## 3 Model Validation and Results  
The model formulated in Section 2 is validated by a comparison to experimental data available from [21]. First, we compared the theoretical BFL transfer function obtained from Equation (5) against the measured one. Figure 2 verifies that the two curves are identical, since both have a comb-like form, consist of continuous maxima (peaks) of uniform wavelength spacing, or \(FSR=0.87\) nm, and minima (notches) located in between at \(FSR/2\) intervals, and exhibit an amplitude difference between peaks and notches, or Peak-to-Notch Contrast Ratio (PNCR), of the order of 25 dB. Second, we considered the theoretical RSOA E/O response for benchmarking against the experiment. In [17], we concisely derived this response using and combing material from the relevant references cited therein that have suitably applied small-signal analysis. For the sinusoidal modulation current used when this response was measured experimentally [21], the RSOA E/O transfer function is reduced to \(T_{RSOA}(\omega)=D(0)/2D(\omega)\), where \(D(\omega)=1-j\omega T_{car}+W\bigg{[}\frac{2P_{CW}}{P_{sat}}\exp\big{(}2\bar{ g}_{0}L_{RSOA}+\frac{2P_{CW}}{P_{sat}}\bigg{)}\bigg{]}\). By substituting the fitted value of the carrier lifetime as well as the values of the rest of the involved parameters from Table 1, this function is plotted against frequency in Figure 3. From this figure, we note that the simulated curve indeed exhibits the low-pass filter characteristic of directly modulated RSOAs [26]. On the other hand, there is a discrepancy between the theoretical  
Figure 2: BFL response curves: (**a**) experimental and (**b**) theoretical. The upper and lower horizontal dash-dotted lines denote the maximum and minimum spectral responses, respectively, whose difference defines the Peak-to-Notch-Contrast Ratio (PNCR). and experimental RSOA modulation responses as we go beyond the 3 dB bandwidth. Nevertheless, this fact will not compromise the essence of the model's predictions because this response is only complementary and not critical for the purposes of modeling. In fact, this function is not directly involved in the calculations of the RSOA and BLF outputs, which in turn are determined by the time-dependent RSOA integrated power gain and the frequency-dependent BFL response, respectively. Additionally, with regard to the principle of operation, the RSOA output is not the absolute but the shifted (due to SPM) frequency content, which is filtered-out and translated into RSOA compensated impairments by the action of BFL. Provided that the BFL response has the opposite slope and is efficiently tailored by properly selecting its FSR and detuning, the BFL can handle this spectral shift and extend the RSOA direct modulation rate. More details in the experimental RSOA modulation response could be captured if the model were improved to include effects such as device parasitics related to RSOA packaging, impedance mismatching and electrical coupling losses related to RSOA driving circuitry, etc. [6; 7]. In this case, however, the developed model would be much more sophisticated than the reduced one employed in this work. Such a complexity could be tolerated only if the goal were to design a special-type RSOA with exceptional modulation capabilities compared to those normally exhibited by the majority of available devices, which is beyond the scope of this paper. Third, we modeled the RSOA when directly modulated and compared the theoretical and experimental waveforms at different encoding data rates of 1 Gb/s and 4 Gb/s, both for the RSOA alone and with the assistance of the BFL. The obtained set of results is depicted in Figure 4 for the same representative segment of NRZ data as in the experiment, i.e., \(1100111010100100100011100\), which is employed for the sake of a convenient and clear demonstration.