Fig. 2: Measured and computed probe absolute transmission T(t) through the interaction region (y = 0 µm) induced by the pump laser pulse on DLC foils, and the calculated plasma electron densities.

a–d Measured (blue) and calculated (red) \(T(t)\) for DLC foils of thicknesses from 5 to 50 nm. The measurements are averaged over four shots with peak intensities \({I}_{{\rm peak}}\sim {10}^{15}-{10}^{16}\,\rm{W/{{cm}}^{2}}\). The blue shaded region is the standard deviation over all shots for each foil. The red curve is computed using the TSI model with \({I}_{\rm{peak}}\sim {10}^{15}\,\rm{W/{{cm}}^{2}}\) and plotted as a function of \({t}_{\rm{pump}}\). The measured and calculated curves are aligned at their inflection points where the relative transmission is 50 %. The red arrows delimit the time intervals for SSI and PIC steps in the TSI model. e Computed time-dependent probe transmission for different interaction models for different DLC foil thicknesses (5 nm: black, 10 nm: red, 20 nm: blue and 50 nm: green): the dashed line, the triangles and the solid line correspond to PIC only, SSI only (up to \({n}_{e}\) ≈ \({20n}_{c}\)) and the TSI model, respectively. The blue and orange arrows correspond to the time intervals given by the shaded regions with the same colors in the laser temporal intensity profile in Fig. 1a. f Maximum electron densities \({n}_{e}^{\max }\) as a function of \({t}_{\rm{pump}}\) corresponding to the different simulations shown in (e). The density obtained from the SSI model does not depend on the foil thickness by construction and is therefore shown in violet. The shaded grey regions in (e) and (f) indicate where the extended SSI model (up to \({n}_{e}\) ≈ \({70n}_{c}\)) was used