## 3 New Pulse Duration Limits of Modelocked Thin-Disk Lasers
### Challenges  
One of the most challenging points to obtain short pulse durations and high-power levels from modelocked TDLs is finding broadband materials that combine a high mechanical strength and excellent spectroscopic properties, suitable for high-power operation and short pulse generation in the thin-disk geometry [20]. Many Yb-doped materials have been modelocked in the past years in this geometry (Figure 15). Typically, Yb-doped broadband materials exhibit a disordered lattice structure that in turn limits their thermal properties [59]. Nevertheless, the excellent heat removal capability of TDLs is suitable to overcome these limitations, and extend high-power operation to the sub-100-fs regime. Another critical point is the maximum tolerable phase shift for soliton modelocking, which was discussed in 2.1. At a given intracavity average power, the intracavity peak power is significantly higher for shorter pulses. This sets a lower limit to the achievable average output power, which is lower than in the case of somewhat longer pulses (Figure 15, left). In addition, typical TDLs aiming for short pulse durations operate with low outcoupling rates: on the one hand because a low overall gain per roundtrip is beneficial to obtain short pulses in the soliton modelocking regime [28,29]; on the other hand, because the gain spectrum of most Yb-doped materials usually becomes smoother at low inversion levels \(\beta\) (corresponding to low output coupling rates). In Figure 16, we illustrate the effect of the inversion level on the gain spectrum in the absence of other intracavity spectrally dependent losses. As a consequence, TDLs with short pulses usually operate at a high ratio of intracavity _versus_ output power, further limiting the achievable output peak power (Figure 15, right). Furthermore, specific SESAM parameters are required to generate high power levels and short pulses from TDLs based on gain media with moderate gain bandwidths. The main challenges are in this case: \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Material** & **Remarks** & \(\mathbf{P_{\mathrm{av}}}\) & \(\mathbf{E_{\mathrm{p}}}\) & \(\mathbf{\tau}\) & \(\mathbf{f_{\mathrm{rep}}}\) & \(\mathbf{P}\) & **Ref.** \\ \hline \multirow{4}{*}{Yb:YAG} & Kerr Lens & & & & & \\  & Modelocking & 17 W & 0.4 \(\mu\)J & 200 fs & 40 MHz & 1.9 MW [61] \\  & (KLM) & & & & & \\  & KLM & 45 W & 1.1 \(\mu\)J & 270 fs & 40 MHz & 3.7 MW [61] \\  & \(\mathrm{KLM}+\) & & & & & \\  & Positive & 17 W & 0.4 \(\mu\)J & 1.7 ps & 40 MHz & 0.2 MW [62] \\  & dispersion & & & & & \\  & regime & & & & & \\ Yb:LuO & & 141 W & 2.3 \(\mu\)J & 738 fs & 60 MHz & 2.8 MW [26] \\  & & 63 W & 0.8 \(\mu\)J & 535 fs & 81 MHz & 1.3 MW [63] \\  & & 40 W & 0.5 \(\mu\)J & 329 fs & 81 MHz & 1.3 MW [63] \\  & & 7 W & 0.1 \(\mu\)J & 142 fs & 64 MHz & 0.7 MW [22] \\  & & 25 W & 0.4 \(\mu\)J & 185 fs & 66 MHz & 1.8 MW [64] \\ Yb:KLuW & & 21 W & 0.6 \(\mu\)J & 440 fs & 35 MHz & 1.2 MW [65] \\ Yb:KYW & & 22 W & 0.9 \(\mu\)J & 240 fs & 25 MHz & 3.3 MW [66] \\ Yb:ScYLO & & 3.9 W & 0.1 \(\mu\)J & 236 fs & 36 MHz & 0.4 MW [67] \\  & & 4.6 W & 0.1 \(\mu\)J & 101 fs & 70 MHz & 0.6 MW & - \\ Yb:SSO & & 28 W & 1 \(\mu\)J & 298 fs & 27 MHz & 3.5 MW [68] \\ Yb:CALGO & & 28 W & 1.3 \(\mu\)J & 300 fs & 21 MHz & 3.8 MW [69] \\  & & 20 W & 0.9 \(\mu\)J & 197 fs & 21 MHz & 4 MW [69] \\  & & 1.3 W & 0.03 \(\mu\)J & 135 fs & 45 MHz & 0.2 MW [69] \\ Yb:YCOB & & 2 W & 0.1 \(\mu\)J & 270 fs & 20 MHz & 0.3 MW [70] \\  & & 4.7 W & 0.2 \(\mu\)J & 455 fs & 24 MHz & 0.4 MW [70] \\ Yb:LuScO & & 7 W & 0.1 \(\mu\)J & 227 fs & 66 MHz & 0.4 MW [71] \\  & & 23 W & 0.3 \(\mu\)J & 235 fs & 70 MHz & 1.2 MW [72] \\  & & 9.5 W & 0.1 \(\mu\)J & 195 fs & 70 MHz & 0.6 MW [72] \\  & & 5 W & 0.1 \(\mu\)J & **96 fs** & 77 MHz & 0.6 MW & [21] \\ \hline \hline \end{tabular}
\end{table} 
Table 5: _Cont._* A somewhat higher modulation depth compared to what is typically used in high-power TDLs is beneficial to push the pulse duration to the bandwidth limit [28, 29]. This contributes to a higher QML threshold [51].