## 3 Results
For this purpose, the MRR transmission properties must be suitably tailored, which involves choosing and controlling the wavelength spacing (FSR) as well as the contrast and the position of the notches, by following and fulfilling the necessary conditions. The general guidelines are that: (a) The FSR must be adjusted by taking into account the trade-off between the margin of the TF spectral border, which is defined by the difference between the reference data and the nearest notch wavelength, the TF passband width, the spectral components' suppression degree dependence on pulse peak amplitude they originate from, and the optical carrier level of transmission after filtering; (b) the repetitive notches must be sharp and deep enough to maximize their magnitude difference from their adjacent transmission peaks, which defines the PNCR; and (c) the notches must occur at a longer wavelength than that of the encoded signal so that the MRR transmittance is decreased as the wavelength is increased. The beneficial effect of an MRR with optimum radius and detuning \(R=20\) um and \(\Delta\lambda=0.65\) nm, respectively, or \(\simeq\) FSR/20, which fall within the range of permissible values specified above, on the encoded signal characteristics at 11 Gb/s is shown in the lower part of Figure 9, where for comparison the same results for the RSOA only are depicted in the upper part. The obtained performance metrics are \(EP=3.56\times 10^{-4}\) (MRR) vs. \(2.86\times 10^{-1}\) (RSOA), \(AD_{1,max}=0.64\) dB (MRR) vs. 3.32 dB (RSOA), \(AD_{1/0,max}=10.63\) dB (MRR) vs. 5.88 dB (RSOA), \(CF=9\)% (MRR) vs. 48% (RSOA), \(EO=87.4\)% (MRR) vs. 44.5% (RSOA) and \(OS=8\)%. In addition, the net gain (NG) of the RSOA-MRR system [51]  
Figure 7: RSOA-encoded pulses (**a**) waveform, (**b**) chirp and (**c**) pseudo-eye diagram at 3 Gb/s (top) and 5 Gb/s (bottom). is 6.54 dB, thus being exploitable for direct modulation purposes [24]. This value can be increased to approach 10 dB provided that the coupling coefficient, \(r\), tends closer to unity, since in this case the creation of the MRR spectral response, according to the general guidelines mentioned above for efficiently mitigating the pattern-dependent impairments of the directly modulated RSOA, is favored. Still, such choice of the specific parameter is practically compromised by the tighter adjustments related to the gap between the straight and bending waveguides. On the other hand, varying the MRR radius from the maximum to the minimum permissible value specified for this parameter does not improve the NG. In fact, this action increases the FSR, which in turn makes the slope of the MRR transfer function less steep. This increases the likelihood that the amplified optical carrier will fail to fall close to the transmission peak, thus suffering by the MRR a greater attenuation of its intensity, which results in less available NG. Figure 10 shows that owing to the MRR, the RSOA modulation bandwidth is extended indeed to 11 GHz. The peaking observed in the modulation response is induced by the MRR transient time dynamics and is the physical result of interference between the light that circulates inside the ring and the light inserted in the bus waveguide from the RSOA [63]. Consequently, its magnitude should depend on the fraction of the power that comes from the RSOA and enters the ring, that is, \((1-r^{2})\times 100\%\). Our simulations conducted in the critical coupling regime thus show that when this quantity is 9.75%, the frequency position of peaking is shifted to its maximum, which however is not exploitable for RSOA direct modulation at the corresponding data rate due to the constraints imposed by \(EP\), \(AD_{1,max}\), \(AD_{1/0,max}\), \(CF\) and \(OS\). In contrast, when the percentage of coupled power drops to \(\sim\)2%, the peaking can be leveraged for enh  
Figure 8: Error probability at MRR output for different MRR radii and detuning at **(a)** 10.5 Gb/s, (b) 11 Gb/s and **(c)** 11.5 Gb/s.