An explicit algorithm for a fluid approach to nonlinear optics propagation using splitting and rezoning techniques

Abstract

The paper presents a three-dimensional analysis of the nonlinear light matter interaction in a hydrodynamic context. It is reported that the resulting equations are a generalization of the Navier-Stokes equations subjected to an internal potential which depends solely upon the fluid density. In addition, three numerical approaches are presented to solve the governing equations using an extension of McCormack predict-corrector scheme. These are a uniform grid, a dynamic rezoned grid, and a splitting technique. It is concluded that the use of adaptive mapping and splitting techniques with McCormack two-level predictor-corrector scheme results in an efficient and reliable code whose storage requirements are modest compared with other second order methods of equal accuracy.