|epsilon|-Near-zero materials in the near-infrared

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. $|{rm Re}(epsilon)| ll 1$ and $|{rm Im}(epsilon)| ll 1$ 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 $|epsilon| ll 1$ is a critical requirement. We show that a simple method for reducing this discrepancy, and hence for achieving a prescribed and very small value of $|epsilon|, $ consists in a subsequent fine-tuning of the nanoparticles volume filling fraction.