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 >/Re (\~{}n) are due to coherent superposition between the scattered far field (propagation) and the refracted field, while HSFLs of) related to a feedback-driven topography evolution. Those results strongly suggest the electromagnetic interpretation of LIPSSs in interplay with an evolving surface topography.