# Surface Plasmon Polariton Triggered Generation of 1D-Low Spatial Frequency LIPSS on Fused Silica
## 3 Results and Discussion  
To generate one-dimensional LSFL, the laser spot was translated across the fused silica specimen by the scanner. For the parameter study, we defined a \(41\times 41\) matrix varying the fluence between 1.40 J/cm\({}^{2}\) and 2.37 J/cm\({}^{2}\) and the laser scanning speed between 50 mm/s and 250 mm/s (i.e., 1681 parameter sets), respectively. Figure 2a summarizes the results for the generation of one-dimensional structures, where we distinguish three regions. For Region I, the scanned lines include more than 50% surface damage (damage > 50%). In Region II, the scanned lines include more than 50% periodic structures (structures > 50%), and finally, in Region III, the scanned lines include more than 50% unstructured areas (unstructured > 50%), respectively. Insets in Figure 2a show examples for the three regions. Apparently, the parameter range including lines with more than 50% periodic structures is a narrow band of combined fluence and scan speed. In addition, 1D-LSFL generation with increasing scanning speeds needs higher fluences to guarantee a certain energy input. Figure 1: Schematic illustration of the experimental setup with the scanning direction being parallel to the polarization (pol.) of the laser. Figure 2b shows SEM images of 1D-LSFL in Region II, i.e., more than 50% of the surface exhibits periodic structures, being generated with different scanning speeds and fluences. Please note that the scanning direction was set parallel to the polarization of the laser (white arrow). Obviously, the generated structures are perpendicular to the laser polarization. Contrary to these observations, different authors reported on the generation of LSFL on fused silica with an orientation being parallel to the polarization of the laser for both scanning and non-scanning (punctual) cases [12; 15; 16; 36; 40]. These parallel structures were never observed in our experiment over the entire parameter range in Figure 2a. Furthermore, the observed LSFL reveal periodicities smaller than the wavelength of the laser with the values summarized in Table 1.  
Figure 3 shows an AFM image having a field of view of 10 \(\upmu\)m \(\times\) 10 \(\upmu\)m (a) and the corresponding modulation profile (b) of the shown structures. The laser parameters are the same as in Figure 2b for the qualitatively most homogeneous 1D-LSFL (140 mm/s and 1.86 J/cm\({}^{2}\)). The structures reveal an average depth of about 260 nm and a modulation profile resembling a \(\mid\)sin(x)\(\mid\) function. Figure 2: **(a)** A 41 \(\times\) 41 matrix including scanning speed variations between 50 mm/s and 250 mm/s and fluence variations between 1.40 J/cm\({}^{2}\) and 2.37 J/cm\({}^{2}\); scanning direction is set parallel to the laser polarization. Different regimes determine whether the line includes more than 50% damaged, structured and unstructured areas. **(b)** SEM images of 1D-LSFL on fused silica including more than 50% structures (Region II) for different scanning speeds and fluences. According to the SPP theory, surface plasmon polaritons are formed at a metal-dielectric interface [21; 22; 23; 41], while their periodicity is calculated with an established equation for the real part of \(\epsilon_{m}\) (Equation (2)) [20; 23; 21; 22; 242]. Here, \(\lambda_{SPP}\) describes the wavelength of the SPP, \(\lambda_{0}\) the wavelength of the applied laser, \(e_{m}^{\prime}\) the real part of the dielectric function of the metallic substrate (\(\epsilon_{m}=e_{m}^{\prime}+\mathrm{i}e_{m}^{\prime\prime}\)) and \(\epsilon_{d}\) the dielectric function of the dielectric. \[\lambda_{SPP}=\Lambda_{LSFL}=\lambda_{0}*\sqrt{\frac{\epsilon_{m}^{\prime}+ \epsilon_{d}}{\epsilon_{m}^{\prime}\epsilon_{d}}} \tag{2}\]  
For laser irradiation in ambient air, the dielectric function \(\epsilon_{d}\) corresponds to \(\epsilon_{d}=1\), where the real part of \(\epsilon_{m}\) has to be \(\epsilon_{m}^{\prime}<-1\).