## 2 DUV Laser Generated by FHG of the 1-um NIR Laser  
Figure 1 depicts the schematic setup of the solid-state DUV laser at the FHG wavelength (258 nm or 266 nm) of 1-um laser, and Table 1 lists the typical results by following this setup including a result by SFG in the LiB\({}_{3}\)O\({}_{5}\) (LBO) crystal. So far, the highest average output power of it was 40 W, which was reported by [PERSON] et al. in the year 2003 [8] as the improvement result of their 20.5 W DUV laser in 2000 [9]. The fundamental laser was an Q-switched diode-pumped Nd:YAG green laser at the wavelength of 532 nm. The 40 W 266 nm laser was obtained by second-harmonics generation (SHG) in a CLBO crystal. Nevertheless, the beam quality of the DUV laser was not good enough because the  
Figure 1: Schematic setup of the solid-state DUV laser by FHG of 1-μm laser (DUV: deep ultra-violet; SHG: second-harmonics generation; FHG: fourth-harmonics generation; YAG:Y\({}_{3}\)Al\({}_{5}\)O\({}_{12}\); BBO: B-BaB\({}_{2}\)O\({}_{4}\); LBO: LiB\({}_{3}\)O\({}_{5}\); CLBO: CsLiB\({}_{6}\)O\({}_{10}\); KBBF: KBe\({}_{2}\)BO\({}_{3}\)F\({}_{2}\)). green laser had a M\({}^{2}\) of 10 [8]. In 2006, [PERSON] et al. reported a 28.4 W average power DUV laser at 266 nm by SHG of a 532 nm laser with M\({}^{2}\) = 6.5 [10]. [PERSON] et al. presented the result of their DUV laser with average output power of 14.8 W by FHG of a Nd:YVO\({}_{4}\) laser at the wavelength of 1064 nm [3]. The output power of the fundamental Nd:YVO\({}_{4}\) laser was 160 W with the beam quality of \(M_{\pi}^{2}\) = 1.28 and \(M_{\eta}^{2}\) = 1.21. After SHG, the beam quality of green laser was \(M_{\pi}^{2}\) = 1.44 and \(M_{\eta}^{2}\) = 1.28. However, the beam quality of DUV laser will be remarkably decayed due to the large walk-off effect of the \(\beta\)-BaB\({}_{2}\)O\({}_{4}\) (BBO) crystal for FHG to 266 nm [6]. [PERSON] et al. reported a 6-W DUV laser at 257.5 nm by FHG in a CLBO crystal which effectively improved the DUV laser beam quality due to the smaller walk-off effect of the CLBO crystal [11] comparing to the previous results using BBO crystals [3; 4; 5; 6]. However, the estimated M\({}^{2}\) of it was still more than 1.5. From the above-reported results, the key point to obtain a high-power, high-beam quality DUV laser is to choose a high power fundamental laser at 1 \(\upmu\)m with a good beam quality and proper nonlinear crystals with a smaller walk-off effect for SHG and FHG. A fundamental laser with a good beam quality is crucial for the final DUV beam quality as well as the nonlinear crystal with a smaller walk-off angle. Due to the thermal lens effect in the solid-state lasers, if the heating management is insufficient, it is not easy to obtain the solid-state laser with a high power and a high beam quality simultaneously. Recently, with the development of the thin disk laser and single-crystal fiber (SCF) laser, a high-power laser at the fundamental wavelength (1 \(\upmu\)m) had been realized with a good beam quality even with a TEM\({}_{00}\) mode beam [4; 24], which would be good candidates for the fundamental of the DUV laser generation. Another candidate for the fundamental is the high-power fiber laser which could be achieved by coherent beam combination with M\({}^{2}\) value less than 1.1 on both axes of the beam. Hence, 4.6 W DUV laser at 258 nm was obtained by FHG of this fiber laser with an M\({}^{2}\) value of 1.3 \(\times\) 1.6, which is the highest average power of the femtoseconds laser at this DUV wavelength so far [7]. Additionally, using the fiber laser as the fundamental, 100-W ultraviolet laser at 343 nm has also been obtained by third harmonics generation with M\({}^{2}\) < 1.4 [25]. Nevertheless, these high-power fiber lasers were achieved by the coherent beam combination requiring electronics systems to lock different amplifier channels, which increases the cost and the complexity.