## 3 Results and Discussion  
Based on the design from TFClac(r), the transmission at 1\(\omega\) can achieve nearly 100%; however, the transmission at 3\(\omega\) is as high as 98.4% for mono-layer 1\(\omega\) coating. As for dual-wavelength coating system, the transmission could exceed 99.5% at both 1\(\omega\) and 2\(\omega\), while the transmission at 3\(\omega\) was about 96%. However, the transmission at 3\(\omega\) still needs further reduction because about 2-10% of the original 3\(\omega\) laser energy could be reflected according to different hohlraum structures [16; 17], and this energy is yet quite harmful. Since UV curing has been applied for the coatings in high-power laser system [18], the UV PI is considered not only to be able to cure the HRI coating but also to absorb the reflected 3\(\omega\) laser energy. In this study, optimized coating design using TFCalc(r) software and 3\(\omega\) energy absorption using UV PI are applied for the FCP in order to meet the spectral demand shown in Figure 1b. Optimized coating design for 1\(\omega\) coating system and dual-wavelength coating system was first performed and the results are listed in Table 1. In order to insert the HRI coating into 1\(\omega\) coating system to endow it with 3\(\omega\) absorption, the transmission of 1\(\omega\) coating at 1\(\omega\) has been sacrificed a little. Therefore, it is found that these two coating systems have nearly the same optimal parameters. The transmission at 1\(\omega\) and 2\(\omega\) could both reach 99.6% while that at 3\(\omega\) was about 95.7% (see Table 1). Thus, 1\(\omega\) coating system and dual-wavelength coating system can be consolidated as one coating system. The preparation of this consolidated coating system was divided into two steps, one was to deposit HRI layers with refractive index around 1.38 and thickness about 127 nm using prepolymer sols, the other was to utilize the colloidal silica nanoparticle sol to prepare LRI layer with refractive index around 1.22 and thickness about 144 nm over the cured HRI layer. A series of consolidated coating systems was fabricated by applying different PI concentration (1%, 2%, and 3%) to form the HRI layer. Nitrogen adsorption-desorption analysis was performed to figure out the behavior of PI molecule inside the HRI coatings. Specific surface area of the coating was analyzed by Brunauer-Emmett-Teller (BET) method, and pore size distribution was analyzed using Barrett-Joyner-Halenda (BJH) method [19; 20; 21; 22; 23; 24]. It is found from Figure 2 that contributing pore size for the pore volume is below 10 nm, implying that large pores hardly existed inside the coating. In addition, the inset of Figure 2 shows that bigger pores contribute more for the pore volume with the \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Type**} & \multicolumn{2}{c}{**HRI Layer**} & \multicolumn{2}{c}{**LRI Layer**} & \multicolumn{2}{c}{**Transmission (\%)**} \\  & **n** & **d (nm)** & **n** & **d (nm)** & **351 nm** & **527 nm** & **1053 nm** \\ \hline
1\(\omega\) coating system & 1.38 & 127.16 & 1.22 & 144.31 & 95.7 & 99.6 & 99.6 \\ Dual-wavelength coating system & 1.38 & 127.18 & 1.22 & 144.29 & 95.7 & 99.6 & 99.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Optimized coating design for 1\(\omega\) coating system and dual-wavelength coating system from TFCalc®. increase of PI concentration, indicating that the PI molecule started the occupancy from the smaller pores inside the coating. Moreover, the specific surface area of the coating gradually decreases with the increase of PI addition (listed in the upper right of Figure 2), which confirms the occupancy of micropores by the increasing PI molecule. The coating refractive index increases with the increasing of PI concentration because of the decrease of coating porosity. Thus, further addition of porous silica nanoparticles is applied to keep the refractive index of HRI coating at 1.38 under different PI doping amounts.