Retrieval of material parameters for uniaxial metamaterials

We present a general method for retrieving the effective tensorial permittivity of uniaxially anisotropic metamaterials. By relaxing the usually imposed constraint of assuming nonmagnetic metal/dielectric metamaterials, we also retrieve the effective permeability tensor and show that multilayer hyperbolic metamaterials exhibit a strong and broadband diamagnetic response in the visible regime. The method provides the means for designing magnetically anisotropic metamaterials for studying magnetic topological transitions in the visible regime. We obtain orientation-independent effective material parameters, which are distinguishable from mere wave parameters. We analytically validate this method for Ag/SiO2 planar metamaterials with a varying number of layers and filling fractions and compare to the results from effective medium theory and Bloch theory.