# Mode-Locking Dynamics in an All-PM Figure-Nine Tm-Doped Fiber Laser
## 3 Results
Figure 3: Relative intensity noise characterization for both exit ports. Upper panel: RIN results; lower panel: integrated RIN. With a decrease of P\({}_{\rm pump}\) below 750 mW, we observed states in which individual pulses traveled at equal and fixed intervals between each other. We first noticed a condition in which three additional pulses appear whose amplitudes are close to the fundamental pulse and propagate at a distance of about 5.8 ns from each other. The triple-pulse emerged at 566 mW of the P\({}_{\rm pump}\) and exhibited a pulse separation of 2.0 ns. This state was significantly rare, only occurring once every 20 courses of pump decrease. The double-pulse operation occurred at around 450 mW of P\({}_{\rm pump}\) and was far more common. Here the pulse separation was equal to about 2.8 ns. Since the distances between pulses in all the described states were not constant, none of them can be classified as harmonic mode-locking. The last among observed states was a single-pulse operation. After reducing the P\({}_{\rm pump}\) below double-pulse operation (428 mW), we have been reaching single-pulse with CW spectral component located at 1972 nm. The CW component was close to the first-order Kelly sideband on the shorter-wave side. Further reduction of power to 405 mW resulted in the disappearance of the CW component. Measured optical spectra were unstable for higher P\({}_{\rm pump}\) and changed rapidly irregularly. With the decrease of pump power, the center wavelength  
Figure 4: Optical spectra (**left**) and recorded oscillograms (**right**) for eight different laser operating states corresponding to given pumping power. Figure 5: Successive temporal traces show a lack of drift among pulses in states: (**a**) 8 pulses; (**b**) 5 + 1 pulses. shifted unpredictably in both directions. However, for weaker pump powers (<474 mW) the direction of movement of the center wavelength was towards shorter wavelengths, with a sudden \"jump\" towards longer wavelengths when the single-pulse operation (without CW) was achieved. Important notice is that the optical spectra of other stable states such as double or triple pulses remained stable during each run. A very interesting detail is visible during the double-pulse and \(1+3\) pulses operation of the laser, where the optical spectrum exhibits an increase in the number and compaction of Kelly sidebands. The \(\Delta\lambda\) of measured spectra has remained consistent along the entire measurement, although the broadest spectrum at output port was recorded for single-pulse (on par with the state of 5 +1 pulses) and equal to 6.4 nm, while the narrowest spectrum belonged to the state of 1 + 4 pulses. The \(\Delta\lambda\) of the optical spectra on the reject port also was not significantly fluctuating and approximated 19 nm. For the next step of analyzing the dynamics of laser operation as a function of P\({}_{\text{pump}}\), we used the power division ratio between the two exit ports. The states of operation were not repeatable every time. However, during observation, we came across a kind of schematic of laser operation which was dependent on the state of self-start dynamics, i.e., the state of operation after self-start dictated the pattern in which the dynamics of laser operation changed up to a single pulse. The results presented in Figure 6 correspond with the measurements in Figure 4. Since we did not want to consider the hysteresis of the system which has already been analyzed in other works [53; 54], we decided to measure the split ratio in the case of gradual reduction of P\({}_{\text{pump}}\) from self-start to a single pulse, and thus within one complete measurement. Analyzing the values of this distribution ratio, it can be found that as the P\({}_{\text{pump}}\) decreases, the difference between the average power measured at the output port versus the power measured at the reject port increases. The only minor deviation is the border between the state of 1 + 6 pulses and the state of 1 + 5 pulses.