I. Introduction
Monolithic semiconductor mode-locked lasers (MLLs) provide sub-picosecond pulses at repetition rates determined by the laser cavity round trip time and possess very interesting attributes over solid-state approaches, e.g., compactness allowing for manufacturing large numbers of devices at wafer-scale, on-chip integration feasibility with silicon photonic circuits via wafer bonding and processing techniques [1], ease of direct electrical driving, ultra-fast carrier dynamics [2], [3], capability of generating pulse trains up to in the terahertz, and wide potential operating wavelengths range. The MLLs are promising as coherent frequency comb sources for many emerging applications such as high precision optical sensing, wavelength division multiplexing transmission, photonic assisted analog-to-digital conversion, arbitrary waveform generation, all-optical signal processing, millimeter wave generation [4], and light detection and ranging (LiDAR) [5]. These applications usually require specific mode locking characteristics, such as very short pulse widths with high peak powers and low radio frequency (RF) linewidths. Moreover, the performance of the MLLs in these applications is mainly dependent on the level of the amplitude noise, phase noise, and optical linewidth [6]. Therefore, investigations of the fundamental physical phenomena of these MLLs, such as mode-locking and noise properties, are key to improving their performance.