## 2 High Diffraction Efficiency and Damage-Resistance Threshold Gratings
### Multilayer-Dielectric-Film Grating
#### 2.2.2 Multilayer Dielectric Film Transmission Grating
\begin{table}
\begin{tabular}{c c c c} \hline
**Years** & **Units** & **Structures/Contributions** & **Performance** \\ \hline
1997 & [PERSON], [PERSON], et al. [30] & Line density 1480 line/mm, duty cycle 0.3, & \(\lambda_{0}\) = 1053 nm, \\  & & (HLL)\({}^{\mathrm{P}}\), HfO\({}_{2}\)/SiO\({}_{2}\) & TE mode \(\theta_{\mathrm{Littrow}}\)=51.2\({}^{\circ}\) \\ \hline
1999 & [PERSON], [PERSON], et al. [31] & Period 380 nm, (HL)\({}^{\mathrm{10}}\) L, Nb\({}_{2}\)O\({}_{5}\)/SiO\({}_{2}\) & \(\lambda_{\mathrm{Littrow}}\)= 532 nm, \\  & & & TE mode, \(\theta_{\mathrm{i}}\) = 45\({}^{\circ}\) \\ \hline
2005 & [PERSON], [PERSON], et al. [33] & Period 560 nm, multilayer dielectric reflective film Ta\({}_{2}\)O\({}_{5}\)/SiO\({}_{2}\) & \(-1\)st DE = 99\%, \\  & & & multilayer dielectric reflective & \(\lambda_{0}\) = 1064 nm, \\  & & & film Ta\({}_{2}\)O\({}_{5}\)/SiO\({}_{2}\) & \(\phi_{\mathrm{i}}\) = 73\({}^{\circ}\) \\ \hline
2007 & [PERSON], [PERSON], et al [34] & 1780 L/mm, multilayer dielectric film (HL) \({}^{\mathrm{P}}\), HfO\({}_{2}\)/SiO\({}_{2}\) & R = 99.5\% @1053 nm; LIDT = 0.67 J/cm\({}^{2}\), \\  & & & (HL) \({}^{\mathrm{P}}\), HfO\({}_{2}\)/SiO\({}_{2}\) & \(\phi_{\mathrm{i}}\) = 70.6\({}^{\circ}\) \\ \hline
2014 & [PERSON], [PERSON], et al. [41] & Line density 1250 line/mm, duty ratio 0.25 & \(-1\)st DE = 99.35\% @1030 nm, \\  & & & dye = 99.7\% @1060 nm, \\  & & & duty ratio 0.25 & \(\phi_{\mathrm{i}}\) = 44\({}^{\circ}\), \\  & & & LIDT = 2.95 J/cm\({}^{2}\) @12 ns \\ \hline
2016 & [PERSON] [42] & Line density 960 line/mm, & \(-1\)st DE = 95\% @1040–1090 nm, \\  & & & & \(\theta_{\mathrm{i}}\) = 30.9\({}^{\circ}\), \\  & & & M\({}^{2}\) = 1.9 \\ \hline
2017 & [PERSON], [PERSON], et al. [43] & Sub+ HR+ Double-Layer Isosceles & \\  & & & Trapezoidal Grating Ridges & DE > 98\% @1023–1080 nm \\ \hline
2018 & [PERSON], [PERSON], et al. [45] & Period 900 nm, & \(\lambda_{0}\) = 1066 nm, \\  & & (HL)\({}^{\mathrm{14}}\)H, HfO\({}^{2}\)/SiO\({}_{2}\), & \(-1\)st DE = 91\% (50\) nm, \\  & & & top grating layer 1338 nm & \(\phi_{\mathrm{i}}\) = 30.9\({}^{\circ}\) \\ \hline
2020 & [PERSON], [PERSON], et al. [46] & 1300 gr/mm, & \(\lambda_{0}\) =1065 nm, \\  & & Quartz [HL]\({}^{\mathrm{16}}\) BGT i C, & Littrow structure, \\  & & Ta\({}_{2}\)O\({}_{5}\)/SiO\({}_{2}\) & \(-1\)st DE > 97\% (30\) nm \\ \hline \end{tabular}
\end{table} 
Table 2: _Cont._trench depths of 1450 to 1650 nm and duty cycles of 0.32 to 0.52. Compared with those of the traditional gold-coated grating, the designed multilayer dielectric grating has a higher diffraction efficiency and anti-laser-damage threshold. The measured anti-laser-damage threshold of the grating under a 170 ns pulse was 2400 J/cm\({}^{2}\). The transmission grating was applied to the ytterbium-doped fiber CPA system to obtain 400 fs pulses with an average power of 76 W.  
[PERSON], [PERSON], et al. devised and built a high-efficiency fused-silica transmission grating in the 1550 nm region in 2006 [50]. No one had considered using a high-efficiency transmission grating of 1550 nm in a dense wavelength-division multiplexing system, according to the report. The grating duty cycle was 0.5, and the grating groove had a rectangular form. Figure 23 depicts the connection between the density of the grating lines, the depth of the grooves, and the diffraction efficiency. It can be seen from the figure that the diffraction efficiency of the grating exceeded 95% when the density of the grating was 650-750 lines/mm and the depth of the grooves was 2500-3000 nm. It is clear from Figure 24 that the sidewall of the grating was steep, the groove depth of the grating was 2500 nm, the linear density of the grating was 674 lines/mm, and the duty cycle was 0.5. The diffraction efficiency of the TM and TE modes in the range of the incident angle range 15-45\({}^{\circ}\) was tested experimentally. The highest diffraction efficiency was 87.1% at 31.5\({}^{\circ}\).