TY - JOUR
T1 - An Efficient Method for Estimating the Electromagnetic Wave Propagation in Three Dimensional Optical Waveguide Structures
AU - Mao Wu , Yu
AU - Lou , Xin
AU - Jin , Ya-Qiu
AU - Hou , Zhaoguo
AU - Xiao , Lizhi
AU - Zou , Ning
AU - Jing Zhou , Hai
AU - Liu , Yang
JO - Communications in Computational Physics
VL - 2
SP - 661
EP - 678
PY - 2020
DA - 2020/06
SN - 28
DO - http://doi.org/10.4208/cicp.OA-2018-0088
UR - https://global-sci.org/intro/article_detail/cicp/16944.html
KW - Wave propagation, fast solver, Lanczos method, perfectly matched layer.
AB - <p style="text-align: justify;">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.</p>