  A metamaterial with frequency dependent double negative effective properties
is constructed from a sub-wavelength periodic array of coated rods. Explicit
power series are developed for the dispersion relation and associated Bloch
wave solutions. The expansion parameter is the ratio of the length scale of the
periodic lattice to the wavelength. Direct numerical simulations for finite
size period cells show that the leading order term in the power series for the
dispersion relation is a good predictor of the dispersive behavior of the
metamaterial.
