  We consider a mixture of metal coated quantum dots dispersed in a polymer
matrix and, using a modified version of the standard Maxwell-Garnett mixing
rule, we prove that the mixture parameters (particles radius, quantum dots
gain, etc.) can be chosen so that the effective medium permittivity has an
absolute value very close to zero in the near-infrared, i.e. |Re(epsilon)|<<1
and |Im (epsilon)|<<1 at the same near-infrared wavelength. Resorting to
full-wave simulations, we investigate the accuracy of the effective medium
predictions and we relate their discrepancy with rigorous numerical results to
the fact that |epsilon|<<1 is a critical requirement. We show that a simple
method for reducing this discrepancy, and hence for achieving a prescribed
value of |\epsilon|, consists in a subsequent fine-tuning of the nanoparticles
volume filling fraction.
