## 3 Results
### Micromachining with High-Energy Pulses in Air and with a Water Layer Covering the Sample
In addition, it does not decrease the transverse dimensions of the beam but produces the two peaks near the peripheral region which are visible in Figure 5 (see intermediate distribution 3). However, it manifests only after approximately 400 \(\upmu\)m of propagation in the case studied, since the phase difference accumulates slowly in the peripheral region while the beam is propagating. It was noticed, that the diffraction term plays a negligible role in the transformation of the beam, in fact, if the diffraction term is omitted from Equation (2), the results shown in Figure 5 do not change. This is reasonable, taking into account the focusing conditions of the studied case as well as the wavelength. In order for the diffraction term to have an impact on the results, the propagation distance should be longer by at least an order of magnitude and this is confirmed via the numerical model. As discussed previously, from the micromachining point of view the flat-top/semi flat-top intensity distribution region is the most interesting for micromachining, since the ablation rate should remain constant as the region of the zero gradient would not contribute to the self-steepening of the channel walls, and ultimately would not produce a drop in the fluence on the surface of the sample. From this simulation, it is deduced that the thickness of the water layer should be set to approximately 100 \(\upmu\)m, since that is sufficient to transform the beam to a flat-top distribution. However, due to the surface tension of the water, water thickness values below 300 \(\upmu\)m are difficult to achieve in practice, though undeniably the lowest values of the water layer should provide the best results in material removal (cutting). Figure 5: Beam intensity distribution dynamics vs. propagation distance in water. The point 0 \(\upmu\)m corresponds to the air-water interface, whereas, the point 1500 \(\upmu\)m would correspond to the water-glass interface. Using the semi-empirical model described in Section 2.3 (using Equation (4)) and the intensity distribution acquired from the results shown in Figure 5, the formation of the craters when a transformed beam produces ablation on the sample was investigated. Two different cases were investigated. First, the beam impinges on the surface of the sample having a Gaussian intensity distribution (the full energy of the pulse is used). Secondly, a transformed semi flat-top beam, which has sustained energy losses due to non-linear absorption in the water, impinges on the surface of the sample. The results are displayed in Figure 6. Here, the case is confirmed that the Gaussian intensity distribution (which has more energy as compared with the semi flat-top intensity distribution) produces deeper craters at first, however due to the changing shape of the crater, the energy density within the impingement zone drops due to the increase of the surface area, and the ablation rate slows down. The change in the energy density (fluence) after consecutive pulses is illustrated in Figure 6. For the semi flat-top intensity distribution, the ablation rate is lower at first as compared with the Gaussian case, since the beam experienced losses of 25% within the water layer. However, due to the differences in the gradient (Gaussian vs. semi flat-top) the semi flat-top intensity distribution does not converge to a V-shape as fast as it does in the Gaussian case. Therefore, from the depth vs. number of pulses plot (see Figure 6e) it is observed that initially the Gaussian pulses produce deeper craters, but ultimately the depth becomes larger in the semi flat-top case, and the two curves cross each other, which agrees well with the experimental data shown in the right side (b) of Figure 4. Note, that the intensity distribution was chosen somewhat arbitrarily between points two and three (see right side of Figure 5), since this is the part that produces the micromachined channels in the real experiments.