Rapid calculation of the energy deposition profiles for processing of dielectrics with femtosecond lasers

The energy deposition profile of a focused beam inside a dielectric material is conditioned by linear and nonlinear propagation effects. This can substantially distort the desired shape of the transformed region in laser processing applications. By solving the nonlinear Schrodinger equation (NLSE) using the split-step propagation technique or similar calculation procedures it is possible to perform accurate estimations of the energy deposition profile. However, this is usually not practical in terms of a balance between computation time and accuracy. Thus, an experimental study considering various parameters (pulse energy, duration, processing depth, beam ellipticity, etc.) is the typical approach to determine a set of optimized "laser writing" parameters that yield the best result.