含有多个阶梯结构的波导的精确分析

用模式匹配方法分析H面阶梯波导，将每个区域的切向场表示为几个矩阵相乘的形式，即一个关于x的函数矩阵F（x）与一个关于z的函数矩阵H（z）以及一个由本区域的场幅系数构成的列向量的乘积。在边界条件的处理上，通过对F（x）矩阵进行加权积分得到线性方程组。以上表达方式的优点是：（1）易于构造线性方程组；（2）易于选取不同的权函数；（3）易于编程应用到多个阶梯级联的情形。在计算场幅系数时，仅涉及一次矩阵求逆运算，未出现相对收敛现象。数值例子验证方法的正确性和灵活性。

An Accurate Analysis of Waveguide with Steps in Cascade

The mode-matching technique(MMT) is applied to analyze H-plane step waveguides.The tangential fields in each region are expressed in terms of the product of several matrices,i.e.,a functional matrix about x-F(x),a functional matrix about z-H(z) and a column vector of amplitudes of the individual region.To transform the boundary conditions into a set of linear equations,we take the inner products of F(x) with weight functions.The formulation given in the above has several advantages.First,it becomes much easier to get the linear equation from boundary conditions by simple matrix operation.Second,the formulation provides more flexibility in selecting different sets of weight functions by replacing the corresponding matrix elements.Third,the general formulation can be applied to analyze a class of waveguides multiple steps in cascade.The relative phenomenon is avoided for only one matrix inversion involved.Numerical results are given to validate the formulation.