Equivalent Boundary Conditions for Isotropic Arrays

Inductive and capacitive isotropic ribbon arrays with a period small compared with the wavelength, placed at the interface between two media, are considered. Boundary value problems for the scattering of plane waves of two polarizations, incident onto the arrays at arbitrary angles, are formulated. The boundary value problems are solved by the Galerkin method. A model of an array is proposed in the form of a semitransparent film on the surfaces of which equivalent boundary conditions relating the fields on both sides of the surfaces are imposed. The theoretical solution is compared with a numerical solutions obtained using a standard system of electromagnetic simulation. It is shown that, in the low-frequency region, the equivalent boundary conditions describe the behavior of the arrays with good accuracy.