Fluid formulation of high intensity laser beam propagation using lagrangian coordinates

Abstract

The complete mathematical modeling of nonlinear light-matter interaction is presented in a hydrodynamic context. The field intensity and the phase gradient are the dependent variables of interest. The resulting governing equations are a generalization of the Navier-Stokes equations. This fluid formulation allows the insights and the methodologies which have been gained in solving hydrodynamics problems to be extended to nonlinear optics problems. To insure effective numerical treatment of the anticipated nonlinear self-lensing phenomena, a self-adjusted nonuniform redistribution, along the direction of propagation, of the computation points according to the actual local requirements of the physics must be used. As an alternative to the application of adaptive rezoning techniques in conjunction with Eulerian coordinates, Lagrangian variables are used to provide automatically the desired nonlinear mapping from the physical plane into the mathematical frame. In this paper we propose a method suitable for the solution of the described problemin one-dimensional cases as well as in two- dimensional cases with cylindrical symmetry. To overcome the numerical difficulties related to the inversion of the Jacobian, an analytical algorithm based on the paraxial approximation was developed.