Asymptotic Green's function for the full wave analysis of underground object

Recently, there has been significant interest in electromagnetic scattering models for the detection of underground targets. Several works have been carried out for the numerical treatment of such problems, based on the solution of Integral Equations (IE) formulated by using a surface or a volumetric formulation. In each case, the basic constituent of the Method of Moment solution of such IEs is the dyadic Green's function for a semi-infinite dielectric slab. It is well known that this Green's function is expressed in terms of Sommerfeld spectral integrals, which exhibit a slowly convergent behaviour. An efficient calculation of these integrals may reduce drastically the calculation time of the overall full-wave analysis. Note that, in several cases, the distance of the buried object from the ground-air interface is large enough to justify an asymptotic approximation. In the paper a uniform high-frequency solution will be proposed for the dyadic Green's function of a semi-infinite dielectric slab, which is particularly well suited for a full-wave analysis formulated by a hybrid technique. The asymptotic treatment of the pertinent Sommerfeld integrals is based on splitting the original integration on steepest descent paths and an integration around a branch cut. Then, using proper decompositions of the integrands, an asymptotic solution is carried out, uniformly valid for any observation points. The final results is expressed in terms of cylinder parabolic functions.