## 2 High Diffraction Efficiency and Damage-Resistance Threshold Gratings
### Multilayer-Dielectric-Film Grating
#### 2.2.1 Multilayer-Dielectric-Film Reflection Grating
In theoretical design and testing, the following connection exists between diffraction efficiency and wavelength (Figure 20). The multilayer-dielectric-film structure is (HL)\({}^{14}\)H, where H represents HfO\({}_{2}\) with a thickness of 146.57 nm, L represents SiO\({}_{2}\) with a thickness of 199 nm, and the top grating layer is 1338 nm; the designed grating was created using holographic-exposure and inductively-coupled-plasma etching technology. As seen in the SEM image in Figure 21, the as-fabricated grating sample was acquired, and is high efficiency, polarization-independent, and broadband. Figure 5.9 SEM image of the as-prepared grating. Figure 5:0 Relationship between the diffraction efficiency and wavelength of the theoretical calculation and the actual measurement. [PERSON], [PERSON], et al. [46] devised and built a polarization-independent multilayer-dielectric-film reflection grating with a larger linear density for spectral beam combining in 2020. The exact structural characteristics were as follows: quartz substrate, 1300 lines/mm scribe line density, center wavelength 1065 nm, better than 97% diffraction efficiency in the bandwidth of under \(-1\) order Littrow structure, and Sub 1 (HL)16 BGT \(\mid\) C multilayer-dielectric-film structure. H denotes Ta\({}_{2}\)O\({}_{5}\) with a thickness of 91 nm, L denotes SiO\({}_{2}\) with a thickness of 284 nm, B denotes Ta\({}_{2}\)O\({}_{5}\) with a thickness of 98 nm, G denotes SiO\({}_{2}\) with a thickness of 151 nm, and T denotes Ta\({}_{2}\)O\({}_{5}\) with a thickness of 332 nm. The top two layers of the GT structure were etched with grating grooves. The discrepancy between the theoretical and actual test diffraction efficiencies was approximately 2%, which is within a tolerable range, and there were discrepancies between the manufactured and intended grooves, as shown in Figure 5:1  
Multilayer dielectric reflection gratings continue to play an important role in the development of ultrashort, high-power laser systems. The most appealing characteristics of such gratings are their better diffraction efficiencies and resilience to laser damage compared with those of ordinary metal gratings. A summary of the above analysis is shown in Figure 5:2 Appropriate groove depth and duty cycle index may improve grating diffraction efficiency while minimizing manufacturing complexity, and laser-damage resistance can be considerably increased by combining materials with high damage-resistance thresholds, such as hafnium oxide and silicon dioxide. Furthermore, in the design and production process of the multilayer dielectric film, the anti-laser-damage ability of the film can be effectively improved by optimizing the design structure of the multilayer dielectric film, for instance, with the introduction of buffer layer technology; the performance of components can also be effectively improved by relieving stress through vacuum step annealing. Threshold, high-efficiency, and high-damage reflection gratings are further prospective study issues. \begin{table}
\begin{tabular}{c c c c} \hline
**Years** & **Units** & **Structures/Contributions** & **Performance** \\ \hline
1992 & LLNL [27] & MDG proposed for the first time & DE \textgreater{} 98\% \\ \hline
1993 & LLNL [28] & First production & DE \textgreater{} 97\% @1053 nm \\ \hline
1995 & [PERSON], [PERSON], et al. [29] & Line density 1550 gr/mm, multilayer dielectric film & \(\lambda_{0}=1053\) nm, (HL)5 H, ZnS/ThF4 & TE mode \(\Phi_{\text{Littrow}}=56^{\circ}\) \\ \hline \end{tabular}
\end{table} 
Table 2: Overview of multilayer-dielectric-reflection gratings in recent years. Figure 22: (**a**) Theoretical diffraction efficiency and (**b**) actual diffraction efficiency.