## 3 Results and Discussion
It was seen that the nanoholes tended to appear at the vertexes of the curved ripples. The spatial interval between adjacent spikes shown in Figure 4d was simply the spatial period of the polarization variation of the focused femtosecond laser beam on the tungsten surface. Therefore, the location of the spike with the maximal number of holes was chosen to indicate the location of the nanoholes. The dependence of the nanoholes' location on the angle of HWP2 is shown as the square dots in Figure 4e. The curved ripples' location is indicated by the bordering between adjacent curved ripples, which is presented by the red solid line in Figure 4a. The dependence of the curved ripples' location on the angle of HWP2 is presented as circular dots in Figure 4d. It can be seen that the locations of the nanoholes and the curved ripples changed synchronously with the increase in the angle of HWP2. Therefore, it was concluded that the nanoholes were generated due to the polarization distribution of the femtosecond vector beam. Figure 4: (**a**) Nanostructures on the tungsten surface fabricated by non-cylindrical femtosecond vector beam when the half-wave plate (HWP2 in Figure 1) was rotated at different angles ranging from 0 to 85\({}^{\circ}\); 0\({}^{\circ}\) indicates the fast axis of HWP2 was parallel to the \(x\)-axis in Figure 1. (**b**) Nanostructures fabricated when the angle of HWP2 was 25\({}^{\circ}\). (**c**) Nanohole distribution extracted from (**b**). (**d**) Number of nanoholes at different locations along the vertical direction. (**e**) Dependences of the locations of nanoholes (square dots) and the vertical laser polarization (circular dots) on the angle of HWP2. It is commonly accepted that the periodic ripples are generated due to the interference between the femtosecond laser beam and its induced SPPs [18]. Therefore, the ripples' radius of curvature can be controlled by the polarization distribution of the incident femtosecond laser beam, as shown in Figure 3. When the orientation of the linear polarization rotated quickly at the beam cross-section, all of the nanoholes appeared at the vertexes of the curved ripples. The vertexes of the curved ripples were the converging point of SPPs, which is schematically presented in Figure 5. Therefore, on the tungsten surface, after irradiation by the femtosecond laser, the vertexes of the curved ripples had the most intensive SPPs. The nanoholes are considered to be generated due to the interference between the femtosecond laser and the focused SPPs [32]. Finally, non-cylindrical femtosecond vector beams with different average powers were employed to irradiate the tungsten target. The morphologies of the irradiated tungsten surfaces are presented in Figure 6. The target scanning speed was kept at 0.06 mm/s, and the scanning direction is indicated by the arrow in Figure 6d. It was seen that as the single pulse energy decreased from 20 uJ to 8 uJ, the region covered by the curved ripples and the nanoholes shrunk to the bottom part of the irradiated region, as shown in Figure 6d. This indicates that the intensity distribution on the cross section of the laser beam was non-uniform and relatively large at the bottom part of the beam cross-section. Therefore, this explains why the nanoholes were more evident in the bottom part of the irradiated surface, as shown in Figures 4b and 6, inferring that the formation of nanoholes not only depends on the polarization distribution of the incident femtosecond laser but also requires proper optical intensity. Figure 1.0 Schematic diagram of converging SPPs induced by the non-cylindrical vectorial femtosecond laser beam.