Modelling of optical breakdown in dielectrics including thermal effects relevant for nanosecond pulses and sequences of ultra-short laser pulses

The authors complemented the rate equation for the free-electron density rho by a term describing thermal ionization. Heating through collision losses and recombination of the free electrons produced by nonlinear absorption, and its counteraction by heat diffusion out of the focal volume are considered. For sufficiently high temperatures, the electron energy distribution reaches across the band gap into the conduction band, and we treat electrons with E > E_gap as thermally ionized. The model performance on the example of breakdown in water is shown by an 8.8-ns, 532 nm pulse, with rho_cr = 0.5 x 10²¹ cm^-3, and tau_c = 1.5 fs. Consideration of thermal ionization and calculation of the breakdown-induced temperature evolution creates a link between the energy deposition by nonlinear absorption and the resulting hydrodynamic phenomena that will greatly improve the understanding of plasma-mediated ablation.