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FITEE
Front. Inform. Technol. Electron. Eng.  2015, Vol. 16 Issue (8): 646-653    DOI: 10.1631/FITEE.1400406
    
有损耗波导中光传播的新计算处理
Jian-xin Zhu, Guan-jie Wang
Department of Mathematics, Zhejiang University, Hangzhou 310027, China
New computational treatment of optical wave propagation in lossy waveguides
Jian-xin Zhu, Guan-jie Wang
Department of Mathematics, Zhejiang University, Hangzhou 310027, China
 全文: PDF 
摘要： 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    
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.
Key words: Adjoint operator    Orthogonal    Chebyshev    Pseudospectral method    Dirichlet-to-Neumann map
收稿日期: 2014-11-27 出版日期: 2015-08-04
CLC:  O42  
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Jian-xin Zhu, Guan-jie Wang. New computational treatment of optical wave propagation in lossy waveguides. Front. Inform. Technol. Electron. Eng., 2015, 16(8): 646-653.

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http://www.zjujournals.com/xueshu/fitee/CN/10.1631/FITEE.1400406    或    http://www.zjujournals.com/xueshu/fitee/CN/Y2015/V16/I8/646

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