## 4 Results
It is noteworthy that although the limit for acceptable \(EP\), \(EP=1\times 10^{-9}\), which is the standard requirement in digital communication systems [39], is several orders of magnitude tighter than that employed in other filtering schemes proposed to enable faster RSOA direct modulation by NRZ data [17; 18; 19], still the BFL managed to successfully confront this ultimate challenge. Since the RSOA nominal modulation bandwidth can be broadened by taking into account, and intervening on, factors such as the dimension [41], optical confinement [42], packaging [43], impedance matching [44] and transport effects [45] of the active device, it can be realized that there is further margin for increasing the RSOA direct modulation speed by means of the BFL. In this direction, the BFL potential was also verified in the time domain and the results are compiled and presented in Figure 12.  
These include encoded pulse waveforms for a representative 25 bit-long segment of 110011101010010100011100 and eye diagrams for \(2^{10}-1\) PRBS. As it can be seen, the uniformity of pulses at the RSOA output at 1 Gb/s (Figure 12a) was not preserved at 4 Gb/s (Figure 12b), since pulses  
Figure 11: Raw BER measurements versus data rate for BFL detuning \(\Delta\lambda=-0.05\) nm. The dashed line indicates the limit for acceptable \(EP\) at \(1\times 10^{-9}\). Figure 12: Top: Encoded pulse waveforms of (**a**) RSOA output at 1 Gb/s, (**b**) RSOA output at 4 Gb/s, (**c**) BFL output at 4 Gb/s for BFL detuning \(\Delta\lambda=-0.05\) nm. Bottom: Corresponding eye diagrams (**d–f**). Vertical scale: 15 mV/div. suffered from pattern-dependent peak-to-peak amplitude fluctuations. This distortion was translated into a poor quality of the eye diagram at 4 Gb/s (Figure 12e) versus 1 Gb/s (Figure 12d), as indicated by the narrow opening at the center and the dispersed histograms' content. The deteriorated outcome of the single directly modulated RSOA could be considerably improved by the properly detuned BFL, which compensated for the pulse amplitude wandering (Figure 12c) and restored the eye's opening and histograms' form (Figure 12f). These improvements were quantified by the significant reduction of the amplitude difference (\(AD\)) of the marks [46], from the inadmissible \(AD\approx 1.55\) dB for the RSOA only, down to the more than acceptable [47]\(AD\approx 0.34\) dB thanks to the BFL, as well as by the increase of the eye opening (\(EO\)) [39], from \(EO_{RSOA}\approx 46.68\%\) to \(EO_{BFL}\approx 70.02\%\). Moreover, in Figure 13a it is observed that the RSOA spectrum is broadened towards the longer sideband, i.e., it is red-shifted. The spectrum retains its form at the output of the BFL at transparency, i.e., for \(\Delta\lambda=0\) nm, since then the BFL does not act as notch filter on the red-shifted RSOA spectral components (Figure 13b). In this case, the spectrum is identical to that at the BFL input, or equivalently at the output of the OBPF right after the RSOA. In Figure 13c it can be observed instead that the corresponding spectrum becomes more symmetric at the output of the BFL, which has been detuned by \(\Delta\lambda=-0.05\) nm to suitably tailor the red-shifted spectral components. Unlike previous works, showing encoded pattern profiles and introducing appropriate indices, such as the AD, is indispensable in order to fully demonstrate and characterize the extent of distortion and amelioration undergone by the encoded signal after the stand-alone RSOA and applied notch filter (BFL in our case), respectively. To this aim, we also tested the BFL capability to allow transmission of the encoded signal over fiber. This required to specify the net gain of the RSOA and BFL combination, \(G_{net}\), which is an important metric of the performance of post-filtering (R)SOA pattern-dependence combating [32].