Full Text:   <1657>

Summary:  <1396>

CLC number: O42

On-line Access: 2015-08-04

Received: 2014-11-27

Revision Accepted: 2015-04-18

Crosschecked: 2015-07-08

Cited: 0

Clicked: 4712

Citations:  Bibtex RefMan EndNote GB/T7714

 ORCID:

Jian-xin Zhu

http://orcid.org/0000-0002-1788-8689

-   Go to

Article info.
Open peer comments

Frontiers of Information Technology & Electronic Engineering  2015 Vol.16 No.8 P.646-653

http://doi.org/10.1631/FITEE.1400406


New computational treatment of optical wave propagation in lossy waveguides


Author(s):  Jian-xin Zhu, Guan-jie Wang

Affiliation(s):  Department of Mathematics, Zhejiang University, Hangzhou 310027, China

Corresponding email(s):   zjx@zju.edu.cn

Key Words:  Adjoint operator, Orthogonal, Chebyshev, Pseudospectral method, Dirichlet-to-Neumann map


Jian-xin Zhu, Guan-jie Wang. New computational treatment of optical wave propagation in lossy waveguides[J]. Frontiers of Information Technology & Electronic Engineering, 2015, 16(8): 646-653.

@article{title="New computational treatment of optical wave propagation in lossy waveguides",
author="Jian-xin Zhu, Guan-jie Wang",
journal="Frontiers of Information Technology & Electronic Engineering",
volume="16",
number="8",
pages="646-653",
year="2015",
publisher="Zhejiang University Press & Springer",
doi="10.1631/FITEE.1400406"
}

%0 Journal Article
%T New computational treatment of optical wave propagation in lossy waveguides
%A Jian-xin Zhu
%A Guan-jie Wang
%J Frontiers of Information Technology & Electronic Engineering
%V 16
%N 8
%P 646-653
%@ 2095-9184
%D 2015
%I Zhejiang University Press & Springer
%DOI 10.1631/FITEE.1400406

TY - JOUR
T1 - New computational treatment of optical wave propagation in lossy waveguides
A1 - Jian-xin Zhu
A1 - Guan-jie Wang
J0 - Frontiers of Information Technology & Electronic Engineering
VL - 16
IS - 8
SP - 646
EP - 653
%@ 2095-9184
Y1 - 2015
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/FITEE.1400406


Abstract: 
In this paper, the optical wave propagation in lossy waveguides is described by the Helmholtz equation with the complex refractive-index, and the chebyshev pseudospectral method is used to discretize the transverse operator of the equation. Meanwhile, an operator marching method, a one-way re-formulation based on the Dirichlet-to-Neumann (DtN) map, is improved to solve the equation. Numerical examples show that our treatment is more efficient.

This submission is an expanded paper of author's prior work, and its main content is the research of optical wave propagation in lossy waveguides by solving a 2D Helmholtz equation with the Chebyshev pseudospectral method. The structure of this paper is great, and its derivations are rigorous. The final numerical results show that the proposed method is valuable to improve the precision.

有损耗波导中光传播的新计算处理

目的:通过改进算子步进方法,实现快速、高精度计算光在有损耗波导中传播性态,有效指导光波导的优化设计。
创新点:提出用共轭微分矩阵在算子步进方法中进行局部基转换,避免了求逆运算。所提处理方法提高了步进计算的稳定性,改善了传播计算精度。
方法:针对光波在有损耗波导中传播的数学模型-带有复折射率的Helmholtz方程,对基于DtN(Dirichlet-to-Neumann)映射(把边值问题化为初值问题)的单侧重构算子步进求解方法进行改进。一方面用切比雪夫伪谱方法离散方程的横向算子,另一方面为避免求逆,采用共轭微分矩阵在算子步进方法中实施局部基转换;最后,用改进所得的算子步进求解方法计算波在有损耗波导中的传播性态。
结论:对带有复折射率的Helmholtz方程的边值问题求解,提出了改进算子步进求解方法。实施该方法能快速、高精度地求解此问题,并得到光波在有损耗波导中传播真实性态,进而有助于光电器件的优化设计。

关键词:伴随算子;正交;切比雪夫;伪谱方法;共轭微分矩阵;Dirichlet-to-Neumann映射

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

[1]Andrew, A.L., 2000. Twenty years of asymptotic correction for eigenvalue computation. ANZIAM J., 42:96-116.

[2]Boyd, J.P., 2001. Chebyshev and Fourier Spectral Methods (2nd Ed.). Dover Publications, Inc., USA.

[3]Canuto, C., Hussaini, M.Y., Quarteroni, A., et al., 1988. Spectral Methods in Fluid Dynamics. Springer-Verlag Berlin Heidelberg, USA.

[4]Costa, B., Don, W.S., Simas, A., 2007. Spatial resolution properties of mapped spectral Chebyshev methods. Proc. SCPDE: Recent Progress in Scientific Computing, p.179-188.

[5]Lu, Y.Y., 1999. One-way large range step methods for Helmholtz waveguides. J. Comput. Phys., 152(1):231-250.

[6]Lu, Y.Y., McLaughlin, J.R., 1996. The Riccati method for the Helmholtz equation. J. Acoust. Soc. Am., 100(3):1432-1446.

[7]Lu, Y.Y., Zhu, J.X., 2004. A local orthogonal transform for acoustic waveguides with an internal interface. J. Comput. Acoust., 12(1):37-53.

[8]März, R., 1995. Integrated Optics: Design and Modeling. Artech House, USA.

[9]Silva, A., Monticone, F., Castaldi, G., et al., 2014. Performing mathematical operations with metamaterials. Science, 343(6167):160-163.

[10]Trefethen, L.N., 2000. Spectral Methods in MATLAB. Society for Industrial and Applied Mathematics, USA.

[11]Trefethen, L.N., 2013. Approximation Theory and Approximation Practice. Society for Industrial and Applied Mathematics, USA.

[12]Vassallo, C., 1991. Optical Waveguide Concepts. Elsevier, Amsterdam.

[13]Waldvogel, J., 2006. Fast construction of the Fejér and Clenshaw-Curtis quadrature rules. BIT Numer. Math., 46(1):195-202.

[14]Zhang, X., 2010. Mapped barycentric Chebyshev differentiation matrix method for the solution of regular Sturm-Liouville problems. Appl. Math. Comput., 217(5): 2266-2276.

[15]Zhu, J., Lu, Y.Y., 2004. Validity of one-way models in the weak range dependence limit. J. Comput. Acoust., 12(1):55-66.

[16]Zhu, J., Song, R., 2009. Fast and stable computation of optical propagation in micro-waveguides with loss. Microelectron. Reliab., 49(12):1529-1536.

Open peer comments: Debate/Discuss/Question/Opinion

<1>

Please provide your name, email address and a comment





Journal of Zhejiang University-SCIENCE, 38 Zheda Road, Hangzhou 310027, China
Tel: +86-571-87952783; E-mail: cjzhang@zju.edu.cn
Copyright © 2000 - 2022 Journal of Zhejiang University-SCIENCE