Retrieval of material parameters for uniaxial metamaterials

We present a general method for retrieving the effective tensorial permittivity of any uniaxially anisotropic metamaterial. By relaxing the usually imposed condition of non-magnetic metal/dielectric metamaterials, we also retrieve the permeability tensor and show that hyperbolic metamaterials exhibit a strong diamagnetic response in the visible regime. We obtain global material parameters, directly measurable with spectroscopic ellipsometry and distinguishable from mere wave parameters, by using the generalized dispersion equation for uniaxial crystals along with existing homogenization methods. Our method is analytically and experimentally verified for Ag/SiO2 planar metamaterials with varying number of layers and compared to the effective medium theory. We also propose an experimental method for retrieving material parameters using methods other than ellipsometry.