## 1 Introduction
This is due to the fluence decrease when a crater is formed (the walls of a deep crater have a larger surface while the spot is projected onto the walls). As the successive pulses impinge on the same surface area, the surface gradually changes from flat to a V-shape. This is caused by the spatial energy distribution of the beam on top of the sample. Since typical femtosecond lasers have a Gaussian energy distribution, the gradient of the Gaussian beam is the driving factor leading to a V-shape. When more and more pulses hit the surface, the fluence decreases from its initial value and may go below the ablation threshold. In that case, the efficiency of the ablation process is low, and the increasing tails of the Gaussian beam produce a constant temperature input with no ablation. In addition, as the channel becomes deeper, the angle of incidence of the light changes, which also lowers absorption. More information regarding the intricacies of V-shape formation may be found in [30]. A possible workaround for this issue is the use of beam-shaping optics which produce a flat-top beam [31; 32], where the area of zero gradient distribution is large and the ablation rate is constant. However, although there are a number of options for beam-shaping optics, in practice the flat-top zone is realized only at a certain position along the propagation direction, after which it breaks apart (takes on a non-flat-top intensity distribution). Furthermore, when a crater is formed on the surface, diffraction from the edges of the walls, and subsequently interference, distorts the flat-top distribution. Therefore, for deep cutting/drilling, beam shapers of this sort are not an option. There are several reports showing that when a layer of water is applied above the samples, better micromachining quality, as well as increased micromachining throughput, is achieved when cutting/drilling various materials [33; 34; 35; 36]. Explanations for these improvements include better cleaning of the micromachined crater due to a lower pressure zone that appears above the micromachined channel as the material expands after the laser pulse hits the surface [34], poor adhesion of the ablated particles to the surface and the walls of the crater which is caused by the slowing down of the species within a viscous medium [37; 38], better cooling of the ablated sample due to the better thermal conductivity of water as compared with air [38; 39], and better energy transfer from the created plasma to the sample since it is confined by a layer of water [34]. These effects mostly contribute to better micromachining quality obtained after cutting/drilling, only partly explain the increase in micromachining throughput, and they also do not explain the shape of the ablated crater. In this study, we present the results of cutting 1-mm thick, soda-time glass samples submerged in water. By changing the pulse energy (repetition rate), thickness of the water layer, scanning speed, and focal position relative to the surface of the sample, we achieve different results in terms of cutting throughput. The differences in the results and the impact of each experimental factor were also studied numerically by modelling the propagation and energy losses of the beam using the nonlinear modified Schrodinger equation. We show that the main driving factor behind the increase in micromachining throughput is the non-homogenous losses of energy within different portions of the beam resulting in a semi flat-top intensity distribution. When a channel is ablated and the ablated depth increases, the shape of the channel gradually changes from flat to a V-shape for a Gaussian intensity distribution beam, at which point the fluence drops dramatically to near ablation threshold values due to the large surface area which the beam is projected on. If the intensity profile is closer to a flat-top beam, the V-shape formation is suppressed, the fluence does not drop as fast, and deeper channels are ablated faster with higher quality.