## 2 Experimental  
We used an ultra short pulsed laser (Pharos 10-600-PP, Light Conversion, Vilnius, Lithuania) with a pulse duration of 220 fs (FWHM) at a repetition rate of 50 kHz. For the generation of the micro- and nanostructures, we used the fundamental emission wavelength of 1030 nm. Figure 1 shows the experimental setup for the surface treatment. The energy of the laser beam was adjusted by an external attenuator. With a half wave plate in front of the focusing unit, the linear polarization of the laser beam was rotated parallel to the onwards used scanning direction. A galvo scanner (RTA AR800 2G+, Newson, Dendermonde, Belgium) was used in combination with a telecentric lens (\(f\) = 100  mm) to focus the beam onto the sample with a spot diameter of 38 \(\upmu\)m \((1/e^{2})\). LSFL were generated on 0.75 mm thick commercial available flat brass (CW 508L, CuZn37), which was cut in square pieces with a size of 16 \(\times\) 16 mm\({}^{2}\). The pieces were ground with a multi-directional polishing machine (LS3V, REMET, Bologna, Italy) with several abrasive strengths and afterwards polished with suspensions down to a grain size of 1 \(\upmu\)m to achieve a reference surface with a roughness \(R_{a}\) between 9 nm. To determine their influence on the generation of LIPSS, the fluence, i.e., the ratio of laser pulse energy and spot area, was varied between 0.87/cm\({}^{2}\) and 1.96/cm\({}^{2}\), and the scanning speed between 16 mm/s and 144 mm/s, respectively. The latter correspond to effective pulse overlaps between 92% and 99%. For each parameter combination, the scanning speed was set to achieve comparable track energies for each fluence (namely 2.5, 5, 7.5, and 10 J/m have been employed). While LSFL and u-ripples generated self-organized periodic structures that appear even for static laser illumination, ablated lines were generated in a periodic fashion by a scanning path that aligned individual lines next to each other. Becausethe ablation width increased with increasing fluence and track energy, the distance between individual ablation lines had to be adjusted for each parameter set in order to avoid damage in between lines and to ensure complete coverage of the surface with a periodic ablation pattern. Therefore, in the experimental evaluation, we also determined a periodicity for the ablated lines (\(\Lambda_{ablation}\), see Table 1), and this periodicity was in turn used in the numerical analysis (Section 3.3). For each parameter combination, three equal samples with structured fields of 4.5 \(\times\) 4.5 mm\({}^{2}\) were generated. The experimental results of the apparent contact angle measurements, as shown in the following diagrams, included the determined mean values and standard deviations. The geometrical dimensions of \(\Lambda_{LSFL}\) and \(\Lambda_{u\text{-}ripple}\) were captured via Scanning Electron Microscopy (Phenom ProX, Phenom World, Eindhoven, The Netherlands) with subsequently picture analysis via 2D Fourier transformation. This approach figures the spatial frequency, the orientation, and the homogeneity of the generated LIPSS [11]. To evaluate the modulation depth of the LSFL and u-ripples, an atomic force microscope (Dimension Icon, Bruker Corporation, Billerica, MA, USA) in PeakForce Tapping Mode and for the determination of the modulation depth of the line ablation, a 3D optical microscope based  
Figure 1: Schematic laser system setup with Light Conversion Pharos 10-600. First, the half wave plate (HWP) and Polarizer allow energy adjustment; second, the HWP controls the orientation of the laser-induced periodic surface structures (LIPSS). on white light interferometry (Contour GT-K, Bruker Corporation) were used. The wetting behavior was investigated using a contact angle measurement system (OCA 25, Data Physics, Filderstadt, Germany). Using a dispensing unit, a droplet (6 \(\upmu\)L) of distilled water with a surface tension of 74 mN/m was deposited on the examined surface. A camera captures the droplet on the surface via the sessile drop method.