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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Dt N(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。
OBJECTIVE: By improving the operator step method, the propagation state of light in lossy waveguide can be calculated rapidly and accurately, which can effectively guide the optimization design of the optical waveguide. Innovative point: Proposed conjugate differential matrix in the operator step method for local basis conversion, to avoid the inversion operation. The proposed method improves the stability of step calculation and improves the accuracy of propagation calculation. Methods: Aiming at the Helmholtz equation with complex refractive index, which is a mathematical model propagating light wave in a lossy waveguide, the unilateral weighting based on Dt N (Dirichlet-to-Neumann) mapping Construction sub-step solution method to improve. On the one hand, the Chebyshev pseudospectral method is used to discretize the horizontal operator of the equation, and on the other hand, to avoid the inversion, the local base conversion is implemented in the operator step method by using the conjugate differential matrix. Finally, with the improved operator step The solution method is to calculate the propagating behavior of the wave in the lossy waveguide. Conclusion: The solution of the boundary value problem of Helmholtz equation with complex refractive index is solved, and the improved operator step solving method is proposed. The implementation of this method can solve this problem quickly and accurately, and get the true state of light wave propagating in the lossy waveguide, which is helpful for the optimization design of optoelectronic devices.