## 4 Self-Referenced DPSSLs in Thin Disk Geometry
The first CEO beat detection in a TDL operating in a high average power regime of \(>\)100 W was reported by [PERSON] _et al._[63]. The SESAM-modelocked Yb:YAG TDL with a similar design to the record-high average power TDL [36] was operated in a low-pressure (150 mbar) helium environment. It delivered 140 W of average power at 9.67 MHz with \(\sim\)750 fs pulses. With this long pulse duration, external compression was necessary to achieve sufficiently short pulses for coherent SC generation. A small fraction of the oscillator output power was thus compressed down to 63 fs by combining spectral broadening by self-phase modulation in a large-mode-area PCF and Gires-Tournois-interferometer (GTI) mirrors. A strong CEO beat with \(>\)33 dB SNR in a RBW of 100 kHz was then detected in a commercially-available _f_-to-_2\(f\) interferometer. Whereas a significant shift of \(f\) CEO with the pump power was observed in this laser, which should enable self-referencing by the common method of pump power modulation, the CEO stabilization could not be achieved. A detailed study of the frequency dynamics of _f_CEO in SESAM-modelocked TDLs was recently reported by [PERSON] _et al._, where the behavior of the aforementioned Yb:CALGO laser with 65 MHz repetition rate and high-power Yb:YAG laser with sub-10 MHz repetition rate was compared [31]. A complete noise characterization of these two laser systems including the measurements of various relevant transfer functions combined with comparison with theoretical models evidenced a fundamentally different behavior of the two TDL resonators. This difference led to the impossibility to CEO-stabilize the high power Yb:YAG oscillator. Even if a comparable RIN of the multi-transverse-mode pump diodes used in these two systems was identified as the main contribution to the CEO noise in each case, the laser cavity dynamics was shown to play an essential role in the CEO frequency dynamics. Whereas the transfer function of _f_CEO for pump modulation was characterized by a highly damped second-order low-pass filter with a cut-off frequency of \(\sim\)12 kHz and a smooth associated phase change in the Yb:CALGO TDL, it behaved like a resonant second-order filter in the Yb:YAG laser with a pronounced resonance at 7.5 kHz. The abrupt phase change associated to this resonance that occurred in a narrow frequency range led to the impossibility to achieve a tight phase lock of _f_CEO in this laser. The different operation point of the SESAMs used for modelocking of these TDLs was identified as the main cause for the different damping factor observed in the cavity transfer functions. More precisely, the relevant parameter was the variation of the SESAM nonlinear loss as a function of the intra-cavity pulse energy. Experimental results were in good agreement with theoretical considerations derived from the complex cavity transfer function obtained for modelocked lasers [79]. As an outcome of this analysis, a laser cavity exhibiting a high damping of the relaxation oscillation by nonlinear intra-cavity elements, for example by operating the SESAM in the roll-over regime, is required for CEO stabilization. This work presented important guidelines towards the future frequency stabilization of multi-100-W TDL oscillators. The importance of the CEO dynamics in the feasibility to achieve a tight CEO lock in a frequency comb shown in the case of these TDLs complements previous observations reported in Section 2.3 for a bulk Er:Yb:glass DPSSL. Alternative stabilization methods that do not use pump current modulation may be used instead to circumvent the TDL cavity transfer function, such as using SESAM OOM for CEO stabilization as previously reported in a DPSSL [44]. The extremely low losses of SESAMs make this technology compatible with high-power and high-energy lasers such as TDLs. Therefore, SESAM OOM appears as a well-suited complementary approach for CEO stabilization of TDLs.