Constitutive parameter extraction of artificial materials based on metamaterial technology using scattering coefficients measured at oblique incidence

Metamaterials are artificial materials, which are commonly structured by a periodic arrangement of resonant elements, such as metallic wires and rings. It is common to assign effective constitutive parameters to a metamaterial, when considering its response to an electromagnetic field with a wavelength that is much larger than the structure's unit cell. Several methods have been suggested for evaluating these parameters; among them are the S-parameters method (X. Chen, T. M. Grzegorczyk, B.I. Wu, J. Pacheco, and J. A. Kong, Phys. Rev. E 70.1, 016608, 2004), and different numerical homogenization methods (D. R. Smith and J. B. Pendry, JOSA B 23.3, 391-403, 2006, I. Tsukerman, JOSA B 28.3, 577-586, 2011). All proposed methods are either bound to artificial materials that posses diagonal effective permeability and permittivity tensors with simple bi-anisotropic constitutive relation, or interpolate the electromagnetic fields distribution within the unit cell of the periodic structure, which can be used for the retrieval of the constitutive relations.