## 2 High Diffraction Efficiency and Damage-Resistance Threshold Gratings
### Multilayer-Dielectric-Film Grating
#### 2.2.2 Multilayer Dielectric Film Transmission Grating
The transmission grating with the best diffraction efficiency is now used in the high-power Yb fiber system. The grating line density was 1250 lines/mm, the groove depth was 1450 nm, and the duty cycle was 0.45. The same year, [PERSON], [PERSON], et al. [59] devised and manufactured a broadband deeply etched two-layer transmission grating with minimal polarization dependency to achieve high diffraction efficiency. The first layer was Ta\({}_{2}\)O\({}_{5}\) with thickness h\({}_{1}\), the second layer was SiO\({}_{2}\) with thickness h\({}_{2}\), the grating period was 1100 nm, the duty cycle was 0.6, and the incident wavelength was 1550 nm. The modal approach was utilized to evaluate the two-layer grating, and the phase accumulation between the excitation modes of the two layers may be used to show the incident-wave propagation process and explain the high-efficiency grating. The precise depth of the two-layer grating layer may be tuned using RCWA. Figure 34 depicts the connection between the two-layer grating's first order diffraction efficiency and grating depth. When h\({}_{1}\) = 1370 nm and h\({}_{2}\) = 470 nm, the TE and TM polarization efficiencies were 98.23 and 97.44%, respectively. In the depth range of 1300 nm \(<\) h\({}_{1}\) < 1390 nm and 360 nm \(<\) h\({}_{2}\) < 490 nm, the two polarization efficiencies still reached more than 95%. When the incident wavelength and angle deviated from the central wavelength and Bragg angle within the incident wavelength range of 1514 to 1650 nm or the angle range of 39.071 to 50.641\({}^{\circ}\), the efficiency exceeded 95% under the Littrow installation. Multilayer-dielectric-film gratings are simpler to create than polarization-independent broadband gratings, and they have a higher efficiency than single-layer dielectric film gratings. [PERSON], [PERSON], et al. [60] created a broadband high-efficiency three-layer all-dielectric rectangular-slot transmission grating with \(-2\) order Bragg incidence in 2020. The three layer structures are composed of Al\({}_{2}\)O\({}_{3}\), TiO\({}_{2}\), and SiO\({}_{2}\). Based on RCWA and a simulated annealing algorithm, the structural parameters of the transmission grating were optimized. The grating period was 1624.6 nm, the duty cycle was 0.4, h\({}_{1}\) was 289.1 nm, h\({}_{2}\) was 904.9 nm, and h\({}_{3}\) was 338.8 nm. At a center wavelength of 1500 nm, with a range of 1454 to 1531 nm and an angle range of 37.32 to 43.3\({}^{\circ}\), the diffraction efficiency of the grating exceeded 95%. The highest efficiency of TE polarization may even reach 99.58% at the second Bragg angle with a wavelength of 1.5 \(\upmu\)m. This was the first  
Figure 23:7 Diffraction efficiency in the \(-1\)st order versus grating depths of the two-layer grating: (**a**) TE polarization and (**b**) TM polarization. time the simplified modal method (SMM) was used to predict the broadband features of multilayer gratings. [PERSON], [PERSON], et al. [61] developed a polarization-independent broadband high-efficiency transmission grating in 2021. The grating structure was made up of rectangular grooves with three layers of dielectric films: SiO\({}_{2}\), Si\({}_{3}\)N\({}_{4}\), and Al\({}_{2}\)O\({}_{3}\). The thicknesses were h\({}_{1}\) = 924.3 nm, h\({}_{2}\) = 571.8 nm, and h\({}_{3}\) = 740.8 nm. The grating period was 1270 nm, and the duty cycle was 0.58. The structure and thicknesses are shown in Figure 23:8 The incidence angle varied from 32.1 to 42.7\({}^{\circ}\) in the 1446-1641 nm range, and the \(-\)1 st order diffraction efficiency under the Littrow structure was 95%. The grating \(-\)1 st order diffraction efficiency was 99.1% at the center wavelength of 1550 nm. The 0.0013 dB loss was insignificant. Summarizing the evolution of transmission gratings in recent years in the Table 3, we conclude that in the visible and near-infrared bands, the majority of transmission grating design structures employ fused silica as the substrate material.