## 2 High Diffraction Efficiency and Damage-Resistance Threshold Gratings
### Multilayer-Dielectric-Film Grating
#### 2.2.1 Multilayer-Dielectric-Film Reflection Grating
Figure 6: Cross-sectional SEM image of the 1550 gr/mm grating. Intense laser light may readily destroy the gratings used in chirped pulse amplification (CPA) devices. To minimize damage and ensure that all incident laser light was reflected to just one diffraction order with a diffraction efficiency close to 100%, [PERSON], [PERSON], et al. [31] presented a complete dielectric reflection grating in 1999, which was primarily formed from a multilayer-dielectric-reflective film and grating layer with a SiO\({}_{2}\) top structure. In this study, sputtering was used to deposit multilayer dielectric films. The multilayer film stack had the structure (HL)\({}^{10}\)L, where H and L are Nb\({}_{2}\)O\({}_{5}\) and SiO\({}_{2}\), respectively. The preparation accuracy and repeatability error were approximately 1%. Electron-beam lithography and ion-beam etching were used to create the grating structure with a period of 380 nm. Figure 9 is an SEM view of the as-constructed diffraction grating. In the Littrow structure, the incident wavelength was 532 nm and the angle of incidence was 45\({}^{\circ}\), with TE polarization. The efficiency was 97% in first-order diffraction (3% loss owing to ghosting and scattering). The anti-laser-damage threshold of the dielectric grating measured by 5 ns laser pulse was 4.4 J/cm\({}^{2}\), and the anti-laser-damage threshold for a 1 ps laser pulse was 0.18 J/cm\({}^{2}\). These values are equivalent to those of a typical gold grating. Figure 8: Efficiency versus depth and duty cycle for a quarter-wave HR stack, with grooves etched completely through the top layer. The grating grooves are lamellar, with 1480 grooves/mm, and the duty cycle is 0.3. The wavelength is 1053 nm at a Littrow angle of 51.2\({}^{\circ}\), with TE polarization. The high-index material is hafnia, and the low-index material is silica. The quarter-waves are defined for the wavelength and angle used. (**a**) High-index surface layer over (HL)\({}^{7}\) stack. (**b**) Low-index surface layer over (HL)\({}^{7}\) H stack. Figure 7: Multilayer dielectric designs of high-index (H) and low-index (L) layers, showing relative locations of substrate, multilayers, and groove corrugations (G). (**a**) Overcoated grating; dielectric layers effectively form a volume grating. (**b**) Undercoated grating; layers form a high-reflectivity (HR) stack under the corrugations. [PERSON] and [PERSON] conducted research in 2003 on the physical mechanism of achieving high efficiency in multilayer-dielectric-film reflection gratings with a \(-1\) order Lit-throw structure, viewing the entire grating as a combination of two independent subsystems, the surface-relief grating and the multilayer-dielectric-film structure. Matrix equations help to understand the inherent physical mechanism of achieving high diffraction efficiency [32]. [PERSON], [PERSON], et al. [33] designed a resonant diffraction grating with a total dielectric reflection grating period of 560 nm, an incident wavelength of 1064 nm, and an incident angle of 73\({}^{\circ}\) in 2005, and a \(-1\)st order reflection diffraction efficiency of 99% under the non-Littrow structure. The high-efficiency diffraction grating proposed in this paper contrasts starkly with the previous gratings pioneered by [PERSON] et al. It is simple to construct, and a groove structure with a depth of tens of nanometers may achieve high diffraction efficiency. As shown in Figure 10.  
[PERSON], [PERSON], et al. [34] investigated and constructed a multilayer-dielectric-reflection grating for ultrahigh-intensity laser-compressor applications in 2007. The density of the grating lines was 1780 lines/mm, and the incident angle was 70.6\({}^{\circ}\). The dielectric film stack structure was (HL)\({}^{7}\)H (H and L are HfO\({}_{2}\) and SiO\({}_{2}\), respectively), with a reflectivity of 99.5% at 1053 nm. [PERSON] created the grating, and Figure 11 depicts the atomic force microscopy (AFM) test-groove profile.