An equivalent boundary-condition model for lossy planar periodic structures at low frequencies

An equivalent boundary-condition model is presented for planar periodic scatterers which, through an effective homogenization, accurately predicts the scattering at low frequencies (i.e., in the absence of higher ordered Floquet harmonics or grating lobes). This new anisotropic resistive boundary-condition model provides accurate wide-angle results for one- (1-D) and two-dimensional (2-D) periodic arrays, provided certain restrictions are satisfied concerning the rotational symmetry and surface resistivity of the target. When applicable, this simulation model provides an enormous reduction in computational costs with virtually no memory storage requirements. The anisotropic nature of the boundary condition arises only when the target possesses a twofold rotational symmetry and, thus, produces significant cross-polarized scattering. A unique feature of this model is that since an equivalent boundary condition is developed, finite arrays are also accurately modeled provided a minimum of approximately five unit cells (five by five for 2-D) are contained in the array.