# SESAM Mode-Locked Yb:Ca3 Gd2(BO3)4 Femtosecond Laser
## 4 SESAM Mode-Locked Operation  
For passively ML operation, the rear mirror M\({}_{3}\) was replaced by a plane-concave mirror M\({}_{4}\) with \(R_{\text{OC}}=-100\) mm to create a second beam waist on the SESAM, ensuring its efficient bleaching. The estimated radii of this second beam waist were 60 and 65 \(\upmu\)m in the sagittal and tangential planes, respectively. The SESAM (BATOP, GmbH) applied in this experiment had a relaxation time constant of \(\sim\)1 ps, non-saturable loss of 0.8%, saturation fluence of 60 \(\upmu\)J/cm\({}^{2}\), and a modulation depth of 1.2%. The intracavity group delay dispersion (GDD) was managed by implementing four flat dispersive mirrors (DMs, characterized by the following GDD per bounce: DM\({}_{1}=-100\) fs\({}^{2}\), DM\({}_{2}=-100\) fs\({}^{2}\), DM\({}_{3}=-100\) fs\({}^{2}\), DM\({}_{4}=-100\  
\(\text{DM}_{4}=-250\) fs\({}^{2}\), \(\text{DM}_{5}=\text{DM}_{6}=-55\) fs\({}^{2}\)) in the other cavity arm. The total negative GDD value was varied by changing the number of bounces on the DMs. Initially, the ML operation was investigated by applying eight bounces (single pass) on the DMs (\(\text{DM}_{1}\)-\(\text{DM}_{4}\)), as shown in Figure 1, yielding a total round-trip negative GDD of \(-2800\) fs\({}^{2}\). Stable and self-starting ML operation was achieved with the 1.6% OC. The sech\({}^{2}\)-shaped spectrum of the soliton pulses was centered at 1052 nm with a FWHM of 8.2 nm, as shown in Figure 4a. The measured SHG-based intensity autocorrelation trace gave a pulse duration of 146 fs by assuming a sech\({}^{2}\)-shaped temporal profile (see Figure 4b). This resulted in a time-bandwidth product (TBP) of 0.324, which was slightly above the Fourier-transform-limited value for a sech\({}^{2}\)-shaped temporal profile. The long-scale SHG-based intensity autocorrelation scan of 50 ps indicated a single-pulse operation without any pedestals or multi-pulses (see inset in Figure 4b). The maximum average output power amounted to 181 mW at an absorbed pump power of 697 mW. The corresponding peak power was \(\sim\)17.5 kW at a pulse repetition rate of 62.4 MHz. The optical conversion efficiency reached 26% with respect to the absorbed pump power. The pulse duration was further shortened by optimizing the total negative GDD value. The shortest pulse duration was achieved by applying six bounces (single pass) on the DMs (\(\text{DM}_{3}\)-\(\text{DM}_{6}\)), as shown in Figure 1, yielding a total negative GDD of \(-1620\) fs\({}^{2}\). Self-starting ML operation of the Yb:GdCB laser with a 2.5% OC produced soliton pulses at the central wavelength of 1045 nm with a spectral FWHM of 12.1 nm, as depicted in Figure 5a. Pulses as short as 96 fs were achieved, as shown by the measured SHG-based intensity autocorrelation trace in Figure 5b. The corresponding TBP of 0.319 indicated generation of nearly Fourier-transform-limited pulses with a sech\({}^{2}\)-shaped temporal profile. A long-scale SHG-based intensity autocorrelation scan of 50 ps, shown in the inset of Figure 5b, confirmed a single-pulse ML operation. The maximum average output power amounted to 205 mW at an absorbed pump power of 696 mW, which corresponded to an efficiency of 29.5%. The soliton pulses had a peak power of 28 kW at a pulse repetition rate of 67.3 MHz. The steady-state pulse train corresponding to the shortest pulses achieved was characterized by a radio-frequency (RF) spectrum analyzer. The first beat note was recorded at \(\sim\)67.3 MHz with a resolution bandwidth (RBW) of 300 Hz, as shown in Figure 6a. No spurious modulations could be observed with a signal-to-noise ratio above 76 dBc. This, together with the uniform 1-GHz harmonic beat notes shown in Figure 6b, was evidence  
Figure 4: SESAM ML Yb:GdCB laser with \(T_{\text{OC}}=1.6\%\): (**a**) optical spectrum and (**b**) SHG-based intensity autocorrelation trace with a sech\({}^{2}\) fit. _Inset_: simultaneously measured long-scale SHG-based intensity autocorrelation trace for the time span of 50 ps.