  Perfect lensing and cloaking based on complementary media are possible
applications of negative refractive index materials. Metamaterials represent
the natural candidates to realize such property by tailoring the effective
dielectric permittiviy and magnetic permeability. The fine tuning of $n<0$ of
metamaterials is limited by coarse grained inclusions which give discreteness
to the electromagnetic parameters as a function of their density. We study the
negative refractive index of a metamaterial as a function of the linear density
of the lattice period at microwave frequency. The negative refractive index is
obtained by a waveguide filled with a split ring resonator array in a frequency
band below the cut off frequency of the waveguide. The special value of $n=-1$
typical of perfect lensing is maintained by tuning the density on a bandwidth
of 1 GHz. A cut-off density above which the metamaterial operates is observed.
A second critical density above which the transmission saturates is found close
to the Pendry limit. Such results on the density of negative refractive index
metamaterials open new paths towards the fine tuning of constitutive parameters
at wanted values by means of transformation optics.
