Composite material made of plasmonic nanoshells with quantum dot cores: loss-compensation and ε-near-zero physical properties.

A theoretical investigation of loss-compensation capabilities in composite materials made of plasmonic nanoshells is carried out by considering quantum dots (QDs) as the nanoshells' cores. The QD and metal permittivities are modeled according to published experimental data. We determine the modes with real or complex wavenumber able to propagate in a 3D periodic lattice of nanoshells. Mode analysis is also used to assess that only one propagating mode is dominant in the composite material whose optical properties can hence be described via homogenization theory. Therefore, the material effective permittivity is found by comparing different techniques: (i) the mentioned mode analysis, (ii) Maxwell Garnett mixing rule and (iii) the Nicolson-Ross-Weir method based on transmission and reflection when considering a metamaterial of finite thickness. The three methods are in excellent agreement, because the nanoshells considered in this paper are very subwavelength, thus justifying the parameter homogenization. We show that QDs are able to provide loss-compensated ε-near-zero metamaterials and also loss-compensated metamaterials with large negative values of permittivity. Besides compensating for losses, the strong gain via QD can provide optical amplification with particular choices of the nanoshell and lattice dimensions.