Method of lines solutions for the three-wave model of Brillouin equations

The purpose of this paper is to present the method of lines (MOL) solution of the stimulated Brillouin scattering (SBS) equations (a system of three first-order hyperbolic partial differential equations (PDEs)), describing the three-wave interaction resulting from a coupling between light and acoustic waves. The system has complex numbers and boundary values.

System of three first-order hyperbolic PDEs are first transformed and then spatially discretized. Superbee flux limiter is proposed to offset numerical damping and dispersion, brought on by the low order approximation of spatial derivatives in the PDEs. In order to increase computational efficiency, the structured structure of the PDE Jacobian matrix is identified and a sparse integration algorithm option of the ordinary differential equation (ODE) solvers is used. The flux limiter based on higher order approximations eliminates numerical oscillation. Examples are presented, and the performance of the Matlab ODE solvers is evaluated by comparison.

This type of solution provides a rapid means of investigating SBS as a tool in fiber optic sensing.

To the best of the authors' knowledge, MOL solution is proposed for the first time for the modeling of three-wave interaction in a SBS-based fiber optic sensor.