavelength. Figure S4: Output power and Q-factor of the upstream signal as functions of the downstream signal wavelength.
Author Contributions: Supervision, X.L.; Writing-original draft preparation, C.Z.; Writing-review and editing, C.Z. Both authors have read and agreed to the published version of the manuscript.
Funding: This research received no external funding.

Conflicts of Interest:
The authors declare no conflict of interest.