# Recent Advances in Laser-Induced Surface Damage of KH\({}_{2}\)Po\({}_{4}\) [PERSON]
## 2 Mechanism of Pulsed Laser-Induced Surface Damage
### Near Surface Impurity Thermal Absorption Damage  
Unlike the manifestations of bulk damage, near-surface impurities will cause surface damage. KDP crystals are easily doped with various metal cation impurities in the near surface during the growth process. [PERSON] et al. [34] studied the KDP crystals and found that the impurity particles contained in the near surface of crystal would scatter or converge the incident laser, resulting in the enhancement of the local light field of the element. In addition, the researchers [35, 36, 37] have found that the incident energy of the laser was strongly absorbed by the impurity ions. Generally, the laser energy absorbed by impurities is several orders of magnitude higher than the intrinsic absorption of crystal materials. Therefore, the strong absorption of the laser by impurities in the crystals will cause the rise of local temperature, which will further lead to the melting and cracking of the material surface. [PERSON] and [PERSON] et al. [31, 38, 39] assumed that the impurities inside the optical materials were in the shape of small balls with the radius of \(r\). Based on this assumption, the thermal explosion  
Figure 1: The physical phenomenon of the interaction of laser and optical crystal materials at different light intensity levels. (TE) model was constructed to explain the absorption of radiation by impurities in the materials. The heat conduction equation can be described to show the radiation absorption of impurities [40; 41]. \[\frac{\partial}{\partial t}(\rho cT)=\frac{1}{r^{2}}\frac{\partial}{\partial r} (r^{2}k\frac{\partial T}{\partial r})+Q(T,Ig(t)) \tag{2}\]  
where \(\rho\), \(c\), and \(k\) are the density, thermal capacity and thermal conductivity of impurities and host materials, respectively. \(T\) is the temperature of impurities, \(Q\) is the power density of the thermal sources, and \(I\) is the laser intensity and \(g(t)\) is the temporal shape of the laser pulse. It is clear that \(Q(T,Ig(t))\) is associated with absorption of radiation by impurities. \[Q(T,Ig(t))=Q(I)\exp\left(\xi\frac{T-T_{0}}{T_{0}}\right) \tag{3}\]  
where \(\xi\) is the material parameter, and \(T_{0}\) is the initial temperature. [PERSON] et al. [35] explored the influence of the near surface impurities in the KDP crystal on its surrounding temperature and stress, as shown in Figure 2, which well explained the strong absorption of energy of impurities. It can be seen that the temperature near the impurity is directly related to the energy density of the incident laser. The greater the incident laser energy density, the more energy the impurity absorbs, resulting in a sharper temperature rise of impurity. The temperature rise of impurities is approximately proportional to the energy density of the incident laser. In addition, the properties of impurities also result in energy absorption. [PERSON] and [PERSON] et al. [42] indicated that the size and density of impurities have an effect on the energy absorption of impurities. [PERSON] et al. proposed that there was a critical impurity size that made the impurities absorb the most energy and had the highest temperature. Once the impurity radius \(a\) is less than or greater than this critical value, the energy absorbed by the impurities after laser irradiation will be very small, and the temperature near the impurity will be very low, which is not easy to cause damage. The type of impurity inside the KDP crystal also absorbs energy differently. The absorption of energy by different  
Figure 2: Effect of near surface impurities in KDP crystal on temperature and stress of materials. **(a)** Distribution of temperature field around impurities under laser irradiation with different energy densities.