## 1 Introduction  
Potassium dihydrogen phosphate (KDP) and potassium dideuterium phosphate (DKDP) crystals are the very important nonlinear optical materials for the laser-driven inertial confinement fusion (ICF) [1; 2; 3; 4; 5; 6]. In the high-power laser driving system, one KDP and one DKDP are combined together as a frequency-converting pair (named as FCP). It is sealed in the terminal vacuum chamber and utilized to turn the incident near-infrared laser (1053 nm, named as 1\(\omega\)) to the short-wavelength one (351 nm, named as 3\(\omega\)). KDP is called second harmonic generating (SHG) element to double the frequency of original laser (partially), and DKDP is called third harmonic generating (THG) element to triple the frequency of original laser as shown in Figure 1a. The incident side of SHG element suffers the irradiation of original 1\(\omega\) laser, and its exit side suffers the irradiation of the residual 1\(\omega\) laser and frequency-doubled laser (527 nm, named as 2\(\omega\)). Meanwhile, the incident side of the THG element suffers the same irradiation as the exit side of the SHG element, and its exit side suffers the irradiation of converted 3\(\omega\) laser. In order to provide enough power to drive the ignition of ICF, the output laser energy from FCP is very high [7], requiring the minimized reflecting loss for all sides. Thus, special coating system should be applied to FCP to improve its transmission and laser-induceddamage threshold (LIDT) at specific wavelengths (also shown in Figure 1a) [8]. On the other hand, inevitable reflection of 3\(\omega\) laser (from the pellet hohlraum) has been proven harmful for the optical elements located before the terminal chamber by inducing irreversible laser damage [4; 9; 10; 11]. Therefore, minimization of the reflected 3\(\omega\) laser back through the terminal chamber should be taken into account. Unfortunately, the structure of the high-power laser system is fixed, and no room is available for an extra 3\(\omega\) laser absorber, neither for the National Ignition Facility (NIF) nor Laser Megajoule (LMJ). It is assumed that applying absorption of 3\(\omega\) laser at the two sides of SHG element and the incident side of THG element is a potential solution, since the 3\(\omega\) laser only generates when the laser beam has passed through the THG element. The optimized coating systems based on this design are depicted in Figure 1b, which could endow the FCP element with outstanding 3\(\omega\) laser output power as well as the protection of upstream elements from damaging by the reflected 3\(\omega\) laser. However, literature referring to this application is rare, and related studies were hardly found. Reports from neither NIF nor LMJ have any specific statement about this application. The main spectral requirement for SHG and THG sol-gel anti-reflective coatings in LMJ is the reflectance per side (R\({}_{1\omega}\) \(<\) 0.5%, R\({}_{2\omega}\)\(<\) 0.5%, R\({}_{3\omega}\)\(<\) 0.7%), without the consideration to minimize the reflected 3\(\omega\) laser [12]. Therefore, the exploration of such coating systems is performed in this work, and the structural, mechanical, and optical properties of this coating system have been investigated as well.  
Figure 1: Schematic diagram of the frequency-converting pair (FCP) in one laser beam from high-power laser system, (**a**) original design; (**b**) optimized design.