Paterson et al.  have presented a numerical model for the ablation of microstructure by excimer laser, based on pulse-by-pulse propagation of the etched surface. The model assumes that a definite ablation threshold exists for the materials and the material removal rate depends only on the laser Tiopronin
flux entering the surface. The side-wall profile of laser machined structure can also be quantitatively predicated by this model. Fan and Longtin  developed a time and position resolved moving breakdown model to accurately predict the nature of laser material interaction responsible for optical breakdown. The model includes the pulse propagation in the focal volume. It was observed that the ns laser ablation is time dependent only whereas in case of fs laser the optical breakdown depends on both the time and position. Zhang et al.  have developed a
numerical model to simulate the micro-scale cavity formation of copper under high intensity pulsed laser radiation. The model uses an enthalpy method to track the solid/liquid interface. It evaluates the heat transfer and associated phase changes inside the target materials by considering the Stefan and kinetic boundary condition at the liquid-vapor interface and property of discontinuity across the Knudsen layer.
Schafer and Urbassek  investigated the ps laser ablation of metals using a hybrid simulation scheme in which the molecular dynamics has been integrated with heat conduction equation to obtain the electron temperature. The finite difference method was used to incorporate the laser energy input into the electron system and the fast electron diffusion taking place inside it. The atomic motion near the surface of sample has been modeled using molecular dynamics. Willis et al.  have developed numerical model to find the transient heat transfer and phase change during ps laser ablation of nickel. In the model reflection of the laser beam, volumetric absorption
of the laser energy, melting and vaporization kinetics were considered to predict the depth of melting and amount of mass lost at the free surface due the evaporation. Finite difference scheme with an implicit time integration technique has been used. Based on the results obtained from drilling of high aspect ratio hole on different types of polymers using KrF excimer laser, an analytical theoretical model was developed by Tokarev et al. . They assumed that absorption of the incident beam takes place only on the side wall, no plume heating of the side walls occurs and attenuation of incident laser beam do not take place. The model predict that the aspect ratio can be increased by using pulses of shorter wavelength, irradiation in vacuum, increasing the absorption coefficient, introducing strongly absorbing dopant into the material and by using the irradiation in a chemically reactive atmosphere.