## 3 Results and Discussion  
### Optimisation of LIPSS Morphology  
Nanometric LIPSS are currently being evaluated to produce next-generation advanced materials in a wide range of application sectors, such as the biomedical, aerospace, automotive, food-handling, home-appliance industries, and so on [16; 17; 18]. The generation of LIPSS over surfaces much larger than the spot size (>>1 cm\({}^{2}\)) is normally achieved by the raster scanning technique. In this case, large-scale LIPSS homogeneity is linked to the laser process parameters, mainly the energy dose \(\Phi\) and the laser beam polarisation orientation [19]. \(\Phi\) corresponds to the cumulative energy deposited on the unit of irradiated surface (J/cm\({}^{2}\)) and takes into consideration key parameters such as the energy per pulse E, the repetition rate RR and the spatial overlap between successive pulses, which in turn play a role in thermal accumulation phenomena [1]. In order to define a set of laser process parameters where LIPSS are generated uniformly, the energy dose \(\Phi\) was fixed at 0.55 kJ/cm\({}^{2}\) and the scan speed at 90 m/s coherently with results reported for similar experimental conditions [1]. Moreover, to maximise the throughput, the average power P was kept constant at 260 W (i.e., the maximum available on the stainless-steel coil after optical losses), and RR was varied in the range of 1-10 MHz, corresponding to E varying from 26 u] to 260 u], respectively. Laser-treated surface morphologies were finally analysed by SEM (Vega3, by Tescan, Brno, Czech Republic). Figure 3 presents SEM images of the laser-treated surfaces, and for each image, the insets show the respective FFT analyses. The yellow arrows represent the orientation of the laser beam polarisation on the irradiated surface. Starting from relatively low RR (RR = 1 MHz and RR = 2 MHz) the LIPSS morphology was irregular and not well-defined. In these cases, the corresponding E (respectively, E = 260 u] and E = 130 u]) was too high, leading to important ablation phenomena and preventing the generation of uniform structures. Increasing RR, E decreased, and structures became more regular. An optimum appeared in correspondence with RR = 5 MHz and E = 52 u] s. Further increasing RR, the E decreased proportionally, and the observed morphology underwent a slight degradation. Similar results have been already reported in the literature for Steel [20; 21] and ascribed to the increase in the spatial overlapping between two successive pulses. In fact, this led to an extension of the surface where the surface plasmon polaritons generated by the second pulse interacted with the pattern generated by the first, thus decreasing the pattern regularity.  
Our trend was confirmed by the FFT analysis, which made it possible not only to extract the LIPSS period value but also the angular dispersion \(\theta\) of the FFT peak. The latter represents an effective and quantitative evaluation of the LIPSS homogeneity [22]: the lower the \(\theta\), the higher the structure's homogeneity.  
As shown in Table 1, a minimum was observed for RR = 5 MHz and E = 52 \(\upmu\)J, where \(\theta\) = 11\({}^{\circ}\). This value is consistent with those previously reported in the literature [20,22]. Finally, we observed that the same experimental approach could be used to extend the above-mentioned results to sheets of metals like Ti, Mo, Ni, Al, Cu, etc. It is worth observing that although for Ti and Mo, we can expect an optimum \(\theta\) value of roughly between 5\({}^{\circ}\) and 10\({}^{\circ}\), for Al, Ni and Cu, it will be much higher, given that the values reported in the literature ranged between 20\({}^{\circ}\) and 30\({}^{\circ}\)[20].