## 4 Discussions  
The performance of coherent networks highly depends on the properties of optical source, such as the number and power of comb modes, OSNR, RIN, phase noise, and timing jitter [43]. The laser investigated in this paper possesses related high individual optical  
Figure 5: (**a**) Normalized first harmonic RF PSD with Lorentzian fit for the laser measured using a Keysight Technologies N9030A 50 GHz PXA signal analyzer at RBW = 51 Hz. (**b**) A typical single side band (SSB) phase noise spectrum L(f) showing the regions of the different noise mechanisms with various slopes, frequency boundaries, and areas of the noise mechanism regions. (**c**) Calculated SSB L(f) from the laser showing the two main noise mechanisms from measured RF PSD at RBW = 10 kHz. powers (over \(-16.6\) dBm) for all 65 modes as shown in Figure 2a. In addition, the extremely high OSNR (>60 dB) with the central wavelength located at the middle of the C-band are benefits for achieving high performance in a multi-channel parallel transmission WDM with high-order advanced modulation formats [44]. The all-modes integrated average RIN of \(-164.4\) dB/Hz achieved for our QDot SSP MLL is much lower than that (\(-140\) dB/Hz) from the QDash SSP MLL reported in Ref [45]. On the other hand, RINs of individual single longitudinal modes are important parameters since each of the modes of the laser are to be used as transmission channels. They are expected to have a higher RIN in comparison to the collective RIN of all the modes due to mode partition noise, which arises due to an intensity anti-correlation between the longitudinal modes [46; 47]. The small values of the average RIN between \(-134.8\) and \(-128.7\) dB/Hz for all 56 modes obtained in this study are attributed to the characteristics of QDot material inside the laser cavity with very low mode partition noise. According to the analysis of tolerance against the laser linewidth (\(\Delta v\)) times symbol duration (\(T_{s}\)) product (\(\Delta v\cdot T_{s}\)) for a receiver penalty of 1 dB at a BER of \(10^{-3}\)[48], the maximun tolerable linewidth for a 28 Gbaud system are 3.92 MHz and 1.12 MHz for the square 16 QAM and 64 QAM modulation formats, respectively. From the measured results shown in Figure 4, all 56 modes of our laser are suitable for the 28 Gbaud 16 QAM system and most modes are suitable for the 28 Gbaud 64 QAM system. The value of the RF linewidth of a semiconductor MLL is strongly affected by the gain material dimensionality. It decreases when moving from bulk to QW and from QW to QDot/Qdash active regions, as shown in Figure 6. Typical values of the RF linewidth lie in the range of a few tens of kilohertz [49] and a few kilohertz [10] for QDash active regions down to a few hundreds of hertz reported in this study for QDot MLLs, compared with the much larger RF linewidth for bulk and QW MLLs. Study of the RF linewidth either from a directly measurement of the RF spectrum or curve fitting of measured phase noise vs. mode number can provide simple and appropriate ways to characterize the pulse-to-pulse timing jitter of a semiconductor passively ML laser. The results from the two methods presented in this work are in excellent agreement. The method of parabola curve fitting from measured phase noise vs. mode number does not require a direct measurement of the RF PSD, which for a high repetition rate laser necessitates the use of a high-speed photodetector. Therefore, this method is not restricted to measuring lasers with repetition rates below the bandwidth of the used photodetector. The femtosecond level pulse-to-pulse timing jitter obtained from the laser studied in this study demonstrates highly stable mode spacing across the whole comb. An integrated timing jitter of 790 fs is reported in the frequency range from 1 to 20 MHz for a 40 GHz InAs/InP QDash SSP MLLs [42]. In order to make a comparison, we  
Figure 6: RF linewidth dependence on gain material dimensionality, where Bulk, Q-Well, and Q-Dash (black) are from [49], Q-Dash (brown) from [10].