## 2 Bulk Crystal Characteristics
### Q-Switching Laser Performance
The center wavelength is 1063.9 nm and the laser profile was detected by CCD (CinCam COMS-1201), which is shown in the inset of Figure 10b and is close to the fundamental transverse electromagnetic mode (TEM00). As presented in Figure 11, the temporal characteristics of self-Q-switching pulses, which are the pump power versus the repetition frequency and pulse width, were determined with an oscillator combined with a silicon detector. Because the pump power improved from 0.81 to 2 W, the pulse width was shortened from 1674 to 541.8 ns; however, when using the 1% output coupler, the repetition frequency presented the opposite trend. In the meantime, the absorbed pump power improved from 1.26 to 2 W and the pulse width reduced from 1329 to 731.1 ns when using the transmittance of the 3% output coupler. Here, the repetition frequency also revealed the opposite trend. These trends are typical in passive Q-switching lasers [53; 54]. Figure 10: (**a**) Absorbed pump power versus average pulsed output power in the self-Q-switching operation (dots for the experimental data and lines for the linear fittings); (**b**) spectra and beam profile of the output laser. As shown in Figure 11a,b, because the absorption pump power increased, the repetition frequency and the pulse width curves flattened. For the 1% and 3% output couplers, the shortest pulse widths were 541.8 ns and 731.1 ns, and the maximal repetition frequencies were 46.1 kHz and 38.8 kHz, respectively. The single pulses with minimum pulse widths, mentioned earlier, are shown in Figure 11c,d, and the relevant pulse trains are shown in the insets. The pulse energy can be calculated from the values of the output power and the repetition frequency. If combined with the pulse width, the peak power can also be obtained. When using the 1% output coupler, the maximal peak power was 9.8 W and the maximal pulse energy was determined to be 5.3 \(\upmu\)J. The maximal peak power was 10.2 W, and the maximal pulse energy was 7.3 \(\upmu\)J as using the 3% transmittance output coupler. The nonlinear optical characteristics of the Yb\({}^{3+}\):ScBO\({}_{3}\) crystal were determined using a Z-scan test. Figure 12 shows the transmittance versus input energy intensity of the crystal when the Yb\({}^{3+}\):ScBO\({}_{3}\) crystal was at a wavelength of 1064 nm. The data were fitted utilizing the equation below [58]:  
\[T=A~{}exp\bigg{[}\frac{-\delta\alpha}{1+I/I_{\mathrm{s}}}\bigg{]} \tag{10}\]  
where \(A\) represents the normalized parameter, \(\delta\alpha\) represents the saturable absorption, \(I\) represents the incident intensity, and \(I_{\mathrm{s}}\) represents the saturation intensity. Furthermore, transmittance and intensity have a nonlinear relationship. Through fitting, the modulation depth of the Yb\({}^{3+}\):ScBO\({}_{3}\) sample was 17.77%. In addition, the absolute modulation depth was 10.2% and the saturation intensity was 4.1 \(\times\) 10\({}^{8}\) W/m\({}^{2}\) at 1064 nm. Figure 11: Absorption pump power versus repetition frequency and pulse width: (**a**) output coupler transmittance of 1%; (**b**) output coupler transmittance of 3%; (**c**) single pulse and pulse train with the output coupler transmittance of 1%; and (**d**) single pulse and pulse train with the output coupler transmittance of 3%. As previously reported, the Yb\({}^{3+}\):ScBO\({}_{3}\) crystal was expected to have strong inversion population accumulation owing to its large excited-state lifetime and small emission cross-section [34]. Hence, the self-Q-switching process in the Yb\({}^{3+}\):ScBO\({}_{3}\) crystal can be attributed to the ground-state reabsorption, which is the saturable nature of the reabsorption loss at the lower level, \({}^{2}\)F\({}_{7/2}\)[59; 60; 61]. All the results contribute to an understanding of the self-Q-switching in gain mediums with strong reabsorption effects, and aid in the development of the highly compact pulsed laser systems.