Effective Parameters for Metamorphic Materials and Metamaterials Through a Resonant Inverse Scattering Approach

We present an inverse scattering approach for the bulk electromagnetic characterization of composite materials, based on a prior proof that artificial metallo-dielectric photonic crystals can be described by effective highly resonant response functions in a wide frequency range, including several passbands/bandgaps. The method becomes complete and unambiguous at high frequencies by employing the analytic continuation of the optical path length and a consistency criterion to ascertain the physical meaning of the extracted effective parameters. It may also be used as a fast simulator or as a measurement-based predictor of the performance of multilayered structures using the scattering matrix (simulated or measured) of a single monolayer of that material. The approach is applied for the characterization of metamorphic materials, which are recently introduced artificial structures that exhibit distinct macroscopic states of behavior as far as the reflected electromagnetic field is concerned. According to interconnect topologies of their scatterers, they appear, at a single frequency, as electric conductors, absorbers, amplifiers, and passive or active magnetic conductors. Detailed evaluations are given of the complex dispersive wave impedance, refractive index, and permittivity and permeability functions for each metamorphic state of a specific three-state metamorphic material. It is found that, as a rule, the electric and magnetic wall states are related to resonant permittivity and permeability values, respectively. Furthermore, the analysis reveals broad regions with negative values of permittivity or permeability. Both resonant and negative values of epsiv_eff, mu_eff occur within bandgaps or at band-edges. Finally, the approach is applied to the negative refractive index metamaterial composed of a cylinder and two split-ring resonators, which reveals the existence of a high-frequency band with negative group velocity