## 3 Results and Discussion  
### Experimental Results  
Figure 1 shows the ablation patterns on BaF\({}_{2}\) induced by 25 accumulated XUV-CDL pulses at different fluence levels as detected by the white light interferometer (WLI). The pattern in Figure 1a was ablated by the full laser energy. In Figure 1b,c, the laser was  
attenuated by Al filters with thicknesses of 200 nm and 400 nm. The corresponding fluence of the XUV laser in Figure 1 was approximately 230 mJ/cm\({}^{2}\), 30 mJ/cm\({}^{2}\) and 15 mJ/cm\({}^{2}\), from left to the right. Ablation craters become smaller as Al foils attenuate the beam, the deepest part of each crater is always located at the crater center.  
The AFM scanned several 10 \(\upmu\)m \(\times\) 10 \(\upmu\)m square areas inside the ablation craters. The corresponding AFM images can be seen in Figure 2. Nanostructures with a uniform morphology have been always registered. The structures exhibit a spatial period decreasing from approximately 1 \(\upmu\)m down to 250 nm when the fluence decreases from 230 mJ/cm\({}^{2}\) down to 15 mJ/cm\({}^{2}\). Figure 3 shows the results obtained at a reduced number of accumulated pulses, i.e., 12 pulses were applied in creating the ablation crater. The spatial periods of the nanostructures remained unchanged with respect to the irradiation by more pulses at the same fluence level. However, the surface inside the ablation crater created by a lower number of pulses shows a higher roughness in comparison to the surfaces processed by more pulses.  
Figure 1: Ablation patterns on the BaF\({}_{2}\) sample exposed to 25 CDL pulses at fluences of (a) 230 mJ/cm\({}^{2}\), (b) 30 mJ/cm\({}^{2}\) and (c) 15 mJ/cm\({}^{2}\).  
Figure 2: Nanostructures on BaF\({}_{2}\) induced by 25 laser pulses with fluences of (a) 230 mJ/cm\({}^{2}\), (b) 30 mJ/cm\({}^{2}\) and (c) 15 mJ/cm\({}^{2}\).  
We may see in Figures 2 and 3 that the nanostructures on BaF\({}_{2}\) induced by a 46.9 nm laser have a specific orientation. To characterize the effect of the orientation, the BaF\({}_{2}\) monocrystalline slab targets were ablated at two different positions with respect to the XUV-CDL beam. Figure 4 provides a sketch of the sample arrangement. First, in position A, the ablation pattern made by 25 laser pulses was obtained. Then, the sample was turned by 45 degrees into position B, where another ablation pattern was created by the same number of laser pulses under identical experimental conditions. Therefore, the only change in this experiment concerns the angle between the tangential plane of the focusing mirror and crystallographic planes of the single crystal of barium fluoride.  
These two ablation patterns were subjected to AFM analysis without moving the sample (this is quite important, because the orientation of the structures observed in the AFM scanning area could change if the sample is moved). In Figure 5a,c, the overview images show ablation craters created in sample positions A and B, respectively. The shapes of these two patterns confirm that the focal spot was rotated by 45\({}^{\circ}\). In Figure 5b,d, the ablated surfaces of samples A and B are visualized by AFM with a higher resolution. It can be clearly seen that, despite the rotation of the focal spot, the orientation of the nanostructures remains the same in both the sample positions. This means that the k-vector  
Figure 4: Schematic diagram of the sample rotation.  
Figure 3: Nanostructures on BaF\({}_{2}\) surfaces exposed to 12 XUV-CDL pulses at fluences of (**a**) 230 mJ/cm\({}^{2}\), (**b**) 30 mJ/cm\({}^{2}\) and (**c**) 15 mJ/cm\({}^{2}\).  
of the grating-like structure is coupled to the orientation of crystallographic planes in the single crystal.