IE-GSTC Metasurface Field Solver Using Surface Susceptibility Tensors With Normal Polarizabilities

An integral equation (IE)-based electromagnetic field solver using metasurface susceptibility tensors is proposed and validated using a variety of numerical examples in 2-D. The proposed method solves for fields generated by the metasurface, which is represented as spatial discontinuities satisfying the generalized sheet transition conditions (GSTCs), and described using tensorial surface susceptibility densities,
$\bar {\bar {\chi }}$
. For the first time, the complete tensorial representation of susceptibilities is incorporated in this integrated IE-GSTC framework, where the normal surface polarizabilities and their spatial derivatives along the metasurface are rigorously taken into account. The proposed field equation formulation further utilizes a local coordinate system, which enables modeling metasurfaces with arbitrary orientations and geometries. The proposed 2-D boundary element method BEM-GSTC framework is successfully tested using a variety of examples, including infinite and finite-sized metasurfaces, periodic metasurfaces, and complex shaped structures, showing comparisons with both analytical results and a commercial full-wave solver. It is shown that the zero-thickness sheet model with complete tensorial susceptibilities can very accurately reproduce the macroscopic fields, accounting for their angular field scattering response and the edge diffraction effects in finite-sized surfaces.