An accurate and systematic surface-wave pole location method for multilayered media

Finding the surface-wave modes in multilayered media is a problem that is of great importance in many full-wave numerical electromagnetic solvers. In this communication, an efficient and systematic method is proposed to locate all of the surface-wave poles for general multilayered structures. It is observed that the characteristic equations can be cast into a function composed of ε_ri, k_z,i and T_i = tan(k _z,id_i), where the T_i occur for the substrates that have finite thicknesses. The pole location method is carried out in the complex k_zM -plane, where k_zM represents the wave number, along the z-axis, for the substrate with the maximum permittivity. Two sets of critical points are determined in the k_zM-plane according to the parameters of the structure. Since there is at most one pole between two consecutive critical points, these critical points establish proper limits for the zero search algorithm. Muller's method can thus be applied to find the pole between the two consecutive critical points if it exists. The proposed method is validated by means of several numerical examples.