## 3 Results and Discussion  
Figure 3 shows the nanostructures on the tungsten surface that were fabricated by femtosecond laser beams with different polarization states. As shown in Figure 1, when the grating vectors of RG1 and RG2 were conjugated relative to the 4\(f\) system, the combined  
Figure 2: (**a**) Cross-sectional intensity distribution of the femtosecond vector beam recorded by the CCD camera in the dashed frame shown in Figure 1. The transmission axis of the linear polarizer (LP2) is indicated by the double-ended arrow, whose orientation is denoted by the angle \(\theta\). \(\theta\) = 0 in the recording of this picture. The blue solid curve shows the polarization distribution of the laser beam. (**b**) Dependence of the dark stripe’s position in (**a**) on the rotation angle \(\theta\) of the linear polarizer (LP2). beam after RG2 was a scalar beam with a vertical polarization. Using the scalar femtosecond laser beam (Figure 3a), we produced periodic ripples on the tungsten surface, which is presented in Figure 3f. By rotating the RG2 around its normal direction, we were able to generate a femtosecond vector beam with different polarization distributions. Using these vector beams, we fabricated curved periodic ripples with different curvature radii on the tungsten surface, which is shown in Figure 3g-j. Since the tangential direction of the curved ripples was perpendicular to the local polarization of the femtosecond laser beam, the formation mechanism of the curved ripples was able to be attributed to the interference between the incident femtosecond laser and laser-induced SPPs. It was also noted that besides curved ripples, as shown in Figure 3g-j, nanoholes were also fabricated on the target surface. It is interesting to find that as the variation period of the polarization of the femtosecond laser decreased, the nanoholes fabricated on the tungsten surface become increasingly more regular in the spatial distribution. In Figure 3j, the nanoholes all appear at the vertexes of the curved ripples, regularly arranged in the horizontal direction. However, in Figure 3f, the nanoholes have a more random spatial distribution. In order to investigate the formation mechanism of these nanoholes, we fabricated the compound surface patterns composed of nanoholes and curved ripples when the half-wave plate (HWP2) shown in Figure 1 was rotated at different angles. The experimental results are shown in Figure 4.  
Figure 3: Nanostructures on the tungsten surface fabricated by femtosecond laser with different polarization distributions. During the fabrications, the target was moved along the \(x\) direction (see Figure 1). (**a–e**) Cross-sectional intensity distribution of the femtosecond laser recorded by the apparatus in the solid frame shown in Figure 1. The transmission axis of the linear polarizer (LP2) was along the \(x\) direction. For vector beams, the period of the polarization variation along the vertical (\(y\)) direction is presented in the uppermost row. The blue solid curve in (**b**) presents the polarization distribution of the vector beam. (**f–j**) Nanostructures fabricated on the tungsten target. The target scanning speed was 0.06 mm/s, and the single-pulse energy of the femtosecond laser striking on the target surface was 20 \(\upmu\)J. When we gradually rotated the HWP2 shown in Figure 1, the local linear polarization of the femtosecond vector beam rotated as a whole, inducing the shift of the nanostructures on the tungsten surface along the direction perpendicular to the target scanning direction, i.e., along the vertical direction shown in Figure 4a. Taking the case that the rotation angle of HWP2 was 25\({}^{\circ}\) as an example (see Figure 4b), using ImageJ software [31], we were able to extract the nanoholes from the SEM picture in Figure 4b. The processed picture is presented in Figure 4c. By counting the holes in Figure 4c, we were able to provide the dependence of the hole number on the location along the vertical direction, which is given in Figure 4d.