## 2 Average Power Scaling of Modelocked Thin-Disk Lasers: Challenges and Milestones
### State-of-the Art Modelocked Thin-Disk Laser with 275 W of Average Power  
#### 2.2.1 Experimental Setup and Results  
The gain element used was a commercial Yb:YAG thin disk glued on a water-cooled diamond heatsink (TRUMPF GmbH). The disk was \(\approx\)100 \(\upmu\)m thick. The thin-disk head was arranged for 24 pump passes through the disk and a pump spot diameter of 4.7 mm. The disk was pumped at its broad absorption line at 940 nm. The measurement of the thermal lensing of this disk showed no significant thermal lensing over the whole pump power range used throughout the experiment, which allowed for robust fundamental transverse mode operation. We used an outcoupling rate of 11.4% for the modelocking experiment, and obtained up to 340 W of cw power at an optical-to-optical efficiency of 39.2% with a diffraction-limited beam (\(M^{2}<1.05\)) (Figure 3). A set of five dispersive mirrors in the cavity introduced approximately \(-\)8100 fs\({}^{2}\) of negative GDD per roundtrip, required for soliton modelocking. A fused silica plate with a thickness of 700 \(\upmu\)m was inserted at Brewster's angle for polarization selection. It was introduced at a fixed position in the  
Figure 3: **(a)** cw fundamental transverse-mode operation with the same output coupler as for the modelocking experiment, using only highly reflective mirrors as cavity mirrors and without polarization control of the laser; **(b)**\(M^{2}\) measurement at the maximum power of 340 W. Inset: Picture of the laser mode at the maximum cw output power. cavity where the beam had a large radius of \(\approx\)1.3 mm. This controls the laser polarization with minimal SPM. Fine control of the total SPM was achieved by changing the pressure in the vacuum chamber by introducing small amounts of nitrogen. The SESAM used in this experiment was designed for high damage threshold and high-power modelocking following the guidelines presented in reference [19] and summarized in paragraph 2.3 of this paper. Special attention was paid during fabrication to obtain a large homogeneous sample for future spot size scaling (Figure 4). It consists of a distributed Bragg reflector (DBR) and three 10-nm InGaAs quantum wells (QWs) as absorbers in an antiresonant configuration. A dielectric topcoating that consists of 3 quarter-wave pairs of SiO\({}_{2}\)/Si\({}_{3}\)N\({}_{4}\) was deposited by plasma enhanced chemical vapor deposition (PECVD). Nonlinear reflectivity and recovery measurements of this sample yielded a saturation fluence \(F_{\mathrm{sat}}\) = 140 \(\mathrm{\SIUnitSymbolMicro\meter^{2}}\), a modulation depth \(\Delta R\) = 0.95%, nonsaturable losses \(\Delta R_{\mathrm{ns}}\) = 0.1% and a recovery time \(\tau_{\mathrm{1/e}}\)=67 ps. The vacuum chamber (Figure 4) was operated at a constant air pressure of 0.5 mbar, which was the lowest value that could be obtained in our setup and with the available vacuum pump. Stable cw modelocking was obtained for average powers ranging from 135 W to 275 W (Figure 5d). When trying to reach higher power levels, the optical-to-optical efficiency decreased but no modelocking instabilities were observed. In order to avoid possible damage of the thin disk, the pump power was not further increased. At the maximum power of 275 W, the pulse duration was 583 fs (Figure 5a). The optical-to-optical efficiency was 32.4%, corresponding to an incident pump power of 839 W. The pulses had a time bandwidth product of 0.329 (ideal \(\mathrm{sech}^{2}\) 0.315), determined with the measured spectral bandwidth of 2 nm (Figure 5b). The repetition rate of the pulses was 16.3 MHz (Figure 5c), resulting in a pulse energy of 16.9 \(\mathrm{\SIUnitSymbolMicro\meter}\). The corresponding peak power of the pulses is 25.6 MW. Operation with a single pulse circulating in the cavity was confirmed using a fast photodiode (25 GHz) and a sampling oscilloscope. Furthermore, the delay of the autocorrelator (80 ps) was scanned in search for cross-correlations of potential parasitic pulses with the main pulse.