Computation of Nonlinear Backscattering Using a High-Order Numerical Method

The nonlinear Schrödinger equation (NLS) is the standard model for propagation of intense laser beams in Kerr media. The NLS is derived from the nonlinear Helmholtz equation (NLH) by employing the paraxial approximation and neglecting the backscattered waves. In this study we use a fourth-order finite-difference method supplemented by special two-way artificial boundary conditions (ABCs) to solve the NLH as a true boundary value problem. Our numerical methodology allows for a direct comparison of the NLH and NLS models and, apparently for the first time, for an accurate quantitative assessment of the backscattered signal.