Dispersion and stability analysis for a finite difference beam propagation method

Abstract

Applying continuous and discrete transformation techniques, new analytical expressions to calculate dispersion and stability of a Runge- Kutta Finite Difference Beam Propagation Method (RK-FDBPM) are obtained. These expressions give immediate insight about the discretization errors introduced by the numerical method in the plane-wave spectrum domain. From these expressions a novel strategy to adequately set the mesh steps sizes of the RK-FDBPM is presented. Assessment of the method is performed by studying the propagation in several linear and nonlinear photonic devices for different spatial discretizations.