Spectral-domain solution to the electromagnetic scattering of a two-dimensional beam by cylinders buried below a flat interface

An analytical-numerical approach in the spectral domain is developed for the scattering problem by buried objects excited by a two-dimensional illumination field. The scatterers are perfectly conducting cylinders, which are placed in a semi-infinite medium below a flat interface. The source field is described by an arbitrary illumination function, and it is represented by means of its plane-wave spectrum. The cylindrical-wave approach is applied to represent the fields scattered by the cylinders. All the field contributions are expressed through spectral integrals, which allow to evaluate their interaction with the interface in terms of a superposition of monochromatic plane waves. Such integrals are evaluated in an accurate way, which can lead to results both in near-field and far-field regions. In this paper, the general theoretical approach is described, and numerical results are given for the case of an incident Gaussian beam. Two-dimensional field maps in both the air and lower regions are reported in the case of one and two scatterers. An application of the technique to the diagnostic of reinforced concrete is reported, showing the use of the radar scattering cross-section ratio to determine the size of rebar diameters. Modelling results validate the assumption proposed by other authors that the radar scattering cross-section ratio can be used to determine rebar diameters using the monotonic behaviour observed at lower frequencies.