## 4 Results  
Since the BFL filtering efficiency is critically determined by the detuning [23], \(\Delta\lambda\), which is defined as the difference between the CW seeding wavelength and the wavelength of the nearest notch in the BFL response, we investigated the impact of this parameter on the operation of the scheme by assessing first the performance against the error probability (\(EP\)). This metric was calculated through [37]\(EP=\frac{1}{2}\text{erfc}(Q/\sqrt{2})\), where \(\text{erfc}(\text{x})\) is the error function and \(Q=\frac{|\mu_{1}-\mu_{0}|}{\sigma_{1}+\sigma_{0}}\) is the \(Q\)-factor, where \(\mu_{1,\ 0}\) and \(\sigma_{1,\ 0}\) are the mean and standard deviation of the peak power of the encoded marks ('1') and spaces ('0') whose values are extracted from the levels of the corresponding histograms. These in turn are obtained from the photodetected voltage samples that are recorded and stored by a digital communications analyzer (DCA). The BFL detuning was practically achieved by fine tuning the CW laser wavelength relative to the adjacent notch's fixed position so that the former was spectrally located on the left-hand side of the latter. This resulted in negative detuning values and made the BFL filter transmission decrease as the wavelength increased, which is necessary [32] in order to suppress the longer-wavelength, i.e., red-shifted, spectral components induced on the encoded signal due to the self-phase modulation (SPM) effect that physically accompanies the RSOA direct modulation [38]. Equivalently, the BFL exhibited in the frequency domain a high-pass filter characteristic which counteracted that of the RSOA so that the combined response could become independent of the electrical modulation frequency for a wider range than for the RSOA only [28]. Figure 9 shows that the \(EP\) could be kept below \(10^{-9}\) for a RSOA direct modulation speed extended up to 4 Gb/s for \(\Delta\lambda=-0.05\) nm. Figure 8: (**a**) BFL notch displacement vs. time, (**b**) BFL transfer function at different time instants. The red arrow shows the notch displacement in time. The feasibility of this extension was supported by Figure 10, which depicts the measured E/O response of the RSOA-BFL combination. It can be seen that compared to Figure 4a, the connection of the BFL after the RSOA shifted the electrical modulation bandwidth of the latter to \(\sim\)3 GHz. This value exceeded the NRZ coding pulses bandwidth, which by definition equals half the repetition data rate [39], as well as the minimum bandwidth required for optimized signal reception, which equals 2/3 times the data repetition rate [40]. The specified detuning value implies that the CW optical signal and BFL notch should be very closely spaced apart at the expense of very delicate experimental handling. In contrast, without the BFL, i.e., for \(\Delta\lambda=-0.45\) nm \(\sim FSR/2\), it was not possible to directly modulate the RSOA at any of the checked data rates shown in Figure 9. These results were further supported by raw BER measurements obtained from the BERT error analyzer and depicted in Figure 11 for data rates between 3 Gb/s and 4 Gb/s. Figure 10: E/O response of RSOA-BFL combination. The dashed line indicates the 3-dB electrical modulation bandwidth. Figure 9: Error probability vs. BFL detuning (\(\Delta\lambda\)) for different data rates. The dashed line indicates the limit for acceptable \(EP\) at \(1\times 10^{-9}\). The lower bound of the displayed data rates was dictated by the fact that below 3 Gb/s, the analyzer did not find any mistakes so the measured BER was zero. In other words, the BER was so low that the analyzer needed very long time to count mistakes. Similarly, for data rates over 4 Gb/s, the analyzer had a synchronization loss since the received data could not be synchronized with the clock of the PPG.