## 3 Results
### Impact of Repetition Rate (Pulse Energy) for Different Thickness Settings of the Water Layer  
The process is significantly impacted by the repetition rate of the laser (pulse energy) while keeping the same average power (10 W), as well as by the thickness of the water layer that is set. Figure 9 shows how the cutting speed varies when changing the repetition rate of the laser and when the thickness of the water layer is varied. On the basis of the considerations provided above with respect to the propagation of the beam when a layer of water is present above the sample, the outcomes when changing these parameters are not as intuitive as they are for ablation in air. It has already been demonstrated for high-energy pulses (\(>\)100 uJ, 18 J/cm\({}^{2}\)) that efficient cutting of the material is possible due to the transformation of the Gaussian intensity distribution. However, it is also evident that after a certain propagation distance, the beam breaks up and the intensity distribution resembles a complicated function with several peaks. The gradient of such a distribution has large absolute values, and overall this case is not suited for material removal since the energy density drops rapidly near the ablation threshold due to the change in the surface area. As shown in Figure 9, for the lowest repetition rate and thickness of the water-layer settings, the cutting rate is always highest and follows a quadratic drop when the repetition rate is increased. However, when changing from the minimum (0.3 mm) to the maximum (1.5 mm) setting of the water depth, the result changes several fold for the low-repetition rate setting and by a few orders of magnitude for the high-repetition rate setting. It appears that there is a linear interaction [51; 52] between these two parameters, i.e., the result (cutting speed) scales as the linear product of the two parameters times a constant. By taking the derivative of the result (cutting speed) over the repetition rate for the three different cases of water, we see that the angle of the derivative increases, confirming that a linear interaction is present (see inset of Figure 9). This shows that the overall process is sensitive to variations in the thickness of the water layer and this sensitivity is dependent on the repetition rate. For the other micromachining parameters listed here, an analogous interaction was not detected. From an engineering point of view, the thickness of the water layer is the most difficult parameter to control since the wettability of the sample plays a part when adjusting the thickness. If the sample exhibits poor wettability due to surface contamination, droplets may form instead of a smooth even surface. Overall it is concluded that the process of micromachining when a water layer is present above the samples is practical only for the high-energy (\(>\)100 \(\upmu\)J, 18 J/cm\({}^{2}\)) pulses (low repetition rate). To explain the interaction between the parameters, the propagation of the beam through 1.5 mm of water was simulated for three different energy settings (for consistency this will be displayed as the ratio P/P\({}_{\text{CR}}\)). The result is described in Figure 10. For the 100 P\({}_{\text{CR}}\), the situation is the same as described previously, i.e., the beam transforms to a semi flat-top distribution after less than 100 \(\upmu\)m of propagation and retains this shape for another 800 \(\upmu\)m of propagation. For the 33 P\({}_{\text{CR}}\), the energy losses are not as rapid, and therefore the transformation of the Gaussian distribution to a near flat-top distribution occurs after approximately 500 \(\upmu\)m of propagation. However, this shape is retained for only another 300 \(\upmu\)m of propagation. This occurs because the beam has propagated for a relatively long distance while still having a Gaussian distribution (and non-zero gradient) and the phase accumulation due to the self-focusing term becomes significant enough to break up the beam relatively quickly after the semi flat-top distribution has manifested.