Backward wave region and negative material parameters of a structure formed by lattices of wires and split-ring resonators

A structure formed by combined lattices of infinitely long wires and split-ring resonators is studied. A dispersion equation is derived and then used to calculate the effective permittivity and permeability in the frequency band where the lattice can be homogenized. The backward wave region in which both the effective permittivity and permeability are negative is analyzed. Some open and controversial questions are discussed. It is shown that previous experimental results confirming the existence of backward waves in such a structure can be indeed explained in terms of negative material parameters. However, these parameters are not quasi-static and thus the known analytical formulas for the effective material parameters of this structure, which have been widely used and discussed in the literature, were not correct, and was the reason for some objections to the authors of that experiment.