Theoretical analysis for constitutive parameters of the periodic electric resonator metamaterials

We begin with Maxwell´s equations and put the thin electric resonance dielectric sheet equivalent into electric surface current. Using periodic boundary conditions and the principle of superposition, we can get the dispersion relation and Bloch impedance of periodic electric resonator metamaterials. Base on the dispersion relation and Bloch impedance, we can obtain the theoretical analytical expressions of Bloch constitutive parameters. Since we consider the impact of the magnetic anti-resonance, we find theoretical predictions match the retrieval results very well, which showed that the analytical expression derived in the paper is extremely effective.