## 2 High Diffraction Efficiency and Damage-Resistance Threshold Gratings
### Multilayer-Dielectric-Film Grating
#### 2.2.2 Multilayer Dielectric Film Transmission Grating
To manufacture a transmission grating close to the design index, a high-quality fused-silica substrate should be utilized, the grating creation process should be accurately controlled, and an appropriate multilayer dielectric film should be coated on the back of the grating after it has been etched. Figure 23: Theoretical efficiency of a fused-silica grating with \(\lambda\) = 1550 nm, m = \(-\)1 order, and TE polarization as a function of groove depth and line density for a rectangular profile with a duty cycle of 0.5. Figure 24: Fabricated fused-silica grating with a density of 674 lines/mm, a groove depth of 2.5 μm, and a duty cycle of 0.5. In a previous report [51], it was noted that the design of rectangular transmission gratings overlooked the reflection effects of air and the substrates. This explained why the diffraction effectiveness of fabricated gratings of this type was always less than the projected 100%. [PERSON], [PERSON], et al. [52] proposed a new method in 2008 that uses the buried method to fabricate a multilayer-dielectric-film transmission grating with 100% diffraction efficiency and high dispersion. Furthermore, the damage and pollution of the grating surface structure were effectively reduced. The grating density of the designed buried transmission grating was 1670 lines/mm, and the incident wavelength was 1064 nm. The commercial software Gsolver was used to simulate and analyze the relationship between the duty cycle, groove depth, and grating diffraction efficiency, as shown in Figure 25. When the duty cycle was 0.57 and the groove depth was 1440 nm, the theoretically calculated diffraction efficiency was 99.9%. As shown in Figure 26, the diffraction efficiency was numerically simulated for the corresponding surface-relief grating, and the diffraction efficiency reached a maximum of 93%, which is insufficient for many optical configurations. [PERSON], [PERSON], et al. [53] suggested a dual-function polarization-selective fused-silica transmission grating with a grating period of 1216 nm and a groove depth of 2314 nm in 2009. FDTD simulations convincingly confirmed the dual function of the transmission grating, with the magnetic field amplitude of the two-port beam splitter exhibiting two-beam interference fringes in the TM mode with a contrast ratio close to 100%. The plot of  
Figure 26: Numerical simulation of the diffraction efficiency of the corresponding surface-relief grating. The maximum diffraction efficiency was 93%. Figure 25: (**a**) Simulation of the diffraction efficiency of a buried grating with a 600 nm period as a function of the profile parameters (wavelength 1064 nm and Littrow configuration). (**b**) Corresponding numerical calculation by rigorous Fourier modal method. the real part of the electric field of the high-efficiency grating in TE mode demonstrates that almost all of the diffracted waves were in the \(-1\) order, as illustrated in Figure 27. The grating may perform the twin functions of a one-to-two beam splitter and a \(-1\) order high-efficiency grating by selecting one of two orthogonal polarization conditions. The transmission grating was created using holographic exposure and inductively coupled plasma; an SEM image is presented in Figure 28. The grating profile was nearly rectangular in form. [PERSON], [PERSON], et al. [54] undertook related research on near-infrared transmission gratings in 2010, designing and fabricating a \(-1\) order transmission grating for high-power CPA systems. At a wavelength of 800 nm, both TE- and TM-polarized diffraction efficiencies were greater than 97%. Both TE- and TM-polarized waves resulted in diffraction efficiencies greater than 92% within the wavelength range of 750 to 850 nm. Theoretical simulation showed that there was a difference between the grating parameters and diffraction efficiency. The relationship is shown in Figure 29. The incident angle was 32.2\({}^{\circ}\), the duty cycle was 0.67, and the groove depth was 1950 nm.