## 3 Results and Discussion  
### Temperature Distribution Caused by the Subsurface Impurity Defects  
#### 3.1.1 Comparison of Temperature Distributions with and without Impurity Defects  
Figure 5 shows the comparison of temperature distributions caused by fused silica optics with and without impurity defects under the irradiation of Gaussian laser pulse with a 355 nm wavelength, 10 ns pulse width and 10 J/cm\({}^{2}\) laser fluence. The typical subsurface impurity defects of CeO\({}_{2}\), Fe and Al are all considered with defect diameter of 1 \(\upmu\)m that is located 1 \(\upmu\)m (the distance between defect center and surface) beneath the optical surface. Figure 5a,b exhibits the temperature curves for fused silica without any impurity defect. It is shown that under the irradiation of Gaussian laser pulse, the temperature field on the silica surface is also distributed in a Gaussian profile. With the increase of laser loading time (\(t<\) 10 ns), the temperatures on the surface rise gradually, and the maximum temperature at the center of Gaussian profile (\(r_{\text{p}}\) = 0 mm) can reach the peak of 1650 K when the laser pulse lasts for 10 ns (pulse width). The peak temperature is lower than the melting point (2173 K) of fused silica so that no laser damage will occur under this condition. The evolution of peak temperature (\(r_{\text{p}}\) = 0 mm) in the heating (\(t<\) 10 ns) and cooling (\(t>\) 10 ns) phases is exhibited in Figure 5b. One can see that when the laser stops heating, the peak temperature will dramatically decrease. The temperature gradually falls down thereafter to a stable and low value at room temperature (\(\sim\)300 K), when the laser pulse ends for 10\({}^{4}\) ns. It means that the simulated temperature field would reach a stable state finally. It should be noted that the central-point temperature in Figure 5b shows a short plateau from \(t\) = 15 ns to \(t\) = 30 ns and the potential explanation is listed below. After the laser ends (\(t>\) 10 ns), when the decreasing surface temperature is close to that in the bulk, the effects of convection and radiation of  
Figure 4: Schematic diagram of the laser path designed for the laser damage experiments (**a**) and the online monitoring system; (**b**) applied for detecting the laser damage initiation. the surface would make the surface temperature keep decreasing. The surface temperature would be then lower than that of the bulk, and the heat energy could be transferred from the bulk to the surface. Owing to the competitive contributions of natural convection, surface radiation and heat transfer, the central-point temperature may remain roughly a short constant. Figure 5c shows the variations of peak temperatures caused by impurity defects of CeO\({}_{2}\), Fe and Al. It can be seen that the peak temperature caused by CeO\({}_{2}\) defect rises more strongly than those caused by Fe and Al defects. The maximum temperature can reach 4458 K, which is much higher than the melting point of fused silica and the melting (2673 K) and boiling (3773 K) points of CeO\({}_{2}\). This means that the fused silica would be seriously damaged with the presence of a CeO\({}_{2}\) impurity defect. The maximum temperatures caused by Al and Fe impurity defects are both above 2200 K, which is also higher than the melting points of Al (933 K) and Fe (1808 K). Hence, the fused silica optics with Fe and Al impurity defects would also suffer from laser damage under the irradiation of an intense laser pulse. It can be concluded that with the presence of impurity defects, the optical materials would strongly absorb the laser energy, melt or even boil, and finally incur optical breakdown under the irradiation of a 355 nm wavelength, 10 ns pulse width and 10 J/cm\({}^{2}\) laser fluence.