  We present a numerical study of the electromagnetic response of the
metamaterial elements that are usedto construct materials with negative
refractive index. For an array of split ring resonators (SRR) we find that the
resonant behavior of the effective magnetic permeability is accompanied by an
anti-resonant behavior of the effective permittivity. In addition, the
imaginary parts of the effective permittivity and permeability are opposite in
sign. We also observe an identical resonant versus anti-resonant frequency
dependence of the effective materials parameters for a periodic array of thin
metallic wires with cuts placed periodically along the length of the wire, with
roles of the permittivity and permeability reversed from the SRR case. We show
in a simple manner that the finite unit cell size is responsible for the
anti-resonant behavior.
