Finite element full-vectorial bidirectional beam propagation method for efficient design of cascaded optical waveguide components

A full-vectorial bidirectional beam propagation method (FV-BiBPM) for the numerical analysis of stair-case optical waveguide components is developed. In this method, a transversal cross section of an optical waveguide is discretized by the finite element method (FEM) based on edge-node hybrid elements and wave propagation in the longitudinal direction is computed by propagation operators. Since an optical waveguide is typically an open system, a perfectly matched layer is employed to treat radiation modes. We show that FV-BiBPM based on the FE scheme (FEFV-BiBPM) can successfully compute wave propagation, including radiation waves, through a numerical analysis of a waveguide gap. As a further numerical validation and an application of the FEFV-BiBPM, a waveguide grating and a coupler between a strip waveguide and a sub-wavelength grating waveguide are analyzed and investigated. The numerical results of the FEFV-BiBPM are in good agreement with well-established 3DFEM using tetrahedra edge elements and show that our method can save computational cost, especially for memory usage, in the design of stair-case optical waveguide components.