New computational treatment of optical wave propagation in lossy waveguides

ZHU Jian-xin; WANG Guan-jie

doi:10.1631/FITEE.1400406

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New computational treatment of optical wave propagation in lossy waveguides

Computational Mathematics | Updated：2022-06-14

- New computational treatment of optical wave propagation in lossy waveguides
- 有损耗波导中光传播的新计算处理
- Frontiers of Information Technology & Electronic Engineering Vol. 16, Issue 8, Pages: 646-653(2015)
- Affiliations：
  
  Department of Mathematics, Zhejiang University, Hangzhou 310027, China
- Author bio：
  
  [ "Jian-xin ZHU, E-mail: zjx@zju.edu.cn" ]
- Funds：
- DOI：10.1631/FITEE.1400406
  CLC： O42
- Received：27 November 2014，
  
  Revised：2015-07-08，
  
  Published：2015-08
- Accepted：
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ZHU Jian-xin, WANG Guan-jie. New computational treatment of optical wave propagation in lossy waveguides[J]. Frontiers of Information Technology & Electronic Engineering, 2015, 16(8): 646-653.
DOI：

ZHU Jian-xin, WANG Guan-jie. New computational treatment of optical wave propagation in lossy waveguides[J]. Frontiers of Information Technology & Electronic Engineering, 2015, 16(8): 646-653. DOI： 10.1631/FITEE.1400406.

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。

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.

关键词

Keywords

references

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