## 2 High Diffraction Efficiency and Damage-Resistance Threshold Gratings
### Multilayer-Dielectric-Film Grating
#### 2.2.1 Multilayer-Dielectric-Film Reflection Grating  
The concept of multilayer-dielectric-film gratings was initially presented by the Lawrence Livermore National Laboratory (LLNL) in the United States in 1992. A diffraction efficiency greater than 98% can be achieved by adjusting the characteristics of the groove structure. For the first time, in 1993, the LLNL constructed the multilayer dielectric grating created the previous year. At 1053 nm, the incident wavelength had the maximum diffraction effectiveness. The grating was made up of eight pairs of dielectric-film materials with high and low refractive indices. The periodic relief structure was transmitted \begin{table}
\begin{tabular}{c c c c} \hline
**Years** & **Units** & **Structures** & **Performance** \\ \hline
2008 & [PERSON], et al. [16] & Period 400 nm, groove depth 350 nm, duty cycle 0.6 & Transmittance TM \(>\) 50\% (\textgreater{}5\) μm, extinction ratio \(\approx\) 20 dB \\ \hline
2010 & [PERSON], [PERSON], et al. [17] & Period 200 nm, aluminum 260 nm, duty cycle 0.4 & Transmission efficiency \(>\) 45\%, extinction ratio \(>\) 3.5 \(\times\) 10\({}^{3}\) \\ \hline
2012 & [PERSON], [PERSON], et al. [18] & Period 500 nm, ridge height 130 nm, Al 120 nm, Cu 50 nm & Transmittance TM \(>\) 60\% (\textgreater{}5\) μm, extinction ratio \(\approx\) 20 dB (2.5–11 μm) \\ \hline
2014 & [PERSON], et al. [19] & Au-Si-Au & Transmission TM \(>\) 90\% \\ \hline
2017 & [PERSON], [PERSON], et al. [20] & Period 574.7 nm, duty cycle 0.82, groove depth 232 nm & DE \(>\) 90\% 6700–1000 nm, LIDT \(=\) 0.95\(\textgreater{}\)/\(\textgreater{}\) cm\({}^{2}\) @60 fs \\ \hline
2018 & [PERSON], [PERSON], et al. [21] & Period 574.7 nm, groove depth 232 nm, duty cycle 0.82 & \(-\)1 st DE \(>\) 90\% 0700–1000 nm, LIDT \(=\) 0.62 J/\(\textgreater{}\)cm\({}^{2}\) \\ \hline \end{tabular}
\end{table} 
Table 1: Overview of metal film reflection gratings in recent years. to the dielectric layer, and the as-prepared grating diffraction effectiveness was greater than 97% (27,28). [PERSON], [PERSON], et al. [29] created a novel high-efficiency multilayer-dielectric-film reflection grating in California in 1995. The reflection and diffraction efficiency of first-order polarized light is greater than 96% due to the correct design of the multilayer dielectric film stack structure and grating structure, and the simulated theoretical diffraction efficiency is given in Figure 5. The scribe line density was 1550 gr/mm, the incident wavelength was 1053 nm, and the Littrow angle in transverse electric (TE) mode was 56\({}^{\circ}\). The multilayer dielectric film was made of ZnS and ThF\({}_{4}\), with ZnS serving as the top layer. Figure 6 depicts the prepared raster SEM image. [PERSON], [PERSON], et al. [30] created an effective all-dielectric reflection grating in 1997. Figure 7 depicts the grating design structure. This multilayer-dielectric-film reflection grating was TE polarized, with a center wavelength of 1053 nm, line density of 1480 lines/mm, Littrow angle of 51.2\({}^{\circ}\), duty cycle of 0.3, and first-order reflection and diffraction efficiency of 95%. The multilayer dielectric film structure is (HLL)\({}^{\text{n}}\) (H: HfO\({}_{2}\), and L: SiO\({}_{2}\)). Figure 7a shows that the top-layer structure is a high-refractive-index material, with the highest or lowest diffraction efficiency, and Figure 7b shows that the top-layer groove is a high-refractive-index material. A large groove depth is required to achieve higher performance indicator values when the top structure is made of a low-refractive-index material. The groove depth in the 900 nm surface-layer thickness is 700 nm (200 nm subgroove thickness) (Figure 8), demonstrating the high-efficiency performance of the grating. This design example shows that H or L can be selected for the top structure to obtain a high-efficiency solution, but the etching material and the ability to resist the damage threshold must still be considered (higher with low-index material on the top layer). Figure 5: Theoretical diffraction efficiency.