ANALYTICAL PARAMETRIZATION OF A 2D REAL PROPAGATION SPACE IN TERMS OFCOMPLEX ELECTROMAGNETIC BEAMS

Gaussian beams constitute a very powerful tool to analyze radiation an d 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 a real propagation space in terms of t he different type of complex beams solutions is presented in this pape r. The analysis in the complex domain arises to different regions in t he real space which may be anticipated and described through analytica l transition regions. Some important conclusions may be derived from t he results obtained, in particular the results related to the complex far field condition.