Generalized impedance boundary conditions are employed to simulate the effects of the parallel-stratified media on electromagnetic fields. Sommerfeld type integral contained in Hertz potential is expressed as the sum of two parts: zeroth order Hankel function and an absolutely convergent series expansion of spherical Hankel functions.

Gaussian beams constitute a very powerful tool to analyze radiation and scattering problems in high frequency regimes. The analysis of this kind of beams may be done by performing an analytical continuation of the real sources into the complex space. This is also a very powerful technique that arise, not only to this kind of solutions, but also to other solutions that may be very useful even for low frequency regimes. A complete parametrization of real propagation space in terms of the different type of complex beams solutions is presented in this paper. The analysis in the complex domain arises to different regions in the real space which may be anticipated and described through analytical transition regions. Some important conclusions may be derived from the results obtained, in particular the results related to the complex far field condition.