## 3 Results and Discussion
### Influence of Machining Point Spacing on Cutting Quality  
When the pulse repetition rate is set to 100 kHz, the incident laser frequency is at 12.5 W and the pulse mode is configured to 2; the cutting results of varying processing point spacings are illustrated in Figure 9. The laser irradiation on the linear shape of the microholes results in molten sputtering. As the processing point spacing increases, the melting area surrounding the microholes gradually decreases. At a processing point spacing of 1 \(\upmu\)m (Figure 9a), the microholes coalesce into an ablative tank. When the processing point spacing exceeds 3 \(\upmu\)m, the microholes become separated, with more pronounced cracks connecting them. At a spacing of 5 \(\upmu\)m, the micropores are more widely dispersed, forming independently. This phenomenon is depicted in Figure 9c. With a treatment interval of 5 \(\upmu\)m, the unaltered area increases, making sample separation challenging. As shown in Figure 9d, intermittent laser ablation cavities can be observed in both the upper and lower layers of the cross-section of the glass-ceramics. These cavities form micron channels with an ablative diameter of approximately 1.88 \(\upmu\)m and a gap between channels of about 3.6 \(\upmu\)m. Similar micron channels were observed at point spacings less than 3 \(\upmu\)m. However, when the distance between processing points is too small, the micron channel influence regions overlap, leading to no distinct channel morphology at a point spacing of 1 \(\upmu\)m.  
The characterization of sample cross-sectional roughness generated by different machining point spacings is presented in Figure 10a. The roughness increases with increasing machining point spacing, particularly near the middle of the sample, which aligns with the variation trend of Bessel beam energy along the z-axis in this experiment. At a point spacing of 1 \(\upmu\)m, there is minimal difference in roughness between regions. As the point spacing increases, the section area of the sample exhibits varied correction forms, resulting in greater regional roughness differences. At a point spacing of 5 \(\upmu\)m, the average roughness difference between region 3 and region 4 reaches 130 nm.  
Figure 9: Laser repetition frequency is 100 kHz, incident laser power is 10 W, and burst mode is 2. (**a–c**) is the cross section and upper surface of the sample when the processing point spacing is 1 \(\upmu\)m, 3 \(\upmu\)m, and 5 \(\upmu\)m, respectively; (**d**) is the cross section of the sample when the processing point spacing is 5 \(\upmu\)m. (**e**) is the SEM image of the edge of the modified layer when the processing point spacing is 5 \(\upmu\)m.  
Additionally, the fracture strength of specimens with different processing point spacings was measured using a hand press tester. The stress variation with the distance between laser processing points is shown in Figure 10b. As the point spacing increases, so does the unmodified zone area, leading to higher stress required for specimen fracture. Combining this with Figure 4, it is evident that increased point spacing results in wider micron channel spacing and larger unmodified areas within the channels, contributing to increased sample roughness. The trends in roughness and fracture strength correlate with changes in point spacing.  
In summary, the optimal processing quality is achieved at a processing point spacing of 1 \(\upmu\)m, where the overall shape remains uniform.