(untitled) (Communications in Computational Physics, 2020)
In this work, the full vectorial beam propagation methods (BPMs) are adopted for the calculations of the electromagnetic wave propagation from the two dimensional and three dimensional optical waveguide structures. First, the full vectorial BPM for the three dimensional optical waveguide structures is introduced. Next, in the transverse directions of the considered waveguide structures, we adopt the second order finite difference method to discretize the electromagnetic components. Then, the Lanczos/Arnoldi fast solvers are adopted to find the leading eigenvalues and eigenvectors of the square root operator in the BPM process of the optical waveguide structures. Furthermore, we propose the rational [(p−1)/p] Padé approximation to approximate the exponential operator in the BPM process. To demonstrate the efficiency of the numerical solvers, the two dimensional symmetric and unsymmetric problems are considered, and good convergence results are obtained. Furthermore, the resulting full-vectorial BPM is adopted to simulate the wave propagation among the three dimensional rib and taper waveguide structures. Numerical results demonstrate the efficiency of the proposed method with respect to both the accuracies and convergence results.