An Efficient Method for Estimating the Electromagnetic Wave Propagation in Three Dimensional Optical Waveguide Structures (Communications in Computational Physics, 2020)
In this work, the full vectorial beam propagation methods (BPMs) areadopted for the calculations of the electromagnetic wave propagation from the twodimensional and three dimensional optical waveguide structures. First, the full vectorial BPM for the three dimensional optical waveguide structures is introduced. Next, inthe transverse directions of the considered waveguide structures, we adopt the secondorder finite difference method to discretize the electromagnetic components. Then, theLanczos/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 efficiencyof the numerical solvers, the two dimensional symmetric and unsymmetric problemsare considered, and good convergence results are obtained. Furthermore, the resulting full-vectorial BPM is adopted to simulate the wave propagation among the threedimensional rib and taper waveguide structures. Numerical results demonstrate theefficiency of the proposed method with respect to both the accuracies and convergenceresults.
Keywords: Wave propagation; fast solver; Lanczos method; perfectly matched layer.