## 3 Results and Discussion  
### Modulation Length and Depth Analysis of Laser-Structured Surfaces  
Figure 2 schematically shows the appearance of the laser-driven structures. The laser scanning direction is along the \(X\)-axis, so the height modulation is along the \(Y\)-axis. Even along the \(Y\)-axis, the u-ripple modulation occurs after femtosecond laser irradiation. Perpendicular to these structures, the LSFL appears along the \(X\)-axis. To visualize these structures, Figure 3 shows the identical area of a laser-structured brass surface for two measurement modes (compositional and topographical mode) of the SEM, generated by different SEM detector settings (Figure 3a,c), highlighting differently generated LSFL and u-ripples using a fluence of 0.87J/cm\({}^{2}\) and a pulse overlap of 98.8%. Whereas in Figure 3a LSFL can be seen with a periodicity of 879 nm, i.e., slightly below the laser wavelength, Figure 3c \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{4}{c}{**Spatial Wavelength \(\mathbf{\Lambda}_{LSFL}\)/nm**} \\  & **2.5 J/m** & **5 J/m** & **7.5 J/m** & **10 J/m** \\ \hline
0.87 J/cm\({}^{2}\) & 905 & 902 & 886 & 879 \\ \hline
1.63 J/cm\({}^{2}\) & 901 & 894 & 884 & 872 \\ \hline
1.96 J/cm\({}^{2}\) & 897 & 891 & 882 & 869 \\ \hline  & \multicolumn{4}{c}{**Spatial Wavelength \(\mathbf{\Lambda}_{n\text{-}ripple}\)/nm**} \\  & **2.5 J/m** & **5 J/m** & **7.5 J/m** & **10 J/m** \\ \hline
0.87 J/cm\({}^{2}\) & 1316 & 1557 & 1788 & 1808 \\ \hline
1.63 J/cm\({}^{2}\) & 1247 & 1316 & 1733 & 1812 \\ \hline
1.96 J/cm\({}^{2}\) & 1280 & 1339 & 1709 & 1800 \\ \hline  & \multicolumn{4}{c}{**Spatial Wavelength \(\mathbf{\Lambda}_{ablation}\)/\(\upmu\)m**} \\  & **2.5 J/m** & **5 J/m** & **7.5 J/m** & **10 J/m** \\ \hline
0.87 J/cm\({}^{2}\) & 25.8 & 27.8 & 28 & 28.4 \\ \hline
1.63 J/cm\({}^{2}\) & 24.5 & 29.6 & 32.1 & 31.2 \\ \hline
1.96 J/cm\({}^{2}\) & 25.2 & 33 & 32.3 & 33.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Spatial wavelength and modulation depth of LSFL, u-ripples, and ablations in the dependence of applied laser fluence (rows) and track energy (columns). The values represent the mean of three measured specimens. depicts u-ripples in the same field of view, being perpendicularly oriented to the LSFL and having a periodicity of 1808 nm. Performing a 2D Fourier analysis on these images yields information on the spatial frequency, orientation, and homogeneity of the periodic structures (Figure 3b,d). Please note that the above given figures for the periodicities are taken from the position of the centroids of the 2D Fourier spectra. Table 1 summarizes the measured periodicities and modulation depths of LSFL, u-ripples, and ablation lines as a function of the applied laser fluence and track energies, respectively. Apparently, in the studied parameter range, the LSFL period \(\Lambda_{LSFL}\) decreases significantly with increasing track energy, i.e., decreasing scanning speed, and decreases slightly with increasing fluence. The decreasing spatial wavelength of the LSFL can be explained by the induction of a surface-plasma wave through the parametric decay of laser light [31]. The increasing pulse number is a result of a feedback mechanism based on a grating assisted SSP excitation and the incident laser radiation [4]. This behavior has similarly been reported for the generation of LIPSS on titanium by [PERSON] et al. [32], on silicon by [PERSON] et al. [4], and on titanium, molybdenum, platinum, and tungsten by [PERSON] et al. [31]. Contrary to these trends of \(\Lambda_{LSFL}\), the spatial periodicity of the u-ripples (\(\Lambda_{u\text{-}ripple}\)) increases with increasing track energy and exhibits similarly small decreases with increasing fluence [5; 33].