# 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 **a4**, the pulse duration is 250 fs and the pulse energy is 4 \(\upmu\)J; (**b**) The shadowgraphs of femtosecond laser ablation of dielectric recorded at six different delay times by TRPP, where S: shockwave front; C: contact front; 1: the first stress wave front; 2: the second stress wave front; and F: filament. The energy fluence on the target surface is 40 J/cm\({}^{2}\), and laser pulse is 50 fs [85; 86]. A series of processes about the gradual initiation of damage under short-pulse laser irradiation were explored. Many models were built for the gradual initiation of damage. The equivalent explosion simulation model of the laser-induced damage process shows the ejection phenomenon under different explosion conditions with the smoothed particle hydrodynamics (SPH) method. [PERSON] et al. [88, 89] established the multi-physics coupling model for the lateral crack defect, which further verified the explosion process of reference [90]. In order to describe the transient characteristics of the damage initiation accurately, [PERSON] et al. [90] introduced the explosion damage threshold (EDT) when exploring the process of damage initiation. Under the irradiation of the laser, the plasma explosion will occur, and the substance ejection will appear near the laser irradiation point once the energy reaches the threshold. This phenomenon can last for several microseconds until the damage pit is finally formed. It can be seen that the damage is formed at a certain angle both in Figure 17(a1,a2). In addition, with the increase of the irradiation time, the damage pits show the trend of expanding from the section of point to cone, with different degrees of expansion in both the horizontal and vertical directions, and eventually form the bowl-shaped damage pits. Therefore, further exploration in terms of damage expansion is needed to study other significant phenomena that may affect the damage formation. Figure 17b shows the temperature variation (parameter T in the model) distribution of the explosion zone with time during nanosecond laser irradiation. It can be seen that the cross-section area of high-temperature region gradually expands. Figure 17(b2) shows the phase state of the ejected material at different times delay clearly. As shown in Figure 17(b1), the temperature at the laser irradiation point is the highest, exceeding the melting point of KDP crystal, which will cause the material in the area to be gaseous state. Since the nanosecond laser irradiation time ensures the thermal conduction, the temperature of the central area will gradually conduct to the vicinity and expand, the thermal damage area will show a growth. Actually, the expansion rate of the high temperature region is particularly severe in the gaseous state, which will lead to significant thermal stress near the damage pit. Figure 17: Evolution process of damage initiation. (**a**) Simulated damage crater formation process in the laser damage area; (**b**) Simulated temperature variation in the laser damage area [88, 90]. In addition, with reference to Figure 17b, high-temperature gaseous substances were ejecting outward during the initiation of damage. In the case of the increase of time delays, it can be seen that in the later physical process of the material being irradiated by laser, the gaseous substance in the earlier stage was converted into a multi-phase mixture composed of solid, gaseous, and liquid states of KDP. This phenomenon is consistent with the substance ejection behavior experimentally that observed in the laser damage processes reported in reference [91]. With the further development of the ejection process, almost all the ejected particles were observed to exist in solid form. [PERSON] et al. indicated that the ejection of solid particles starts at about the 100 ns delay, which also means the initiation of mechanical damage.