## 2 High Diffraction Efficiency and Damage-Resistance Threshold Gratings
### Multilayer-Dielectric-Film Grating
#### 2.2.2 Multilayer Dielectric Film Transmission Grating
Fused-silica gratings were fabricated by holographic exposure and inductively coupled plasma-etching techniques, and the as-prepared grating morphology is shown in Figure 30. The experimental results were consistent with the theoretical values. Figure 23:0 SEM image of the manufactured a dual-function transmission grating. Figure 23:1 Near-field distribution for a dual-function grating with a period of 1216 nm and a depth of 2314 nm, using the FDTD method at a wavelength of 1550 nm. The incident light was from the bottom, and output waves traveled upward through the grating. (**a**) Amplitude of the output magnetic field for TM polarization, indicating the two-beam interference that was due to the propagation of two equally split beams of the grating. (**b**) Real part of the output electric field for TE polarization, indicating the highly efficient diffraction at the \(-1\)st order direction of the grating. In the same year, [PERSON], [PERSON], et al. [55] designed a high-efficiency triangular-grooved fused-silica transmission grating for the polarization-independent C + L band. After using rigorous coupled-wave analysis (RCWA) optimization to acquire the exact grating parameters, the diffraction efficiency at 101 nm (1500-1601 nm) TE and TM polarizations was better than 90%, while the diffraction efficiencies of both polarizations were greater than 99% at a wavelength of 1550 nm. This is a novel approach to fabricating a transmission grating out of highly dispersive material that can eliminate any reflection loss and achieve 100% diffraction efficiency. Figure 31 depicts the link between grating parameters and diffraction efficiency. Figure 23:2 SEM image of the manufactured grating. Figure 23:3 Theoretical and experimental (lines with markers) diffraction efficiencies of the manufactured grating at different incidence angles for TM and TE polarizations. In 2011, [PERSON], [PERSON], et al. [56] in Japan developed and manufactured a \(170\times 40\times 1\) mm\({}^{3}\) high-efficiency fused-silica transmission grating with a line density of 1250 lines/mm for terawatt-scale Ti-sapphire lasers. The incidence angle was 30\({}^{\circ}\), and the backside was anti-reflection (AR)-coated. Figure 32 depicts the as-fabricated grating morphology. The diffraction efficiency of the transmission grating in the 750-850 nm band was greater than 90%. The relationship between the duty cycle, groove depth, and diffraction efficiency is shown in Figure 23:4 Under TE polarization, the incidence angle was 30\({}^{\circ}\), the wavelength band was approximately 800 nm, the duty cycle was 0.49, and the depth was 1380 nm; the diffraction efficiency of the transmission grating reached up to 98%. Figure 23:5 (**a**) Contour of the minimum \(-1\)st order diffraction efficiencies between TE and TM polarizations versus groove depth and grating period. (**b**) Plot of the \(-1\)st order diffraction efficiencies versus incident wavelength, with grating period \(\Lambda\) = 1080 nm, h = 10,300 nm, and \(\theta_{1}\) = 45.85\({}^{\circ}\) (Littrow angle for 1550 nm incident wavelength). Figure 23:6 Representative SEM image of the transmission grating. Expected efficiency was 93.7%, with an actual duty cycle of 0.56 and a depth of 1350 nm. [PERSON], [PERSON], et al. [57] created a high-efficiency fused-silica transmission grating with a deeply etched triangular groove shape in 2012. The wavelength at the center was 1064 nm. When the diffraction efficiency of the triangular-groove grating was compared with those of the rectangular grating and the blazed grating, it was determined that the triangular-groove grating was the most efficient diffractive optical element in the \(-1\) order. Transmission gratings designed with fused silica can exhibit significantly improved laser-damage thresholds [41] and have potential applications in high-power laser systems. [PERSON], [PERSON], et al. [58] devised and manufactured a 180 \(\times\) 40 mm fused-silica transmission grating with a diffraction efficiency of 96% for an ytterbium fiber laser CPA system in 2013.