## 2 Experimental Procedure  
The experimental setup, shown in Figure 1a, was essentially identical for the two lasers studied in this work. First, we sketch the configuration of the Fabry-Perot resonator, whose emission was focused at 1.95 \(\upmu\)m. At one end we used a highly reflective PM fiber Bragg grating (PM FBG 1, >99% reflectance, \(\lambda_{\text{B}}\) = 1951 nm, and 140 pm bandwidth at \(-\)3 dB) and at the other end a SESAM (relaxation time constant of 10 ps and a high reflectance bandwidth between 1900 and 2080 nm). On the other side, Figure 1b shows the measured spectrum of PM FBG. These spectra contain two peaks representing the slow and fast axes and are the result of measuring PM FBG with a 2 \(\upmu\)m unpolarized amplified spontaneous emission light source. The medium gain was a PM TDF from Nufern(r) (length of 2 m, PM-TSF 9/125, 0.15 numerical aperture, cutoff wavelength of 1750 nm, and 9 \(\pm\) 2 dB/m absorption at 1180 nm). However, to protect the SESAM from excess pump power that was not absorbed by the medium gain, we also incorporated a PM wavelength division multiplexer into the system (PM WDM, 1550/1950 nm, with an insertion loss from the transmit port to the common port <0.6 dB at 1950 nm, and an insertion loss from the reflect port to the common port <0.5 dB at 1550 nm). A dichroic mirror was then used to redirect the excess pump power back into the cavity. A PM fiber optic coupler (PM OFC, 90/10, with a central wavelength of 1950 nm and a blocked fast axis) was then added to complete the cavity. As for the pump source, indirect pumping into the \({}_{3}\)F\({}^{4}\) energy level (peak absorption at 790 nm) is quite common, while direct in-band pumping into the \({}_{3}\)H\({}^{4}\) energy level (peak absorption at 1610 nm) is known for near-optimal performance [31]. We chose the latter because it has much higher efficiency. Consequently, a high-power laser diode (7.7 W) emitting at 976 nm was used to pump a custom continuous wave (CW) laser emitting at 1561 nm with a maximum power of 820 mW. At a laser threshold of 47 mW, the pumping unit's slope efficiency was 10.57 \(\pm\) 0.08%. This pump power was injected into the resonator through the remaining port of the PM FBG. Finally, to prevent unwanted reflections in the resonator, a second optical isolator (PM I, central wavelength of 1950 \(\pm\) 20 nm, peak isolation of 28 dB, and insertion loss of 0.6 dB) was inserted into the 10% port of the PM OFC, where the output power was obtained. The design of the second laser was largely the same as that of the laser emitting at 1.95 \(\upmu\)m; only the components that were incompatible with the new emission wavelength were changed [32]. The design includes PM WDM (1550/2070 nm, with an insertion loss from the transmit port to the common port <0.6 dB at 2070 nm and from the reflect port to the common port <0.5 dB at 1550 nm), a new 90/10 PM OFC (fast axis blocking and central wavelength 2070 nm), a new optical isolator (PM I, peak isolation of 28 dB and central wavelength at 2070 \(\pm\) 20 nm), and a longer PM TDF of 3.2 m (instead of the 2 m originally used for emission at 1.951 \(\upmu\)m). This last adjustment was necessary because the emission maximum for the \({}^{3}\)F\({}_{4}\)\(\rightarrow\)\({}^{3}\)H\({}_{6}\) transition occurs at an emission wavelength of 1.837 \(\upmu\)m, which is a long way away at 2.07 \(\upmu\)m. Consequently, the emission cross section decreases by 72%, compared to the maximum at 1.837 \(\upmu\)m [33].