## 3 Simulation Results and Discussion
### Simulation Results
#### 3.3.1 Effect of Single Pulse Energy on the Ablation Depth of Different Micro-Structures
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **Single Pulse Energy (\(\upmu\))** & **Value (\(\upmu\)m)** \\ \hline Initial depth & 80 & 29.4 \\  & 100 & 40.5 \\  & 120 & 46.4 \\ Absolute distance & 80 & 16.1 \\  & 100 & 20.5 \\  & 120 & 26 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Additional processing parameters of femtosecond laser ablation for TTM simulation. -focal plane (Figure 5b), which is fully consistent with the linear increase. Figure 5c depicts the total ablation depths of the three different single pulse energies. As one moves away from the focal plane, the total ablation depth increases, resulting in deeper ablation at the bottom of the micro-hole compared to the orifice, and thus the depth of the micro-hole increases. Because the variation of micro-hole depth is directly proportional to the variation in the total ablation depth at each location, the variation of ablation depth is critical for controlling the material's surface roughness. As a result, we examined the trend of total ablation depth for three different single pulse energies, and the rate of change is depicted in Figure 5d. The rate of change of the three single pulse energies remains nearly constant at about 120 \(\upmu\)m from the upper surface of the specimen, related to the relationship between the energy and the ablation depth,  
Figure 5: (**a**) Variation of laser fluence (three descending curves) and beam radius (increasing curve) with distance from the focal plane; (**b**) variation of ablation (three descending curves) and average pulses per point (increasing curve) with distance from the focal plane; (**c**) variation of ablation depth of single point with distance from the specimen upper plane; (**d**) variation of the derivative of the effective ablation depth with distance from the specimen upper plane; (**e**) variation of micro-pore depth with the number of laser scans: simulation and experimental results. as shown in Figure 3a. Within 120 \(\upmu\)m, the abundance of the single pulse energy at 80 \(\upmu\)J peak fluence reaches about 4.4 \(\times\) 10\({}^{9}\) J/cm\({}^{2}\). In Figure 5a, the energy is approximately linear between the energy and the ablation depth, and the change in the ablation depth for the same pulse energy initially increases and then decreases, which is attributed to the gaussian distribution of the pulse energy. With decreasing energy, the rate of change decreases gradually. The three different single pulse energies show a similar variation trend. Once the total ablation depth at each \(Z\) position is determined, the initial data for the micro-hole at the three different single pulse energies in Table 3 can be substituted for the calculation. The hole and the bottom of the hole are given new \(Z_{1}\) and \(Z_{2}\) values with each laser scan, and the difference between the two (i.e., depth) changes as a result. Figure 5e depicts the experimentally measured and simulated results of the micro-hole depth variation with scan number. The experimental and simulated results at various single pulse energies are found to be in good agreement. The micro-hole depth increases with the number of scans, and at higher single pulse energy, the ablation depth is deeper. The results show that the model is feasible, but more surface roughness control is required to investigate the effect of more femtosecond laser processes on the ablation process. In fact, the pre-processes of microstructure evolution observed experimentally are not considered in the present model, which may risk inaccuracies in the simulation results. However, as mentioned earlier, the model equates the energy at each point, which makes the deposition energy at each location consistent with the experiment. Moreover, the pre-process of microstructure evolution is transient, and the surface morphology stabilizes only after the micro-hole is created, so it is acceptable to ignore this short-term process while ensuring energy consistency.