## 2 Average Power Scaling of Modelocked Thin-Disk Lasers: Challenges and Milestones  
Several issues have, so far, limited scaling of modelocked TDLs to average output powers in the kilowatt range. One challenge is achieving fundamental transverse mode operation at high average powers, which is a crucial aspect for stable passive modelocking. As a result, average power and energy scaling of passively modelocked TDLs goes hand-in-hand with progress in power scaling of TDLs operating in single fundamental transverse mode. In most bulk lasers, thermal aberrations that occur in the gain medium mainly limit the available power. TDLs are ideally suited to partially overcome this limitation. Significant efforts have been carried out in the past years to optimize fabrication and contacting of standard thin gain media to minimize these thermal aberrations, in particular for the most commonly used gain material for TDLs, Yb:YAG [12, 23, 24]. Until now, 500 W of continuous wave (cw) power with diffraction limited beam quality (\(M^{2}<1.1\)) have been demonstrated using one disk based on this material [25]. For novel gain materials such as Yb:LuO or Yb:LuSoO, small residual thermal lensing can be compensated by adapting the resonator design [26]. These novel materials such as Yb:LuO have a large potential to outperform Yb:YAG in terms of efficiency and pulse duration, when growth and contacting techniques are perfected. The challenges of achieving single-transverse mode operation from high-power TDLs in the context of modelocking have already been discussed in detail in reference [27]. Here, we will focus on the challenges of achieving soliton modelocking at high average powers and high pulse energies.  
One important point is avoiding an excessive nonlinear phase shift due to self-phase modulation (SPM) that can destabilize the pulses in the soliton modelocking regime [28, 29]. In the past, the dominant source of unwanted SPM was the nonlinearity of air. We will discuss different approaches that have been demonstrated in the past years to reduce this parasitic nonlinearity. In particular, a new approach to overcome this limitation in the context of modelocked TDLs was recently demonstrated, which consists of operating the oscillator in a vacuum environment. In this way, the nonlinearity of the ambient environment is reduced by several orders of magnitude enabling high average powers and pulse energies in simple oscillator geometries, with a low number of passes through the gain medium and low output coupling rates. Furthermore, only a small amount of dispersion is required even at very high intracavity pulse energy to compensate for this phase shift within one round-trip in the laser cavity. With this approach, the latest step in average power scaling was achieved, reaching an average power of 275 W at a pulse duration of 583 fs using the well-established gain material Yb:YAG. The laser operates at a repetition rate of 16.3 MHz resulting in a pulse energy of 16.9 \(\upmu\)J and a peak power of 25.6 MW. We will review this latest step in power scaling, which opens the door to future kilowatt-level oscillators.  
Another point that has only recently been investigated is possible limitations of SESAMs in terms of damage and lifetime. As a result of a detailed investigation, simple guidelines to design robust SESAMs with high-damage thresholds and optimized parameters for operation at extreme intracavity conditions were recently developed [19]. This is a crucial point for future kilowatt-level oscillators. We will review these guidelines and discuss further improvements.  
Ultimately, thermal effects and damage that occur in different cavity components limit average power scaling of modelocked TDLs. This is particularly the case in simple thin disk oscillator geometries with low gain per roundtrip, where the circulating intracavity power can reach several kilowatts of average power. We will discuss critical points and future improvements.