## 4 Self-Referenced DPSSLs in Thin Disk Geometry
The CEO frequency had a high sensitivity to the pump current owing to the strong amplitude-to-phase coupling induced in the silica plate Kerr medium. Therefore, pump current modulation was first implemented for CEO-stabilization. With the use of a phase-lead filter to overcome the measured 3 dB roll-off frequency of 3 kHz in the response of _f_CEO to a modulation of the pump current, a residual integrated in-loop phase noise of 250 mrad was achieved (1 Hz-500 kHz). Improvement of the CEO stabilization was obtained using direct laser intra-cavity power modulation via an acousto-optic modulator (AOM) placed inside the resonator to overcome the limitation of the 1 ms long lifetime of Yb and the correspondingly low achievable servo-loop bandwidth. In this case a residual integrated phase noise of 100 mrad in-loopand 200 mrad out-of-loop were reported. However, the use of an intra-cavity AOM appears more difficult to be implemented in TDLs with higher intra-cavity power due to thermal issues. A refinement of these initial results including a more thorough characterization of the CEO stabilization was recently reported by the same group [62]. The output power of the oscillator was increased to 40 W and the external compression reduced the pulse duration to 17 fs after a first stage of spectral broadening/compression and down to 7.7 fs using tailored dispersion mirrors in a second stage. Due to the bandwidth limitation of the CEO control by the pump current (3 dB point of 1.5 kHz) resulting from the 1 ms gain relaxation time, stabilization with the intra-cavity AOM was preferred. The AOM placed at the Brewster angle within the cavity was used as a loss modulator with a maximum modulation amplitude of 2%. In-loop integrated phase noise of 180 mrad was achieved, and 270 mrad out-of-loop (1 Hz-500 kHz). This difference was partly attributed to amplitude-to-phase (AM-to-PM) noise conversion in the SC generation process and partly to the digital phase detector used in the CEO loop, possibly resulting from nonlinearities in the behavior of this device according to the observations reported in [45]. The first SESAM-modelocked TDL was reported by [PERSON] _et al._[30]. The Yb:CALGO TDL generated 90 fs pulses at 65 MHz repetition rate with an average output power of 2.1 W at a center wavelength of 1052 nm. A pump laser diode made of two diode stacks VHG-stabilized to a wavelength of 979.5 nm with a maximum output power of 400 W was used to pump the gain medium in an arrangement with 24 passes over the disk. A fraction of only 65 W of pump power was used in the reported results, which was coupled into a multimode fiber with 400 m diameter and an \(M^{2}\) value of about 140. The sub-100 fs pulse duration of this laser was among the shortest produced directly from a TDL oscillator at this time and was made possible by the broadband gain of the Yb:CALGO crystal. Consequently, no external pulse compression was needed for SC generation and subsequent CEO beat detection in a quasi-common-path _f_-to-_2\(f\) interferometer. A fraction of about only 2% of the laser output power was used for SC generation in a PCF, resulting into a soliton order \(N_{\mathrm{sol}}=5\) that supported the generation of a coherent octave-spanning SC spectrum resulting in the detection of a CEO beat signal at 680 nm with 33 dB SNR in a RBW of 100 kHz. A tight CEO lock was achieved by feedback to the pump current with a loop bandwidth of 30-40 kHz. This was implemented using in-house designed modulation electronics capable of applying a small modulation with a bandwidth of about 100 kHz on top of the laser DC current delivered by a standard power supply. An in-loop integrated phase noise of 120 mrad was achieved for the tightly locked CEO beat, resulting in an rms frequency fluctuation of \(f\) CEO of 8.8 mHz observed over a period of 17 min for the 26 MHz CEO frequency, corresponding to a contribution \(<\)10\({}^{-16}\) to the frequency instability of an optical comb line.