## 3 Results
Figure 9: RSOA output (top) and MRR output (bottom) encoded pulses **(a)** waveform, **(b)** chirp and (c) pseudo-eye diagram at 11 Gb/s. bandwidth to an extent that is determined approximately by the detuning between the encoded signal and the MRR notch at resonance, that is, \(\approx\delta/2\pi\)[24]. On the other hand, according to the above justification for the appearance of peaking, the latter is not affected by changes in the ring radius values, which alter the order of resonance but not the spectral position of the notch. This happens in our case, since the derived permissible values of the MRR radius follow this pattern by being integer multiples of 4 \(\upmu\)m. From a mathematical perspective, this leaves intact the parameter \(\delta\) and accordingly the degree of peaking. Finally, Figure 11 depicts the MRR transfer function and its impact on the spectral components of the maximum and minimum logical '1's and '0's within the RSOA-encoded data stream. According to [24], it can be seen that the spectral peaks of the encoded logical '1's are shifted to the longer sideband relative to the optical carrier, while those of the encoded logical '0's are shifted to the shorter sideband. In order to combat the deleterious consequences of RSOA direct modulation provoked by the limited RSOA modulation bandwidth, the spectral peaks of the encoded '1's must lie in the falling slope of the MRR TF, with the peak of the maximum '1' being located closer to the TF notch than the peak of the minimum '1', so that the MRR transmits the former less than the latter. Moreover, the spectral peaks of the encoded logical '0's must be confined around the flat portion of the MRR TF, with the peak of the minimum '0' being located nearer to the MRR TF transparency point than the peak of the maximum '0', so that the MRR favors the former more than the latter. These requirements are efficiently satisfied by using the specified optimum parameters of the MRR, whose spectral response figures-of-merit thus are [40]\(FSR=\lambda_{enc}^{2}/(2\pi n_{eff}R)=13.5\) nm, resonance peak full-width at half-maximum \(FWHM=\lambda_{enc}^{2}(1-rl)/(2\pi^{2}n_{eff}R\sqrt{rl})=0.44\) nm and finesse \(F=FSR/FWHM=31\), which have been calculated by substituting \(\lambda_{enc}=1550\) nm, \(n_{eff}=1.41\), \(R=20\)\(\upmu\)m, and \(r=l=0.95\) so that the PNCR is ideally infinite. Then, the MRR can act upon the spectral components of the encoded pulses so that the peak differences can become more even for pulses of the same binary content, that is, '1's vs '1's or '0's vs '0's, and more distinguishable between pulses of different binary content, that is, '1's vs '0's. In addition, the absolute magnitudes of marks and spaces can become more enhanced and suppressed, respectively. In this manner, the MRR transforms the pattern-dependent distortions, which have been mapped on the encoded signal's spectral components, into pulse amplitude variations [15] that cancel those present right after the directly modulated RSOA, thus restoring the quality of the encoded pulses. \[EP=\frac{1}{2}\text{erfc}\bigg{(}\frac{Q}{\sqrt{2}}\bigg{)}, \tag{10}\]0 Modulation response of RSOA alone (black line) and with the addition of MRR (red line). The MRR target operation wavelengths are those mostly utilized in the applications mentioned at the beginning of the Section 1, that is, in the standard transmission windows of fiber communication systems [57]. Operation at these wavelengths is enabled both by the RSOA broad gain bandwidth and adjustable active medium material composition as well as by the MRR periodic comb-like transmission profile. The latter feature can be exploited provided that the center wavelengths of the encoded data are spaced apart by integer multiples of the free spectral range. In this case, the wavelength allocation should be coarse, in terms of the standardized wavelength division multiplexing grid spacing, or, if a more dense arrangement is desired so as to accommodate more channels, multiple MRRs can be cascaded along the same waveguide bus [64].