# Mode-Locking Dynamics in an All-PM Figure-Nine Tm-Doped Fiber Laser
## 3 Results  
In the process of examining the setup, we found several wave plate settings that enabled self-starting ML operation. Once the given setting was found, the wave plates were not tuned, and as the threshold of P\({}_{\text{pump}}\) was reached, self-starting operation with the central wavelength ranging from 1950 up to 1990 nm proceeded. Different wave plate settings resulted in different central wavelengths of the generated pulses since the phase shift introduced by NRPS depends on the wavelength [30]. For various settings, the P\({}_{\text{pump}}\) threshold of ML ranged from about 800 mW to about 1860 mW and depended mainly on the setting of the QWP\({}_{2}\). Unfortunately, not every setting leads to single-pulse operation by decreasing the P\({}_{\text{pump}}\). For this reason, we present the results acquired for the angle settings as follows: \(\theta_{\text{QWP}_{1}}=28.5^{\circ}\), \(\theta_{\text{HWP}}=90.0^{\circ}\) and \(\theta_{\text{QWP}_{2}}=82.5^{\circ}\), which provided repetitive self-starting and effortless achievement of the single-pulse operation. In this setting, P\({}_{\text{pump}}\) needed for self-start and single pulse were 980 mW and 405 mW, respectively. We used the following instruments to characterize the source: an optical spectrum analyzer (Yokogawa, Tokyo, Japan, AQ6376, OSA), a 3 GHz radio frequency (RF) spectrum analyzer (Rohde and Schwarz, Munich, Germany, FPL1003), a 6 GHz digital oscilloscope (Agilent, Santa Clara, CA, USA, DSO90604A), an InGaAs high-speed photodiode (Discovery Semiconductors, Trenton, NJ, USA, DSC2-50S), an optical power and energy meter (Thorlabs, Newton, NJ, USA, PM400 and Thorlabs S405C), and an autocorrelator (APE GmbH, Berlin, Germany, pulseCheck 50 USB, AC). To characterize RIN, we used a setup consisting of a 200 MHz oscilloscope (Rohde and Schwarz RTA4004), an InGaAs fixed gain amplified detector (Thorlabs PDA10D2, PD), and a 4 MHz low-pass filter. The results of single-pulse operation at a P\({}_{\text{pump}}\) of 405 mW are shown in Figure 2. For the output port, the laser emits pulses centered at 1985 nm with 6.4 nm of the full width at half maximum (\(\Delta\lambda\)) bandwidth (without taking into account the Kelly's sidebands [49]), 650 fs pulse duration and 177 pJ energy. From the reject port, pulses with 19.2 nm \(\Delta\lambda\), 1.28 ps and 57 pJ were generated. The \(\Delta\lambda\) was determined including the dip inside the spectrum (visible in Figure 2b). Figure 1: Experimental setup of all-PM NALM-based Tm-doped fiber laser. WDM: wavelength division multiplexer; PBC/PBS: polarization beam combiner/splitter; TDF: Thulium-doped fiber; FR: Faraday rotator; QWP: quarter-wave plate; HWP: half-wave plate; M: mirror, NRPS: non-reciprocal phase shifter. To investigate the noise properties, we measured the RIN of the free-running laser and integrated it in the range from 10 Hz to 488 kHz. The results are shown in Figure 3. Integrated RIN in this range is 0.29% and 0.98% for output and reject port, respectively. As our setup was not stabilized either thermally or via electronic locking methods, the RIN levels were relatively high compared to other ultrafast oscillators employing NALM in figure-nine architecture [26, 30, 37, 50]. However, our goal was to compare integrated RIN values between exit ports for the solitonic laser operating at around 2000 nm. In the case of the reported oscillator, the integrated RIN value is over 3 times lower for the output port than in the case of the reject port. Interestingly, the output port reigns supreme over the reject port in all measured parameters but the optical spectrum bandwidth, which was 3 times narrower. The difference in characteristics between ports can be explained by the operating principle of the APM technique in which the coherent addition of pulses can, in a way, be treated like a Mach-Zehnder interferometer. The intensity-dependent phase differences are achieved with an asymmetrical gain medium.