## 3 Model Validation and Results
These results are complemented by the corresponding eye diagrams in Figure 5, in which the experimental part refers to a \(2^{31}-1\) bit-long PRBS, while the theoretical part refers to a \(2^{7}-1\) bit-long PRBS so that simulation is affordable with the available computational resources. Note that the \(2^{7}-1\) bit-long PRBS is appropriate for correctly capturing and investigating the pattern effects that limit the directly modulated RSOA performance and are combated by the BFL. In fact, the minimum PRBS order required for this purpose is analogous to the RSOA carrier lifetime and data rate, as expressed in [30]. Using the values of 408 ps and (maximum considered) 14 Gb/s, respectively, results in a 7-order PRBS, or equivalently in a PRBS of length \(2^{7}-1=127\) bits, which is exactly what we used in our simulations. The comparison confirms that the profile of the theoretical waveforms is identical to that of the experimental ones, while the former reproduces well the trend of the latter, i.e., the encoded pulse stream resembles the applied  
Figure 3: RSOA modulation response curves: theoretical (dashed line) and experimental (solid line). The horizontal dashed-dotted line denotes the 3 dB modulation bandwidth. electrical excitation at the lower rate of 1 Gb/s, while it is deformed at the higher rate of 4 Gb/s due to the induced pattern dependence. Moreover, the BFL combats the pattern-dependent distortions and improves the quality of the encoded signal. On the other hand, the theoretical and experimental eye diagrams are not exactly the same. This discrepancy is due to the different ways that they have been obtained. Specifically, the former are actually the so-called pseudo-eye diagrams (PEDs) [31], which are formed by superimposing each simulated encoded bit within a single period and monitoring the outcome, while the latter are recorded after following the standard process specified for this purpose [32] with the aid of a Pulse Pattern Generator and a Digital Communications Analyzer (DCA). Thus, in the first case, the effect of any impairments, such as distortion due to pattern effects and noise, is inevitably smoothened, so that PEDs are not as informative as the classical eye diagrams. Still, they are useful as they can capture and make evident the operating features of the system under consideration that are critical for its performance. The validity of the theoretical outcomes is further supported by the excellent matching between the calculated and measured Amplitude Difference (\(AD\)) level between encoded marks. In fact, the model predicts that \(AD\) is dropped from 1.21 dB after the RSOA to 0.10 dB after the BFL, or by 1.11 dB, while in the experiment the corresponding \(AD\) was 1.55 dB vs. 0.34 dB, or a reduction by 1.21 dB [21]. Therefore, the model correctly and accurately captures the change of the RSOA \(AD\), which is made acceptable owing to the BFL action. Figure 4: Encoded signal waveforms. **Upper row**: RSOA output at 1 Gb/s. **Middle row**: RSOA output at 4 Gb/s. **Lower row**: BFL output at 4 Gb/s. **Left column**: Experimental results. **Right column**: Simulation results. Experimental results time scale—**Upper row**: 2.55 ns/div; **Middle row**: 650 ps/div; and **Lower row**: 650 ps/div. The information derived from the extensive model validation concurs thus the BFL potential to allow for RSOA direct modulation at 4 Gb/s. This is also evident from the results shown in Figures 6 and 7, and is consistent with the relevant measurements (see Figure 12 in [21]). Since the BFL aims at enhancing the RSOA modulation bandwidth, we further explored to what extent this is possible. For this purpose, we calculated the Error Probability (\(EP\)) from \(EP=0.5\,\text{erfc}(Q/\sqrt{2})\), where \(\text{erfc}(x)\) is the error function and \(Q=(P_{1}-P_{0})/(\sigma_{1}+\sigma_{0})\) is the \(Q\)-factor, where \(P_{1,0}\) and \(\sigma_{1,0}\) are the mean and the standard deviation of the peak power of the encoded marks ('1') and spaces ('0'), respectively [32].