## 4 Conclusions  
In this study, a micromachining process was investigated where soda-lime glass samples are covered with a layer of water and high-energy femtosecond pulses (\(>\)100 uJ, 18 J/cm\({}^{2}\)) are focused on the surface. The acquired data, in terms of micromachining throughput and shape of the provided craters, were compared with the conventional case of focusing the laser pulses in air. In addition, a theoretical basis is provided in order to numerically simulate the propagation of the femtosecond pulses through the non-linear medium, as well as for the formation of ablation craters. By studying the shape of the ablation craters produced, it was noticed in both cases that the craters produced while focusing femtosecond pulses in air exhibit a sharp apex near the bottom, while the craters produced in water appear blunt with steeper sidewalls. By numerically simulating the propagation of the beam and the formation of ablation craters we were able to show that this result is due to the transformation of the beam to a semi flat-top intensity distribution, which is maintained approximately throughout the thickness (1 mm) of the sample. As a consequence of the near flat-top distribution, the micromachining throughput overall is significantly higher when cutting the thick, practically macroscale samples. Since the energy density does not drop as fast due to the increase in the surface area while the depth of the crater increases, efficient ablation occurs at various depths of the sample, whereas, for the conventional case of focusing in air the ablation efficiency drops rapidly once a certain crater depth is reached inside the sample due to the increase in the surface area. In addition, we provide insights as to why there are different results while varying the micromachining parameters such as: focal position, repetition rate (pulse energy), and beam translation speed (when performing vector cutting). Interestingly, we find that that such a process is mostly usable with high energy pulses (\(>\)100 uJ, 18 J/cm\({}^{2}\)) due to the properties of the materials that are responsible for the intensity transformation process of the beam. In addition, due to the diffraction of light, such a process is not likely to perform well when focusing the beam within a water layer using sharper focusing optics (f \(<\) 5 cm).  
[PERSON] prepared the data for the article, assembled the experimental setup and organized the experiments, carried out part of the experiments, conceptualized the semi-empyrical model used for the simulation of ablation craters and peformed the numerical simulations, and wrote the article. [PERSON] prepared the basis for the theoretical model of beam propagation through non-linear media, performed the numerical simulations aided in various consultations. [PERSON] carried out part of the experiments and aided in editing the article. [PERSON] aided with numerical modelling consultations regarding crater formations and algorithm stability issues. [PERSON] aided in experiment planning, organizing, and advised on the technical aspects of the micromachining setup. [PERSON] oversaw the entire study and consulted on various physical and technical aspects.  
This project was partially funded from the European Regional Development Fund (ERDF), Grant No. 1.2.2-LMT-K-718-02-0017.  
The authors declare no conflict of interest.  
Figure 12: Beam propagation in water (**a**) and in a medium having lower non-linear losses and n\({}_{2}\). (**b**).