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本文基于加权余量法,阐述了利用边界元法求解矢量亥姆霍兹方程的数学基础-亥姆霍兹方程的边界积分方程;并推导了数值求解该边界积分方程的方法;利用推导结果,编写计算机程序分析了圆光波导的模式场分布情况。实验结果表明,该方法可以在较低方程组阶数,较少输入数据量的前提下准确地分析微结构光波导内模式场的分布情况。
In this paper, based on the weighted residual method, the boundary element method is introduced to solve the mathematical basis of the Helmholtz equation - the boundary integral equation of the Helmholtz equation. The numerical solution of the boundary integral equation is deduced. Computer program was written to analyze the mode field distribution of circular waveguide. The experimental results show that this method can accurately analyze the distribution of the mode field in the microstructured optical waveguide with a lower number of equations and less input data.