Ultra-Short Pulses Laser Heating of Dielectrics: A Semi-Classical Analytical Model

Femtosecond laser pulses are currently regarded as an emerging and promising tool for processing wide bandgap dielectric materials across a variety of high-end applications, although the associated physical phenomena are not yet fully understood. To address these challenges, we propose an original, fully analytical model combined with Two Temperatures Model (TTM) formalism. The model is applied to describe the interaction of fs laser pulses with a typical dielectric target (e.g., Sapphire). It describes the heating of dielectrics, such as Sapphire, under irradiation by fs laser pulses in the range of (10¹²-10¹⁴) W/cm². The proposed formalism was implemented to calculate the free electron density, while numerical simulations of temperature field evolution within the dielectrics were conducted using the TTM. Mathematical models have rarely been used to solve the TTM in the context of laser-dielectric interactions. Unlike the TTM applied to metals, which requires solving two heat equations, for dielectrics the free electron density must first be determined. We propose an analytical model to solve the TTM equations using this parameter. A new simulation model was developed, combining the equations for non-equilibrium electron density determination with the TTM equations. Our analyses revealed the non-linear nature of the physical phenomena involved and the inapplicability of the Beer-Lambert law for fs laser pulse interactions with dielectric targets at incident laser fluences ranging from 6 to 20 J/cm².