The expansion wave concept. 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