Impedance boundary conditions for finite planar or curved frequency selective surfaces embedded in dielectric layers

We consider the time-harmonic electromagnetic scattering problem from a finite planar or curved structure made up of infinitesimally thin frequency-selective surfaces (FSSs) embedded in dielectric layers, with possibly nearby located objects. In order to avoid the meshing of the unit cells that constitute the FSSs, this problem is solved by employing an integral equation (IE) or finite-element (FE) formulation in conjunction with approximate impedance boundary conditions (IBCs) prescribed on the sheets that model the FSSs. The impedances in the IBCs are derived from the exact reflection and transmission coefficients calculated for the fundamental Floquet mode on the infinite planar structure illuminated by a planewave at a given incidence. When the structure is curved and/or the direction of the incident wave is unknown, higher order IBCs are proposed that are valid in a large angular range and can be implemented in a standard IE or FE formulation. Their numerical efficiencies are evaluated for finite planar or curved two-dimensional structures, or radomes, where the FSSs are strip gratings. As an example, for a curved radome surrounding a conducting plate, it is shown that, when the Floquet modes of the gratings are evanescent, these IBCs allow an accurate calculation of the radar cross section of the whole structure with far smaller computing resources than would have been required by a full-wave formulation.