The expansion wave concept - Part I: Efficient calculation of spatial Green's functions in a stratified dielectric medium

A procedure is given to perform the inverse Fourier transformation relating a spatial Green's function to its spectral equivalent. The procedure is applied to the spectral Green's functions of the double scalar mixed-potential integral expression formulation of the electromagnetic field in a stratified dielectric medium, The extraction technique is used to annihilate every type of "problematic" behavior of the spectral Green's functions. Every annihilating function is inverse Fourier transformed analytically. It is shown that the annihilation of both the surface wave poles and the singularities at the branch point results in a set of analytical spatial functions, which are a very good approximation of the exact spatial Green's function down to relatively small lateral distances. Some very important characteristics of these functions will play a crucial role in Part II of the paper, where a new technique is introduced to model mutual coupling.