Role of Kerr-type self-focusing in femtosecond laser ablation of thin films irradiated through dielectric substrates.

The Liu method extracts laser-induced damage thresholds from the dependence of the damage area on the peak fluence of an incident Gaussian beam. Here, we develop a nonlinear Liu-plot description for femtosecond laser ablation of absorbing thin films irradiated through nonlinear Kerr-type dielectric substrates. We derive an analytical expression for the effective Gaussian fluence distribution incident at the film/substrate interface. This approach retains the construction of the Liu plot while allowing the size of the ablation crater to evolve in a nontrivial way with pulse fluence. The model predicts zero-gradient fluence regions, where the ablation-crater size becomes locally insensitive to pulse-energy fluctuations, suggesting a possible route toward more precise ultrashort-pulse thin-film nanofabrication.