# Recent Advances in Laser-Induced Surface Damage of KH\({}_{2}\)Po\({}_{4}\) [PERSON]
## 4 Simulation and Experimental Exploration of Laser-Induced Damage Behavior in the Later Stage
### Exploration of Transient Behavior at the Initiation of Damage
In order to investigate the thermal stress and mechanical stress caused by plasma during explosion, the shock wave evolution process that showed with TRPP technology and simulation means are also used to characterize the energy conversion and the process between the initial energy deposition stage and the final damage crater formation indirectly. The propagation of air shockwave was directly extracted from the results of FEM (Finite Element Method) simulation [90; 92], as shown in Figure 18(a1-a3). It can be seen that the attenuation of the shockwave speed follows the exponential law, which has been summarized in the Figure 18(a4). In addition, Figure 18(a7) shows the shockwave velocity well by experiments. It is clear that the shockwave velocity increase with the increment of laser fluences. The propagation paths of shockwave in Figure 18(a5,a6) and Figure 18b are consistent, which also validates the correctness of the simulation results in Figure 18(a1-a3). Figure 18: The evolution diagram of shock wave. (**a**) Air shockwave propagation under different explosion conditions. **a1**, **a2**, and **a3** are the simulated condition that \(E_{exp}=1\mathrm{e}^{-9}\), \(E_{exp}=2\mathrm{e}^{-9}\), and \(E_{exp}=5\mathrm{e}^{-9}\), respectively, with **a4** the influence of explosion energy on the shockwave velocity. **a5** and **a6** are the time-resolved image series of laser-induced KDP surface damage process with fluences 20 J/cm\({}^{2}\) and 50 J/cm\({}^{2}\), respectively, and **a7** the shockwave velocity [90; 93]; (**b**) The propagation of shockwave in pump laser pulse duration from 0.2 ns to 100 ns [69]. Based on the above simulation of damage initiation process and the detection of TRPV technology under nanosecond laser irradiation, it can be inferred that thermal stress plays an important role in the process of damage initiation and damage forming. In order to verify the influence that thermal stress plays in damage forming, a series of exploration had been conducted by researchers. Combined with the properties of KDP crystals, it can be found that a non-uniform temperature field will form inside the crystal material when the heat transferred from the center of the laser beam to the area of the surrounding area gradually, causing a temperature gradient inside the material. The existence of temperature gradient inside the crystal will cause compressive stress in the material. In order to explore the magnitude and effect of stress more concisely, [PERSON] et al. [94] conducted further investigation and found a second wave would be generated inside the fused silica due to the high back-pressure of the laser-generated plasma, as shown in Figure 19b. In addition, [PERSON] et al. [95] explored and compared the kinetic behavior of KDP and fused silica under laser irradiation. It is clear that the expansion of shockwaves in air in Figure 19a is quite similar in both materials at the same delay time, which also suggests that the initial energy deposited in a single laser-induced breakdown event was roughly the same. Although there are relatively few observations on the internal response of KDP crystals at present, it is reasonable to infer that the back-pressure induced shockwave with a propagation pattern approximated shown in Figure 19b will also occur inside KDP crystals based on the principle analysis of thermal stress on KDP crystals and the comparative exploration of shockwave between fused silica and KDP. However, considering the anisotropy and soft brittleness of the KDP crystal, the shape and directionality of the back-pressure shockwave generated inside the material need to be further studied and explored. Figure 19: The effect and distribution of stress. (**a**) Comparison of the shockwave in fused silica and KDP. The shockwave propagating is denoted by an arrow [94]; (**b**) Propagation of shockwaves in materials. The shock front (S), back-pressure induced shock wave (B); (**c**) Analysis of the stress action on crystal material under laser irradiation [95].