**2. Multiphysics simulation of laser processing**

## **2.1. Introduction**

In general, for a solid, the laser ablation process strongly depends on the absorption of photons by the material. Hence, it relies on the laser wavelength, its pulse duration, its fluence (energy density per surface area), and also on the material properties. The photon energy is absorbed and converted into kinetic energy by vibration of the electron cloud. This energy is then transmitted to the volume by phonon-electron coupling [7, 8]. Above picosecond pulse duration, a laser beam can be treated as a heat source. Hence, whether it is drilling, cutting, welding…, a laser process can be seen as a thermodynamic problem and the classical heat transfer equation (Eq. (4)) can be used to determine the spatial and temporal distribution of the temperature in the workpiece. Then for advanced studies, the Navier-Stokes equations can be implemented when phase transition is involved (Eq. (2)). The final thermo-mechanical state of the substrate or the plasma generation during laser ablation and its effect on the efficiency of the laser process can be investigated as well.

To be precise, there should be one equation describing the temperature evolution for the electron network and another one for the ions lattice (Section 2.3.1). Indeed, the characteristic time of energy transfer between electrons and ions is between 0.1 a few ps. For pulse duration longer than 500 fs, electrons and ions are both heated during the laser pulse. Hence, one equation is sufficient. Below 500 fs, the lattice is poorly affected because it is decoupled with the electrons and two equations are required [9]. However, as seen in the literature, one temperature model could be used to describe glass welding [10] or the formation of wave‐ guides with femtosecond laser when high frequency is used (hundreds of kHz to MHz range) [11]. After a short review of the use of multiphysics simulation, the heat transfer model will be detailed and will lead to the investigation of picosecond laser induced periodic surface structuring (LIPSS) on copper film.
