Coherence in ultrafast laser-induced periodic surface structures

Ultrafast laser irradiation can trigger anisotropically structured nanoscaled gratinglike arrangements of matter, the laser-induced periodic surface structures (LIPSSs). We demonstrate here that the formation of LIPSS is intrinsically related to the coherence of the laser field. Employing several test materials that allow large optical excursions, we observe the effect of randomizing spatial phase in generating finite domains of ripples. Using three-dimensional finite-difference time-domain methods, we evaluate energy deposition patterns below a material's rough surface and show that modulated pattern, i.e., a spatially ordered electromagnetic solution, results from the coherent superposition of waves. By separating the field scattered from a surface rough topography from the total field, the inhomogeneous energy absorption problem is reduced to a simple interference equation. We further distinguish the contribution of the scattered near field and scattered far field on various types of inhomogeneous energy absorption features. It is found that the inhomogeneous energy absorption which could trigger the low-spatial-frequency LIPSSs (LSFLs) and high-spatial-frequency LIPSSs (HSFLs) of periodicity $\mathrm{\ensuremath{\Lambda}}>\ensuremath{\lambda}/\text{Re}(\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{n})$ are due to coherent superposition between the scattered far field (propagation) and the refracted field, while HSFLs of $\mathrm{\ensuremath{\Lambda}}<\ensuremath{\lambda}/\text{Re}(\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{n})$ are triggered by coherent superposition between the scattered near field (evanescent) and the refracted field. This is a general scenario that involves a topography-induced scattering phenomenon and stationary evanescent fields, being applied to two model case materials that exhibit large optical excursions upon excitation (W, Si) and nonplasmonic to plasmonic transitions. We indicate the occurrence of a general light interference phenomenon that does not necessarily involve wavelike surface plasmonic excitation. Finally, we discuss the role of interference field and scattered field on the enhancement of LIPSSs by simulating interpulse feedback effects and provide the electromagnetic origin of grooves $(\mathrm{\ensuremath{\Lambda}}>\ensuremath{\lambda})$ related to a feedback-driven topography evolution. Those results strongly suggest the electromagnetic interpretation of LIPSSs in interplay with an evolving surface topography.