An Excitation of Anisotropic Homogeneous Impedance Elliptic Metasurface by Electric or Magnetic Current Filaments

The solution of the general excitation problem of an anisotropic elliptic metasurface (MS) with a surface homogenized impedance tensor of general form is considered using the method of eigenfunctions. The field sources are external 3D currents or 2D filaments of electric or magnetic current. Exact analytical formulas are obtained for the partial scattering coefficients of a homogeneous MS with an impedance tensor from the class of deviators. Some general properties of the partial scattering coefficients of such an impedance elliptic MS and similar (in shape) PEC and PMC cylinders and an elliptic cylinder with perfect electromagnetic conductivity are analyzed. It is shown that the scattering coefficients of the impedance MS are explicitly written in terms of the scattering coefficients of a similar PEC (or PMC) cylinder. The parameters of the impedance tensor of an elliptic MS equivalent to a similar black Macdonald cylinder are given. The equivalence is observed for co-polarizations for any shape of the compared cylinders, for any observation angles and any filament arrangement.