## 3 Results  
We found first if and how the RSOA can be directly modulated on its own without performance degradation. For this purpose we investigated the impact of the parameters associated with the optical and electrical RSOA excitation signal on the error probability (\(EP\)) which, for acceptable performance, should not exceed the forward error correction (FEC) threshold of \(3.8\times 10^{-3}\)[22; 24]. The error probability is analytically extracted through the \(Q\)-factor, which is defined as  
\[Q=\frac{P_{1}-P_{0}}{\sigma_{1,pe}+\sigma_{0,pe}}, \tag{9}\]  
where \(\bar{P}_{1}\), \(\bar{P}_{0}\) are the mean and \(\sigma_{1,pe}^{2}\), \(\sigma_{0,pe}^{2}\) are the variances of the peak power of encoded marks ('1's) or spaces ('0's), respectively, which are numerically computed according to the details provided in the previous section, in the presence of pattern effects manifested due to the RSOA direct modulation (hence the subscript 'pe'). Because the amplitude distortions incurred by these effects on the encoded bits at the RSOA output are intense, the variances in the denominator of (9) dominate over the variances of conventional noise components, such as those associated with the RSOA amplified spontaneous emission (ASE) [30]. Moreover, given that the statistics of these distortions follow the Gaussian distribution [30], the relationship between the \(EP\) and the \(Q\)-factor reads [57]  
\[EP=\frac{1}{2}\text{erfc}\bigg{(}\frac{Q}{\sqrt{2}}\bigg{)}, \tag{10}\]  
where erfc(.) is the complementary error function. Figure 2 shows the \(EP\) versus the RSOA CW input power and bias current for three different direct modulation rates. This figure has been obtained for the RSOA structural and physical parameter values employed or derived in [28]. The values of the total injection current characteristics that have been used in deriving Figure 2a are \(I_{bias}=1.2I_{0}\) and \(I_{m}=0.1I_{0}\), where the current at transparency is \(\sim\)75 mA and \(t_{r}=17\%T\). On the other hand, Figure 2b has been obtained for a CW input power of \(-10\) dBm. The \(EP\) is acceptable for all scanned parameters' range at 2.5 Gb/s, but as we go to 3 Gb/s and beyond, it is necessary to provide more CW power and bias current. The physical explanation for this behavior of the \(EP\) is that the increase of the RSOA driving optical power and applied electrical bias accelerates the RSOA response [10] and widens its modulation bandwidth [58], so that the RSOA is allowed to handle data of higher rate. According to this fact, the continuous increase of the examined parameter values would seem natural for supporting faster RSOA direct modulation. However, there are physical limitations in this trend, which are imposed by the RSOA CW gain and the maximum amplitude difference, that is, extinction, between marks and spaces, \(AD_{1/0,max}\)[24]. In fact, increasing too much the CW power forces the RSOA to enter into the deep saturation regime where it provides a reduced optical gain, while increasing too much the bias current shifts the RSOA electrical modulation to occur beyond the linear gain-current region, that is, into the hard limit where the information-driving current is made to experience an almost flat RSOA optical gain [58]. For these physical reasons, the electrical current-induced RSOA optical gain perturbation conditions become such that they degrade the encoded output quality due to the modulated signal's decreased extinction in the first case and increased clipping in the second one. The CW gain should not fall below 10 dB so that the encoded signal, after undergoing the subsequent filtering action, can still have enough power to be used in RSOA direct modulation applications [13]. \(AD_{1/0,max}\) should exceed 10 dB [13] so that the encoded marks are sufficiently distinguished from the encoded spaces. Then, from Figures 3 and 4 it can be observed that these requirements can simultaneously be satisfied for some input power and bias current values only up to 3 Gb/s.