中文摘要：

为了搜索三层媒质二维谱域Green函数中的全部模式极点,提出了一种路径追踪算法.该算法首先利用数学变换,将三层媒质二维谱域Green函数的特征方程替换为复平面上的4个超越方程;然后,应用路径追踪法和Newton-Raphson迭代法求解各超越方程的根,得到谱域Green函数的全部模式极点,即表面波极点、漏波极点和反常极点.该算法克服了围线积分法中积分路径穿过分支割线进入不同Riemann面时容易造成失根的缺点,可应用于离散复镜像方法和最陡下降路径积分法中,以实现三层媒质二维空域Green函数近场和远场的精确、快速计算.最后,利用数值算例验证了该算法的正确性和有效性.

英文摘要：

To locate all the mode poles of the 2D spectral Green＇s function for three-layered medium,a path tracking algorithm is proposed.In the algorithm,the characteristic equations of the 2D spectral Green＇s function are first substituted with four transcendental equations in the complex plane by mathematical transformation.Then,the path tracking method and the Newton-Raphson iteration are used to solve the roots of the transcendental equations.And all the mode poles of the spectral Green＇s function,including surface wave poles,leaky wave poles and improper wave poles,are obtained.This algorithm can overcome the shortcomings of the contour integral method that roots are always lost when the integral paths enter different Riemann sheets through branch cuts.It can be applied to the discrete complex image method and the steepest descent path method to calculate the near field and the far field of the 2D spatial Green＇s function quickly and accurately.The numerical experiment results show that the proposed algorithm is accurate and efficient.