# Mode-Locking Dynamics in an All-PM Figure-Nine Tm-Doped Fiber Laser
## 3 Results
This causes differential phase changes to be experienced by pulses counterpropagating in the amplifying loop as a result of self-phase modulation. The phase shift in the nonlinear medium is selected so that the pulse maxima interfered constructively causing an increase in pulse intensity. This causes the transmitted pulses (output port) to have a higher peak power value. On the other hand, the non-transmitted part (reject port) consists of this radiation that interfered destructively. Since pulse slopes are characterized by lower peak power than the central peak, the radiation at the reject port generally takes the form of two local maxima between which there is a dip, which is the case with our oscillator [27, 38]. The results are consistent with earlier studies, mainly with lasers operating at 1000 and 1550 nm [30, 38, 51]. It can be noticed that the highest increase in RIN value covers the frequency range below 25 kHz, similarly to the laser presented in [52]. Figure 2: Measured single-pulse operation characteristics. Optical spectrum at the output (**a**) and reject (**b**) port. Autocorrelation trace with \(\mathrm{sech}^{2}\) fit at the output (**c**) and the reject (**d**) port. RF spectrum of the first harmonic (**e**) and the broad spectrum of harmonics in the 3 GHz span (**f**), measured with resolution bandwidth 50 Hz and 1 kHz, respectively. The combination of an artificial SA with a negative GDD value and an all-PM configuration resulted in the ability to control the dynamics of laser operation with a change of Ppump exclusively without changing the settings of the absorber itself. This situation is typical for ML lasers based on artificial SAs such as NALM or NOLM. Self-starting occurs with relatively high Ppump, thus leading to multi-pulse operation. Then, as a result of decreasing the value of the Ppump, transitional stages of operation are produced to reach a single pulse in the cavity as the last step. To monitor the dynamics of the laser over the entire range of Ppump, we analyzed oscillograms and optical spectra for each Ppump value. We decided to present these results for the output port as it was particularly steadier than the reject port in terms of RIN value. Given the use of all-PM and NALM configurations, we ensured the lack of polarization state influence on the dynamics. This allowed us to reach states that are purely pumping power-driven. We recorded 8 different states of pulse operation whose transitions occurred after exceeding a certain value of Ppump and were characterized by a slight hysteresis. However, the reproducibility of changes between states and the patterned response of the system to pump manipulation aroused our interest and resulted in an attempt to investigate its behavior. The results of our observations are shown in Figure 4.  
The dynamic of pulse-state changes was not repeatable, meaning each time the laser was turned on, the transition from multi-pulse to single-pulse operation was not identical, but it followed a certain pattern. In high Ppump states (750 mW \(<\) Ppump \(<\) 980 mW) the laser pulse operation changes in time without modulation of Ppump. The three states obtained from the self-starting power to around 750 mW are characterized by packets of pulses irregularly spaced between the fundamental pulses given by round-trip-time. We have been able to observe three different patterns of 8 pulses of similar amplitude (black waveform in Figure 4), 1 main pulse and 6 additional ones (red), and 1 main and 5 additional pulses (green), successively. Interestingly, upon closer analysis of the divergence times in pulse positions (over 11 consecutive round trips) we did not note significant pulse drift for the 980 and 750 mW Ppump (Figure 5). The stability of the separation indicates the previously observed phenomenon of densely bunched solitons, although in previous work, changing between states most often also requires changing the pumping power of the active fiber [46; 47]. This means that our laser generates a condensed soliton phase state on a small time scale.