Green’s functions of planar layered media are formulated in this paper in the spatial domain. Discrete Complex Image Method (DCIM) is used to transform the spectral Green’s functions from the spectral domain back to the spatial domain. Two-level sampling algorithm is adopted which eliminates the need for the analytical treatment of the asymptotes of the spectral Green’s functions at high spectral values. The formulation is written to be consistent with the quadruple-dyadic spectral Green’s functions recently presented by the authors. These four dyads describe all possible kinds of reactions between currents and fields. The infinitesimal dipole current source can be electric or magnetic oriented either tangential or perpendicular to the layers. All electric and magnetic field components due to these general current sources are obtained. The 34 non-zero elements in these dyads are expressed in terms of 18 spectral Green’s functions and 6 spectral coefficients. The presented formulation in this paper allows obtaining the corresponding 18 spatial Green’s functions in a straight forward way. This analysis integrated with the preceding spectral analysis leads to quadruple-dyadic spatial Green’s functions which may appear in the kernel of any integral equations formulation whatsoever. The implemented two-level DCIM is validated by comparison with published results. Very good agreement is obtained. Then, it has been used to calculate the spatial Green’s functions of the basic plasmonic layer structures, which are Insulator/Metal (IM), Insulator/Metal/Insulator (IMI), and Metal/Insulator/Metal (MIM).
Soliman et al. (Thu,) studied this question.