“…We have proposed an interpretation of the observed LIPSS spacing, where we assume that LIPSS generation occurs through the following process: (1) plasma waves are induced on the surface by the femtosecond laser pulse; (2) spatially localized ion-rich areas Coulomb-exploded into vacuum [49,50], and consequently the thin layer is ablated and the interspaces of the gratings are printed during the first several pulses (the number of pulses depends on the laser energy fluence, and at certain high fluence values, only a single pulse is involved in this stage and the following one); and (3) the electric field is enhanced near the initially printed structures by subsequent pulses, and near-field light ablates the surface, thus deepening the grating structures [51][52][53]. When a plasma wave (electron wave) is driven in a bulk plasma by a laser pulse, the plasma wave dispersion is given by ω 2 = ω p 2 + 3/2v th 2 k 2 , where ω and k are the angular frequency and the wavenumber of the plasma wave, v th is the thermal speed of electrons in the plasma, and ω p is the plasma frequency.…”