# Mode-Locking Dynamics in an All-PM Figure-Nine Tm-Doped Fiber Laser
## 4 Discussion  
The ability to evaluate pulse dynamics as a function of Ppump in all-PM artificial SA-based ML fiber laser has become even more needed now with the rapid development of robust setups and their industry-level applications [26; 34; 55]. Unlike many previous works [42; 43; 44; 45; 53; 54; 56], we focused on studying the dynamics of a laser with a linearly polarized beam in which the only variable at fixed parameters of the SA is Ppump. We were able to isolate the dynamics of laser operation from the polarization state of the beam, thus neglecting the non-arbitrary introduced by a PC. To obtain informative data about our laser in the single-pulse regime, we characterized a number of its properties shown in Figures 2 and 3. Pulse durations directly from the oscillator were 650 and 1279 fs for output and reject port, respectively. Based on measurements of optical spectra and autocorrelation, time-bandwidth product 0.316 and 1.859 values were derived for output and reject port, respectively. Assuming the typical shape of a conventional optical soliton, we found that pulses from the output port were very close to the limit defined by the transform while pulses from the reject port had a non-zero chirp. Additional noise analysis confirmed both the comparatively satisfactory noise properties of the oscillator and the differences in performance between the output and reject ports. The 0.29% result for the output port is comparable to other lasers operating at similar wavelengths and using similar ML mechanisms [52; 57]. It implies that the presented laser can be used in the future as a low-noise seed laser for ultrashort pulse amplification systems [58]. On the other hand, in order to maximize the energy of the generated pulses, it would be necessary to replace the active single-clad fiber with Tm,Ho-co-doped fiber with a double-clad. Holmium ions used as a sensitizer would provide higher efficiency of pumping. Regarding a further integration of the setup, it would eliminate the free-space optics components and could significantly reduce the inherent noise level which, in the case of our laser, increases very rapidly for frequencies below 25 kHz. In the second part of our investigation, we studied the pulse dynamics. As NALM-based lasers require a high Ppump for self-starting, we focused our attention on possible scenarios of multi-pulse ML operation. We demonstrated eight different states that, despite similar optical spectra, differed in the relationship between the average power at the two ports and the waveforms recorded on the high-speed photodiode. Solitons propagating together in a cavity can self-organize, or the distances between them can change between passes through the cavity. We observed states that are not stable in the long term, but solitons form a condensed phase in the short term. Interestingly, in states with lower Ppump, we could observe additional solitons equidistant from each other. By analyzing the power ratio between the output and reject port, we were able to distinguish both the different states of laser dynamics and, more importantly, the changes between these states. This technique cannot determine precisely how many pulses are propagating in the cavity at any given time, but it can be a diagnostic clue for figure-nine architecture lasers. From the perspective of repetitive laser self-starting, knowledge of potential intermediate states can be crucial. Transitions between different states can introduce disturbances in the dynamics (e.g., collisions) which can cause loss of ML. From a practical point of view, the most desirable is a single-pulse operation (perhaps even with a CW component) immediately for Ppump threshold. Unfortunately for NOLM/NALM-based lasers, this is not achievable in anomalous dispersion. While this behavior is common in dissipative systems such as net-normal and stretched-pulse regimes [29; 31], lasers in the soliton regime tend to transition into multi-pulse mode due to the area theorem limiting single soliton energy [59].