A theory of metamaterials based on periodically loaded transmission lines: Interaction between magnetoinductive and electromagnetic waves

The propagation of waves in a metamaterial consisting of split ring resonators (SRRs) and metallic rods is considered in several steps. The first involves the rods in isolation, the second the SRRs in isolation, and the third a combination of the two, which includes the coupling between neighboring SRRs and allows the propagation of magnetoinductive (MI) waves. The mathematical formulation is based on a conventional description of loaded transmission lines. A dispersion equation is derived to show the main features of known experimental results, including all the stop bands and passbands, the latter exhibiting both forward and backward waves. The interaction between electromagnetic and MI waves is presented in the form of a coupled dispersion equation. The applicability of the approaches based on negative material parameters is discussed.