An Efficient Closed-Form Derivation of Spatial Green´s Function for Finite Dielectric Structures Using Characteristic Green´s Function-Rational Function Fitting Method

A uniform and closed-form spatial Green´s function for finite dielectric structures is derived by using a combination of the characteristic Green´s function (CGF) and rational function fitting method (RFFM). Employing the concept of quasi leaky waves, CGF-RFFM represents both of the discrete and continuous spectrum contributions efficiently by using the modified VECTFIT algorithm. The method is examined for 2-D truncated dielectric slab while it can be implemented for 3-D structure straightforwardly. An error of less than 0.2% is achieved compared with the direct numerical integration of the spectral integral. The derived Green´s function is exact for separable structures while it is approximate for nonseparable structures like truncated dielectric substrates where the corner regions are replaced with fictitious materials. To obtain more accurate results, mode conversions due to the surface waves (SWs) incident on the end-facet are considered by employing the scattering matrix in the formulation for structures supporting several guided modes. The main advantage of this method lies in its speed as well as accuracy. Excellent agreements with the rigorous method of moments (MoM) are shown in several examples.