## 2 Average Power Scaling of Modelocked Thin-Disk Lasers: Challenges and Milestones
### Harnessing Intracavity Nonlinearity
Usually, the presence of a Brewster plate is beneficial as it offers control over the total amount of SPM when placed at a position in the cavity close to a focus, and ensures linear polarization of the laser output. In cavities where a fine control of the SPM can be achieved otherwise (for example with the air pressure, when the oscillator is operated in a vacuum chamber) a thin-film polarizer can be chosen instead of a Brewster plate to select the polarization. * Cavity optics: The nonlinearity introduced by the coatings of different cavity optics has been, until now, always considered negligible. However, in simple cavities where a low number of passes through the gain medium is chosen, they can become an important contribution to the total soliton phase shift at extreme intracavity peak powers. * Air atmosphere: The contribution of the air atmosphere was initially ignored, since the nonlinear refractive index \(n_{\mathrm{2,atm}}\) is orders of magnitude smaller than the refractive index of, for example, a fused-silica Brewster plate. However, typical MHz TDLs have cavity lengths in the order of several meters to several tens of meters. Furthermore, in most modelocked TDLs, the intracavity peak power is substantially higher than the output peak power and can exceed 100 MW [17, 32]. Therefore, intracavity SPM introduced by the ambient air in the cavity can become the main contribution to the total soliton phase shift [33]. In order to compensate for this phase shift and obtain stable soliton modelocking, large amounts of negative GDD are required. If this phase shift becomes excessive (typically larger than some hundred mrad), modelocked operation is destabilized [28, 34]. Different approaches have been suggested in the past years to overcome this limitation:
* Helium flooding Helium has a nonlinear refractive index \(n_{\mathrm{2}}\) that is approximately 8 times smaller than air (\(n_{\mathrm{2,air}}\approx\) 3\(\cdot\)10\({}^{-23}\) m\({}^{2}\)/W, [35] and \(n_{\mathrm{2,He}}\approx\) 0.4\(\cdot\)10\({}^{-23}\) m\({}^{2}\)/W [36]). Therefore, replacing the air in the cavity by helium enabled the demonstration of the 10 \(\upmu\)J pulse energy milestone in 2008. In this result, 11 \(\upmu\)J were obtained at an average power of 44 W from a SESAM modelocked TDL based on Yb:YAG [32]. In this oscillator, the disk was used in a single-pass configuration, resulting in a high intracavity pulse energy of \(>\)110 \(\upmu\)J. The required dispersion to generate the 791-fs pulses was, in this case, \(-\)20,000 fs\({}^{2}\). * Multiple gain passes through the same disk Another approach to lower the SPM in the cavity is to reduce the intracavity peak power by using a higher output coupler transmission. An important advantage of this approach is that the fluence on the SESAM and the thermal load on all components inside the laser cavity are reduced. Efficient laser operation with a higher output coupling transmission is only possible if the gain per cavity round trip is increased accordingly. This can be achieved by multiplying
the number of passes through the same gain disk, which results in an increased overall gain per cavity roundtrip. This geometry, most commonly referred to as \"active multi-pass cell\" in a modelocked TDL, was introduced by [PERSON] _et al._[37, 38]. Using this approach, 145 W of average power were demonstrated with a pulse energy of 41 \(\upmu\)J using a 72% output coupling transmission and 11 passes through the Yb:YAG thin disk [18]. In this case, the intracavity pulse energy was below 60 \(\upmu\)J and operation in air was possible with a total GDD of -236,000 fs\({}^{2}\). In addition to the large amounts of negative GDD required in this approach, a large amount of passes through the thin disk significantly increases the demands on the disk quality, since the cavity stability zones shrink significantly with the number of passes [27]. Another potential disadvantage is the reduced \(Q\)-factor of the cavity, resulting in a higher intrinsic noise level.