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Frontiers of Information Technology & Electronic Engineering
ISSN 2095-9184 (print), ISSN 2095-9230 (online)
2015 Vol.16 No.8 P.646-653
New computational treatment of optical wave propagation in lossy waveguides
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
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。
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DOI:
10.1631/FITEE.1400406
CLC number:
O42
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On-line Access:
2015-08-04
Received:
2014-11-27
Revision Accepted:
2015-04-18
Crosschecked:
2015-07-08