An Accurate Derivation of Spatial Green's Function for Finite Dielectric Structures Using Characteristic Green's Function-Perfectly Matched Layer Method

A closed-form spatial Green's function for a truncated dielectric slab is derived by using a combination of the characteristic Green's function (CGF) and perfectly matched layer (PML) method. The original structure is terminated by PML that is backed by perfect electric conductor (PEC) in semi-infinite layer at the top and/or bottom. The eigenmodes of the closed structure by PML construct the continuous spectrum contribution of the original structure efficiently. Derived Green's function is exact for separable finite structure while it is approximate for nonseparable one especially in the corners. Generalized scattering matrix (GSM) of truncating surface which contains possible conversions between all modes is computed with mode-matching method. It is demonstrated that by importing GSM in CGF formulation, more exact results for nonseparable structures can be obtained. The source and observation points dependence is analytically available in derived expression and allows very efficient computation and storage of the spatial Green's function. Very close to the source, where the large number of modes must be considered, Shank's transform is used to preserve the efficiency of the method. The main advantage of the method lies in its accuracy and low dependency of the result to the PML parameters. Excellent agreements with the rigorous method of moments (MoM) are shown in several examples.