Combination of beam propagation method and finite element method for optical beam propagation analysis

A combined method of the beam propagation method (BPM) and the finite element method (FEM) is proposed for the analysis of reflections of both transverse electric (TE) and transverse magnetic (TM) polarized waves in waveguiding structures containing longitudinal discontinuities. BPM based on FEM is applied to slowly varying regions, and FEM is applied only to regions including abrupt discontinuities. In order to avoid nonphysical reflections from computational window edges, the perfectly matched layer boundary condition is introduced. To show the validity and usefulness of the present approach, numerical examples for an optical directional coupler and a beam splitter are presented.