Role of ferrites in negative index metamaterials

The periodic composite structures consisting of magneto-dielectric constituents as well as metallic wires, flakes leads to determine a particular configuration which may lead to electrical and/or magnetic properties which naturally cannot be obtained from single constituents. It was shown that the periodic wires structure led to negative effective permittivity.Furthermore, split ring resonators (SRR) gave rise to a negative permeability. The negative index may be obtained by having both wires and ferrites in a meta-material ferrite structure. Such a structure is vastly more practical in shape and size than the wire-SRR construct. We assume a TEM mode of propagation such that is parallel to the wire axis and is perpendicular to the wire. The magnetization of the ferrite, M, is also along the wire direction. We represent the wire element as a lumped element. The region between the wires is treated as a continuous ferrite medium. From the determination of the 4 elements of the transfer matrix, the scattering S-parameters may be easily calculated. The effective refractive index and impedance may now be calculated in terms of S11 and S21.