## 2 High Diffraction Efficiency and Damage-Resistance Threshold Gratings
### Multilayer-Dielectric-Film Grating
#### 2.2.1 Multilayer-Dielectric-Film Reflection Grating
In order to investigate the anti-laser-damage  
Figure 10: Fresnel reflection mechanism on a mirror-based corrugated dielectric film: direct reflection, field trapping, leaky-mode propagation, and re-radiation. The corrugation balances the direct-reflected and re-radiated field moduli, ensuring 100% \(-1\)st-order efficiency. The inset represents the fabricated multilayer-grating structure. Figure 9: SEM image of the dielectric grating. threshold, a one-to-one test was performed utilizing a laboratory-developed CPA laser system. Figure 12 depicts the findings for a 1740 lines/mm gold-plated grating tested under 72.5\({}^{\circ}\) TM polarization, which are similar to the previous results, with a high level of consistency [35; 36; 37; 38; 39]. The anti-laser-damage threshold of the multilayer-dielectric-reflecting grating disclosed in this study is 3.5-5 J/cm\({}^{2}\), which is substantially higher than the previously published multilayer-dielectric-grating data. The laser-induced damage threshold at 1 ps on a 77.2\({}^{\circ}\) and 1780 lines/mm multilayer dielectric grating was 2.5 J/cm\({}^{2}\), which was similar to the 2 J/cm\({}^{2}\) at 500 fs reported by [PERSON] [36]. The laser-induced damage threshold of [PERSON]'s [37] 1740 lines/mm multilayer dielectric grating was 5.16 J/cm\({}^{2}\) at 10 ps, which is comparable to 2.6 J/cm\({}^{2}\) at 500 fs. E\({}^{2}\) determines the damage threshold. [PERSON] et al. [40] combined four 2.1 kW fiber lasers with a polarization-independent reflection grating to achieve an output power of up to 8.2 kW in 2011. The efficiency of light and \(-\)1 st order diffraction were both better than 95%. Ultrafast lasers often require a main oscillator power amplifier arrangement to achieve high peak power and energy. Owing to nonlinear effects, fiber-based laser amplifiers have evident peak power restrictions, and CPA technology is frequently employed to overcome this, using prisms or gratings, but the downside of this approach is that there is a significant loss of diffractive optical components. Its efficiency was rather low until recent advances, and the stated value of diffraction efficiency of reflection gratings is improving, generally in the region of 95 to 97%. [PERSON], [PERSON], et al. [41] developed a high-efficiency reflecting broadband compression grating in 2014. Figure 13 depicts the grating-layer structure analyzed, which consisted of 29 levels of dielectric films, with each layer shown. The angle of incidence was 44\({}^{\circ}\), and the physical thickness of the high or low refractive  
Figure 11: AFM measurement on a PW08 sample (section analysis). Figure 5.0 Example of damage probability on a 1740 lines/mm gold grating. Testing was performed at an incidence of 72.5\({}^{\circ}\) in TM polarization mode. The damage threshold (maximum value at which the damage probability is null) is 0.67 J/cm\({}^{2}\). index film recorded. Interference lithography and reactive-ion-beam etching were used to create the grating layer. The grating had a 1250 lines/mm structure and a duty cycle of 0.25. Figure 14 shows a photograph and an SEM image. The efficiency was 99.35%, the diffraction efficiency in the 1060 nm band was 99.7%, and the anti-laser-damage threshold was 2.95 J/cm\({}^{2}\), as shown in Figure 5.1  
Figure 5.2 SEM image of the grating structure on a cleavage-test sample. Figure 5.3 Schematic diagram of the reflection grating structure. Figure 5.4 Relationship between the reflection grating and diffraction efficiency. In 2016, [PERSON], [PERSON], et al. [42] reported a spectral-beam-combining (SBC) system of eight 1.5 kW ytterbium-doped all-fiber superfluorescent light sources at a wavelength of 1070 nm, with the eight output elements coupled to a self-developed, polarization-independent, multilayer-dielectric-film reflection grating. The beam was spectrally mixed, with an output power of 10.8 kW and a combined efficiency of 94%.