Combined CGF-PML and CGF-RFFM for efficient and uniform modal derivation of Green´s function of planar layered media

A closed-form series representation for spatial Green´s function of planar layered media for all distances from source, is presented. By terminating the structure by perfectly matched layer (PML) backed by perfect electric conductor (PEC), the discrete set of surface wave (SW) poles is complemented by eigenmodes of the closed structure by PML poles which construct the continuous spectrum contribution of the original structure. Then applying the characteristic Green´s function (CGF) technique, a closed-form representation of spatial Green´s function is derived. Very close to the source, where the large number of modes must be considered, the method is become inefficient. In very near field regions, by combining CGF technique and rational function fitting method (RFFM), Green´s function would be efficiently constructed with few number of poles extracted in modified VECTFIT algorithm in similar form of CGF-PML result. In this way, an efficient modal series representation is derived by using CGF-PML and CGF-RFFM for far from and close to the source respectively. The main advantage of this representation is that for desired accuracy the number of required modes is controllable. Excellent agreements with direct numerical integration of the spectral integral are shown in several examples.