## 3 Results
### Impact of Focal Position when Cutting the Samples in Air and While Covered with a Water Layer  
We observed that, for cutting in water, the position of the focal point relative to the surface of the sample exhibits an unusual departure from the conventional case of focusing the pulses in air. Figure 6: The numerical evolution of the crater profiles while multiple pulses impinge on the surface. (**a**), 240 pulses impinge on the surface (Gaussian (top left inset) intensity distribution), (**b**) the evolution of the energy density due to the change in the surface area. (**c**), 240 pulses impinge on the surface (semi flat-top shape intensity distribution) and the total energy is 25% lower as compared with the Gaussian case, (**d**), the evolution of the energy density. (**e**) The depth is plotted against the number of pulses for the two cases. The individual lines show the shape after multiples of 10 pulses. Figure 7: Craters produced when ablating in air and when the samples are covered with a water layer. A different number of scans is required to reach a specific depth, one can estimate this number for both cases of cutting in air and in water in Figure 4. The images were acquired with an optical microscope in transmission mode. Fabrication efficiency is highest when the focal position is shifted below the surface of the sample and remains constant for a specific range of the focal position setting (in our studied range of parameters this was approximately 1 mm). It is worth mentioning that, given our focusing conditions, the Rayleigh range is approximately 1.1 mm which is larger than the thickness of the sample. In the graph presented in Figure 8 two different cases of cutting in air and in water are presented. The cutting rate is defined as an average cutting throughput for 1-mm thick, soda-lime glass samples at different focal position settings. For cutting in air, the cutting throughput is approximately the same within the Rayleigh range regardless of which direction (up or down) the focus is shifted. The graph peaks at the focal position as is expected and drops going in both directions, since the fluence scales as the square of the diameter of the beam and the diameter has the lowest value at this point. It should be mentioned that through-cuts (in 1-mm thick samples) were not produced for the cutting in air and the graph represents a dependency when 400 \(\upmu\)m deep trenches were ablated. The cutting speed absolute values are valid only for the cutting in water; therefore, the curve that represents cutting in air should only be taken as a reference for the shape. For cutting in water, a peak exceeding the error values was not observed. Instead, the cutting rate is somewhat constant, in the range from 1.5 mm to 0.5 mm below the surface of the sample, and afterwards it starts to drop. The ideal point for cutting would be to set the focus at approximately 0.75-1 mm below the surface of the sample. Interestingly, the cutting rate is lower by approximately 20% if the focal position is set at the surface of the sample (the ideal case when focusing in air). Shifting the focal position upwards even further results in a steep drop in cutting rate which ultimately becomes zero (meaning that it is impossible to produce a through-cut regardless of how long the fabrication is carried out) if the focal position is shifted 1 mm above the surface of the sample. It is worth mentioning  
Figure 8: Cutting speed plotted against the focal position relative to the surface of the sample for cutting in air and in water. The scanning speed is 150 mm/s, pulse energy is 200 \(\upmu\)J.  
that the focus positions are understood as the geometrical position relative to the surface plane, and the refraction of the beam passing through two materials having different refractive indices (water and glass) was not taken into consideration since the focusing was carried out with a long focal length (low NA) lens and the angle at which the beam hits the surface is near perpendicular.