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Volume 28, Issue 2
An Efficient Method for Estimating the Electromagnetic Wave Propagation in Three Dimensional Optical Waveguide Structures

Yu Mao Wu, Xin Lou, Ya-Qiu Jin, Zhaoguo Hou, Lizhi Xiao, Ning Zou, Hai Jing Zhou & Yang Liu

DOI: 10.4208/cicp.OA-2018-0088

Commun. Comput. Phys., 28 (2020), pp. 661-678.

Published online: 2020-06

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  • Abstract

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.

  • Keywords

Wave propagation, fast solver, Lanczos method, perfectly matched layer.

  • AMS Subject Headings

78M25, 78M16, 78A45

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-28-661, author = {Mao Wu , YuLou , XinJin , Ya-QiuHou , ZhaoguoXiao , LizhiZou , NingJing Zhou , Hai and Liu , Yang}, title = {An Efficient Method for Estimating the Electromagnetic Wave Propagation in Three Dimensional Optical Waveguide Structures}, journal = {Communications in Computational Physics}, year = {2020}, volume = {28}, number = {2}, pages = {661--678}, abstract = {

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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2018-0088}, url = {http://global-sci.org/intro/article_detail/cicp/16944.html} }
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 -

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.

Mao Wu , YuLou , XinJin , Ya-QiuHou , ZhaoguoXiao , LizhiZou , NingJing Zhou , Hai and Liu , Yang. (2020). An Efficient Method for Estimating the Electromagnetic Wave Propagation in Three Dimensional Optical Waveguide Structures. Communications in Computational Physics. 28 (2). 661-678. doi:10.4208/cicp.OA-2018-0088
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