## 3 Simulation Results and Discussion
### Simulation Results  
#### 3.3.1 Effect of Single Pulse Energy on the Ablation Depth of Different Micro-Structures  
To calculate the effective ablation depth at each Z position for the pulses with a given repetition rate in Figure 3b, we first calculate the peak fluence of a single pulse in the \(z\)-direction. Figure 5a depicts the variation of peak fluence with distance from the focal plane for three different single pulse energies. The fluence at the focal plane is maximum for all three pulses and rapidly decreases along the \(z\)-direction away from the focal plane. As can be seen from Equation (6), the beam radius becomes larger as Z increases. Therefore, since the pulse energy is constant, the fluence decreases accordingly (Equation (5)), a phenomenon known as the defocusing effect [35]. When the distance reaches approximately 600 \(\upmu\)m, the laser injection volume gradually decreases. The ablation depth at different laser fluences combined with Figure 4 demonstrates that the laser injection volume is insufficient to ablate the material after a certain distance away from the focal plane. Moving away from the focal plane changes the beam radius as well as the peak fluence, as shown in Equation (6). Because the change in single pulse energy has no effect on the change in the beam radius, the trend of diameter change is the same at all three single pulse energies. Contrary to the laser fluence, the beam radius at the focal plane is the smallest and continues to increase as the \(z\)-direction moves away from the focal plane, as shown in Figure 5a. It is clear from this that the energy and beam radius of a single pulse change as it moves away from the focal plane. The decrease in energy also decreases the ablative depth of the material, as shown in Figure 3a. For the same material, the ablative depth is determined solely by the laser fluence if the other laser parameters remain constant. As a result, the ablative depth for a single pulse at different Z positions can be calculated, and the results for three decreasing curves are shown in Figure 5b. It is worth noting that the calculated ablative depth decreases approximately linearly, which is related to the fact that, as previously stated, the ablation depth does not significantly improve with increasing energy. However, because Equation (1) states that the effective number of pulses is determined by the beam radius with constant scanning speed and repetition frequency, the average effective number of pulses at each position increases as the beam radius in the \(z\)-direction increases, as shown in Figure 5b. Unlike the previous study, the pulse overlap in the \(y\)-direction is not considered in this experiment because \(\Delta\)1 = 40 \(\upmu\)m, and according to Figure 5a, the beam diameter is not equal to 35 \(\upmu\)m at 1000 \(\upmu\)m from the focal plane, implying that there is theoretically no overlap of the spot in the \(y\)-direction [22]. The effective ablation depth and the number of effective pulses of a single pulse at each Z position can be obtained from the preceding work when processing with three different single pulse energies, and thus the total ablation depth at each Z position can be calculated. The total ablation depth at that location is then calculated as the product of the ablation depth of a single pulse at the same location in the \(z\)-direction and the number of effective pulses at that location. It is well known that the ablation depth increases with the increasing number of pulses [36]. More specifically, [PERSON] et al. calculated the ablation depth over a range of 1000 pulses at different energies using a two-temperature model [25]. The results showed that the ablation depth increased linearly with the number of pulses within the first 200 pulses, and then the increase became slow. In the present study, the scanning speed was 500 mm/s, and there were only about seven pulses at a point of 1000 \(\upmu\)m from the