## 3 New Pulse Duration Limits of Modelocked Thin-Disk Lasers
### State-of-the Art and Recent Experimental Results
These isotropic materials combine high mechanical strength, excellent thermal properties and high absorption cross sections. Although these cubic sesquioxide materials are known since 1957 [97], the high melting temperature of about 2400 \({}^{\circ}\)C has limited the growth of high quality large crystals suitable TDL operation. This resulted for many years in a poor crystal quality and moderate optical-to-optical efficiencies [100, 101]. In the meantime, the heat exchanger method (HEM) was developed and enabled the growth of high quality, large sesquioxide crystals suitable for the fabrication of thin-disk crystals [96]. It is worth noting that very recently,preliminary results were presented with a modelocked TDL based on a polycrystalline ceramic sesquioxide Yb:Y\({}_{2}\)O\({}_{3}\)[102]. The most promising sesquioxide material in terms of average power scaling is Yb:LuO [94, 103]. This material exhibits a higher thermal conductivity than Yb:YAG of \(\kappa_{\mathrm{Lu3O3}}\)(5 at.%) = 11.7 W\(\cdot\)m\({}^{-1}\cdot\)K\({}^{-1}\) compared to \(\kappa_{\mathrm{YAG}}\)(10 at.%) = 6.6 W\(\cdot\)m\({}^{-1}\cdot\)K\({}^{-1}\), for an equivalent doping concentration of 1.4 \(\times\) 10\({}^{21}\) cm\({}^{-3}\). Furthermore, it has a higher absorption cross-section at the zero-phonon line (ZPL) (976 nm) than Yb:YAG at its typical pump wavelength of 940 nm. This does not only allow for fabricating thinner disks, but also reduces the thermal load in the crystal, as the quantum defect is lower. Pumping at the ZPL requires the use of volume Bragg grating stabilized diodes [104], which are currently commercially available. Pumping Yb:YAG at its ZPL (969 nm) is also possible [105]. However, in Yb:YAG, the peak emission cross section at the ZPL has a similar value to that of the broad peak at 940 nm. Therefore, the benefit of pumping at the ZPL is, in this case, limited to the lower quantum defect. Given the small advantage in terms of possible efficiency and the higher constraints imposed on the pump linewidth that require using VBG stabilized diodes currently limited to \(\approx\)800 W of output power, it seems more likely that future Yb:YAG modelocked TDLs will still be pumped at its broader absorption line at 940 nm. In addition, the availability of very thin disks with excellent quality that can be cooled efficiently further weakens the need to pump Yb:YAG at the ZPL. In the context of modelocked TDLs, Yb:LuO exhibits nearly twice the emission bandwidth of Yb:YAG, making it an excellent candidate for the generation of short pulses at high power levels. The first modelocked TDL based on this material delivered an average power of 25 W with a pulse duration of 523 fs [103]. Subsequent power scaling led to the demonstration of an average output power of 141 W in 738 fs long pulses [26], which was, for many years, the highest output power reported from a modelocked oscillator demonstrating the large potential of this material for high-power operation. 2.1 Short Pulses from Yb:Lu\({}_{2}\)O\({}_{3}\) and First Experiment of CEO Detection of a Modelocked TDL  
The full potential of Yb:LuO for short pulse generation in the thin-disk geometry was not exploited until the recent demonstration of 142 fs at an average power of 7 W [22]. In this result, a large fraction (\(\approx\)70%) of the emission bandwidth of the laser material was exploited (Figure 17), confirming the potential of this material also for short pulse generation. The short pulses of this TDL enabled the generation of a coherent super-continuum (SC), without the need for external pulse compression or amplification. The SC (Figure 18, bottom left) after the highly-nonlinear photonic crystal fiber covered more than an octave and was launched into a standard _f_-to-2\(f\) interferometer [106] for CEO beat detection. A schematic of the interferometer is shown on the top right hand side of Figure 18. The detected CEO beats had a signal-to-noise ratio (SNR) of more than 25 dB in a resolution bandwidth (RBW) of 3 kHz (Figure 18, bottom right) and 30 dB in a RBW of 1 kHz.