Characterization of a planar artificial magnetic metamaterial surface

We explore the electromagnetic characterization of a planar artificial magnetic metamaterial. Because the composite structure is two- rather than three-dimensional, it does not form a medium with assignable bulk properties, such as the electric permittivity and magnetic permeability. However, we find that it is possible to characterize the expected bulk response of a structure composed of repeated layers of metamaterial planes, from a reflectance measurement of a single metamaterial surface made at an oblique angle. We present an analytical theory that relates the reflectance of a single plane to the expected bulk permeability and permeability of the composite, as well as supporting experiments and numerical simulations. Our results show that the recent use of reflectance measurements to characterize planar split ring resonator samples can reveal the presence of circulating currents in a sample-the precursor to artificial magnetism-but are insufficient to provide quantitative results unless the symmetry of the underlying metamaterial elements is carefully specified.