## 2 DUV Laser Generated by FHG of the 1-um NIR Laser
This high-power, high-beam quality DUV laser is also following the schematic setup as depicted in Figure 1. In detail, the fundamental laser was at 1030 nm which was from a master oscillator power amplifier (MOPA). The frequency conversion stages consisted of a noncritical phase-matching (NCPM) LBO crystal (5 \(\times\) 5 \(\times\) 30 mm\({}^{3}\)) for SHG from 1030 nm to 515 nm and a CLBO crystal for FHG from 515 nm to 258 nm. The seed laser of the MOPA was a distributed-feedback (DFB) laser diode (LD), and it was electrically modulated by a pulse generator with the repetition rate of 160 kHz and with a pulse duration of 10 ns. The repetition rate was lowered down to 10 kHz by an acousto-optic modulator (AOM). After 3 stages of fiber amplifiers, the signal was amplified to about 2 W. One stage of Yb:YAG ceramics thin rod (CTR) amplifier and one stage of Yb:YAG SCF amplifier (TARANIS, Fibercryst Inc., Decines-Charpieu, France) were used as the main amplifiers. The Yb:YAG CTR was in the dimension of \(\Phi\) = 1 mm \(\times\) L = 40 mm with Yb\({}^{3+}\) ion doping of 1 at. % as well as the Yb:YAG SCF. The pump source of this stage was a 940 nm LD with 100 W output and the output power was 25 W by use of a double-pass configuration. The Yb:YAG SCF amplifier was pumped by a 200 W LD at the wavelength of 969 nm which was stabilized with a volume Bragg grating. The Yb:YAG SCF amplifier was a single pass configuration with 35 W output at 100 W pumping. The conversion efficiency of SHG from NIR to green and FHG from green to DUV was 73% and 42%, respectively, corresponding to a conversion efficiency of 31% from NIR to DUV. This was highest conversion efficiency for the DUV lasers with average powers of more than 10 W. Furthermore, the beam quality was near-diffraction-limited for both amplifiers (Yb:YAG CTR: \(M_{x}^{2}\) = 1.06 and \(M_{y}^{2}\) = 1.03; Yb:YAG SCF: \(M_{x}^{2}\) = 1.02 and \(M_{y}^{2}\) = 1.04). Hence, the DUV laser had an excellent beam quality owing to the good beam quality of the fundamental laser and the optimized frequency conversion stages. The measured value of M\({}^{2}\) was \(M_{x}^{2}\) = 1.02 and \(M_{y}^{2}\) = 1.05 for DUV laser at 3 W. Although the DUV beam became a little worse at 9-10 W (\(M_{x}^{2}\) = 1.37 and \(M_{y}^{2}\) = 1.46), it is still the best laser beam quality with M\({}^{2}\) < 1.5 for the DUV laser power more than 10 W [13]. The average power of the NIR laser still has the potential to be improved to tens of watts such as 70 W [26] if the double-pass configuration could be utilized for the Yb:YAG SCF amplifier stage. Hence, if the conversion efficiency of 31% from NIR to DUV could be still maintained at this higher power condition, the average output power of the DUV laser at 258 nm could be more than 20 W, which would be a remarkable power level for the DUV laser and lead to the unanticipated DUV laser machining results. Moreover, for high-power DUV laser, the UV damage of the nonlinear crystal, including the windows for CLBO crystal and the mirrors, is another important parameter for long term and stable operation. On the other hand, the beam quality of this higher power DUV laser would become worse due to more serious thermal and nonlinear effects. Hence, the frequency conversion processes should be carefully designed to mitigate the aforementioned effects. Thus, a high-power DUV laser at the FHG of 1 \(\upmu\)m with a good beam quality could be obtained and will be beneficial for obtaining the shorter wavelength DUV lasers such as 193 nm by SFG.