Unified homogenization theory for magnetoinductive and electromagnetic waves in split-ring metamaterials

A unified homogenization procedure for split-ring metamaterials taking into account time and spatial dispersion is introduced. It is shown that electromagnetic and magnetoinductive waves propagating in the metamaterial are obtained from this analysis. Therefore, the proposed time and spatially dispersive permeability accounts for the characterization of the complete spectrum of waves of the metamaterial. Finally, it is shown that the proposed theory is in good quantitative and qualitative agreement with full wave simulations.