Studying femtosecond laser ablation of wide band gap insulators, with BaF2 as a representative, we observe a complex structure of fine ripples at the bottom of the ablated crater, which are oriented perpendicular to the beam polarization. A second, wider periodic structure oriented parallel to the beam polarization appears superimposed on the first one. To check the idea of an interference pattern translating into ripples, a controlled interference was created in the target in a non-collinear two-beam experiment. However, no signature of it was observed in the ablated spot. This calls the classical interpretation for ripples formation into question. More likely, we assume that the ripples structures are due to self-organization structure formation during the relaxation of the highly non-equilibrium surface after explosive positive ion emission. (C) 2002 Elsevier Science B.V. All rights reserved.