中文摘要：

提出了一种求解波导阵列耦合特性的方法．采用拉普拉斯变换，将同时考虑相邻和次相邻波导耦合作用的波导阵列耦合模方程组变为一个线性方程组，利用矩阵的LU分解法（将系数矩阵分解为单位下三角阵L与上三角阵U的乘积）求出该线性方程组的解．然后根据给定的初始条件进行拉普拉斯变换反演，求出耦合模方程组的解．采用该方法研究了五波导阵列，光从中间一个波导入射和从五个波导入射时的耦合特性，给出了每个波导中光功率变化规律曲线，并将所得结果与同样条件下仅考虑相邻波导耦合的结果做了比较．采用该方法可以求出任意数目波导组成的阵列，考虑任意波导之间耦合的耦合模方程组的解．

英文摘要：

A method for solving coupling characteristics of a multi-waveguides array is proposed. The coupled- mode equations of a multi-waveguides array are transformed into a group of linearity equations by using Laplace transform and then solution of the linearity equations is obtained using the LU decomposition method. With incidence condition, solution of the coupled-mode equations can be obtained by inversion of the Laplace transform. Furthermore, coupling characteristics of a five-waveguides array are studied under two conditions that light beam incidence upon both the middle waveguide and five waveguides, respectively. Then variation characteristics of optical power in each waveguide are given. This method can be used to solve coupled-mode equations of a multi-waveguides array with considering coupling among any waveguides.