## 3 Model Validation and Results
Figure 8 shows that the use of the BFL can extend the RSOA direct modulation rate even above the experimentally derived [21] of 11 Gb/s while keeping the \(EP\) below the Forward Error Correction (FEC) acceptable limit of \(3.8\times 10^{-3}\)[33]. The theoretically specified maximum data rate does not contradict that in [21], since the former is in principle more optimistic while the latter was obtained under inherently tighter conditions. A more realistic prediction would be possible if the simulation included effects such as those mentioned earlier, which have been neglected in the employed RSOA reduced model. Although such an intricate model would help reduce the said discrepancy between theory and experiment, adding  
Figure 5: Encoded signals eye diagrams. **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**: 150 ps/div; **Middle row**: 50 ps/div; and **Lower row**: 50 ps/div. Finally, it would be useful to observe the \(EP\) dependence on the modulation rate with and without BFL, both theoretically and experimentally. This is shown in Figure 11, where the limit for an acceptable \(EP\) is set to \(10^{-9}\), according to the standard requirements in digital communication systems [32], and also in order to heavily stress the scheme and further assess its operating capability under tight conditions. From this figure, we can make the following observations: First, owing to the BFL, the \(EP\) is improved and becomes acceptable for a modulation rate being at least twice that without the BFL both in theory and experiment. Second, the theoretical \(EP\) is better than the experimental one, and this also holds for the \(EP\) improvement. This difference in the \(EP\), which is subsequently reflected by the maximum supported data rate as well as on the form of the simulated RSOA output, is attributed to the different ways employed to derive the experimental and theoretical \(EP\). Specifically, and as described in [21], the experimental \(EP\) was found using voltage  
Figure 10: Encoded signal eye diagrams at RSOA output (**left column**) and BFL output at 11 Gb/s (**right column**). **Upper row**: Experimental results. **Lower row**: Simulation results. Figure 9: Encoded signal waveforms at RSOA output and BFL output at 11 Gb/s. samples from the encoded data histograms that were recorded with a diagnostic instrument (DCA) of limited sampling efficiency. This inevitably affected the acquired information and accordingly the \(EP\), which could not be perfectly reconstructed subject to the (pseudo-) randomly occurring pattern effects. A (less cost-effective) Bit Error Rate Tester capable of sampling data directly at the line rate would help resolve this information gap issue related to the frequency of occurring events. In contrast, although the theoretical \(EP\) was found using the same basic formula, still due to the statistical approach followed to calculate the \(Q\)-factor, and from it the \(EP\), the latter was comparatively overestimated. Nevertheless, the observed trends and drawn conclusions still hold and highlight the BFL critical role in rendering feasible a faster RSOA direct modulation. Further insight into the operation of the RSOA-BFL pair can be gained by using the theoretical formalism to predict the scheme's behavior as critical parameters are varied. Two such critical parameters are the RSOA carrier lifetime and alpha factor, whose effect on the \(EP\) is shown in Figure 12 and Figure 13, respectively. From these figures, it can be seen that the \(EP\) is improved as the RSOA carrier lifetime is decreased and the alpha factor is increased. This improvement is physically explained by noting that a faster carrier lifetime enhances the maximum amplitude difference between encoded marks [34], which is the primary goal pursued via the BLF-enabled optical notch filtering.