A full vectorial generalized discontinuous Galerkin beam propagation method (GDG–BPM) for nonsmooth electromagnetic fields in waveguides

In this paper, we propose a new full vectorial generalized discontinuous Galerkin beam propagation method (GDG–BPM) to accurately handle the discontinuities in electromagnetic fields associated with wave propagations in inhomogeneous optical waveguides. The numerical method is a combination of the traditional beam propagation method (BPM) with a newly developed generalized discontinuous Galerkin (GDG) method [K. Fan, W. Cai, X. Ji, A generalized discontinuous Galerkin method (GDG) for Schrödinger equations with nonsmooth solutions, J. Comput. Phys. 227 (2008) 2387–2410]. The GDG method is based on a reformulation, using distributional variables to account for solution jumps across material interfaces, of Schrödinger equations resulting from paraxial approximations of vector Helmholtz equations. Four versions of the GDG–BPM are obtained for either the electric or magnetic field components. Modeling of wave propagations in various optical fibers using the full vectorial GDG–BPM is included. Numerical results validate the high order accuracy and the flexibility of the method for various types of interface jump conditions.