Importance of Mueller matrix characterization of bianisotropic metamaterials

We present a study on the optical properties of metamaterial layers containing U-shaped resonators. Using Finite Element Methods, we show that the description of the optical properties on one isolated resonator requires taking into account permittivity, permeability and magneto-electric tensors. The effect of weak spatial dispersion in arrays of resonators can be reproduced by adding two elements in the permittivity and magneto-electric coupling tensors. We show how the symmetries of the Mueller matrix of the sample can be used to discriminate the contributions of the different tensor elements. Generalized ellipsometry measurements made on a sample realized by e-beam lithography confirm the qualitative findings of the theoretical study. A quantitative determination of the different elements of permittivity, permeability and magneto-electric coupling is obtained by using oscillators with Lorentzian lineshape, to fit to the measurements.