Locating All the Modes of Green´s Function for a Three-Layered Medium Based on the Path Tracking Algorithm

Through a mathematical analysis on the relationship between the characteristic equations of the microstrip geometry and a configuration with a three-layered medium, a method based on the path tracking algorithm is proposed for precisely locating all the modes for a three-layered medium with moderate thickness, including surface wave modes, leaky wave modes and improper real modes. With this method, the difficulty caused by branch points and cuts in the contour integral method could be avoided. This method can be applied not only in the discrete complex image method (DCIM), but also in the steepest descent path (SDP) method. The proposed method can be extended to more complicated configurations.