Predicting the spatial output field of a laser beam in a thermally self-induced inhomogeneous medium.

摘要

Laser beam propagation in a thermally self-induced inhomogeneous medium is investigated to find the transient spatial output field for an arbitrary incident field. The paraxial wave equation is coupled with the heat diffusion equation to predict the beam output field as the index of refraction transiently changes due to absorption of light by the medium. The coupled equations are nondimensionalized and are explicitly expressed in full nonlinear form. Limits for the validity of using the coupled wave-diffusion approach are given, with respect to bulk fluid motion and the transverse wave assumption. An explicit, finite-difference method (FDM) for solving the heat diffusion equation is coupled with an implicit FDM solution of the paraxial wave equation. The reasons for choosing these schemes are presented, along with a mixed-mode parallelization method in which OpenMP is used for the explicit solver, and MPI for the implicit solver. Convergence, stability, and code performance is presented. Numerical results are then compared to exact solutions and experiments for Gaussian and multi-mode laser beams, which verify that this approach is accurate in the range of validity, and describes local, transient self-focusing in multi-mode beams. This model is then further developed to show the importance of considering the nonlinear laser-material interaction when describing laser-assisted chemical etching (LACE). The exponential relationship between LACE rates and surface temperature means that very small changes in laser beam intensity field, and thus surface temperature distribution, has a very large effect on the etch profile. Numerical calculations of LACE microfabrication of borosilicate glass in a sulfur hexafluoride process gas with a 10.6 micron wavelength laser beam are given. These results show how the surface morphology of the glass wafer is changed by the inhomogeneous laser beam interaction with the process gas.