# Monitoring of Evolving Laser Induced Periodic Surface Structures
## 1 Introduction  
Laser induced periodic surface structures (LIPSS) have been in the focus of surface functionalization for a many years. They have been observed for the first time by [PERSON] in 1965 [1] and can be generated by linearly polarized laser pulses on almost all material classes, for example, metals [2; 3; 4; 5], semiconductors [6; 7; 8], dielectrics [9; 10; 11]. LIPSS are easy to fabricate with femtosecond laser systems of moderate power and have found widely spread application (cf. e.g., Reference [12] and references therein) influencing the physical and chemical properties of surfaces. They can be applied to control wettability and friction of surfaces [13; 14], to generate structural colors [15] or to optimize cell growth in biomedical applications [16]. There are two different LIPSS types: Low Spatial Frequency LIPSS (LSFL) with periods on the order of the laser wavelength and High Spatial Frequency LIPSS (HSFL) with periods significantly shorter than the laser wavelength. The orientation of the LIPSS depends on their type and the material. In metals, LSFL are oriented perpendicular to the laser polarization. The formation of LIPSS in metals by ns pulses can be described by the interference of the incident laser beam with a surface-scattered electromagnetic wave [17; 18; 19] leading to inhomogeneous energy deposition into the material. The formalism has been extended towards fs-pulse interaction with metal surfaces by [PERSON] and coworkers [9; 20]. There is no consensus yet on the underlying principles leading to HSFL. Different models have been discussed covering nonlinear frequency conversion [9; 21], nanoplasmonic excitation [22] and self-organization [23]. In order to study the formation process and to gain information on the underlying principles, different monitoring processes have been developed, for example, in situ diffraction [24], in situimaging deploying a microscope [25] and in situ surface second harmonic generation [26]. In situ imaging and diffraction requires a pump probe setup, that is, a probe beam at lower wavelength in addition to the patterning beam. Here, we present another monitoring method which is based on an interesting discovery in our recent experimental work. In that work, LIPSS on titanium and Si\({}_{3}\)N\({}_{4}\) samples were fabricated in-situ as targets for laser particle acceleration and X-ray generation [27; 28]. In such experiments laser pulses with ultra-high intensity \(\sim\)(\(10^{18}\ldots 10^{20}\)) W/cm\({}^{2}\) are applied to a solid target, where ions from a contamination layer at the target rear side are accelerated due to the target normal sheath acceleration (TNSA) mechanism [29]. Depending on the target material, an X-ray flash is released in addition as result of the high intensity laser target interaction [30]. LIPSS have been generated by the same but strongly attenuated laser pulses. As soon as LIPSS have been formed, a characteristic fringe pattern in the back-reflected light is observed which is the basis of the proposed imaging system. The method proposed in the present work does not require an additional monitoring beam but analyzes the backscattered light of the patterning laser. Currently, much effort is spent to advance such secondary radiation sources towards repetitive applications. LIPSS formation is a very promising target manufacturing method capable to provide optimized laser-target interaction and--given the availability of a monitoring system--compatible with high repetition rate applications. Such simple monitoring system will not only be essential in facilitating efficient high repetition rate laser driven secondary radiation sources but will be helpful in any application that needs very fast evaluation of LIPSS formation processes (ideally while writing the structures), such as required for inspection of large surface in industrial applications [31]. In this work we investigate the origin of the fringe pattern with the help of of a 3D Maxwell solver based on the finite difference time domain (FDTD) method.