Effective refractive index of a silicon dioxide with implanted Ag nanoparticles and Er${}^{3+}$ ions

We consider light propagation in a silicon dioxide substrate with implanted ${\mathrm{E}\mathrm{r}}^{3+}$ ions and silver nanoparticles that are randomly and homogeneously distributed in the substrate. When their densities are large enough, the medium can have a negative refractive index over a certain range of frequencies, within which the following exotic property ensues: increasing the electric and magnetic plasma frequencies, the medium transparency is augmented.