Three-dimensional higher-order pade approximant-based wide-angle beam propagation method using complex jacobi iteration

Wide-angle scalar beam propagation methods (BPMs) for effective modelling of optical propagation in three-dimensional (3D) waveguides are usually limited to the low-order-accurate Pade(1, 1) approximant. Presented is a 3D wide-angle scalar BPM based on higher-order Pade?? approximant operators which is factored into a series of simpler first-order Pade(1, 1) approximants. This results in a multistep method where each step can be cast in terms of a 2D Helmholtz equation with source term, which can be treated accurately and effectively by the new complex Jacobi iterative technique.