Negative refractive index induced by percolation in disordered   metamaterials
  An effective medium model is developed for disordered metamaterials containing a spatially random distribution of dielectric spheres. Similar to effective medium models for ordered metamaterials, this model predicts resonances in the effective permeability and permittivity arising from electric- and magnetic-dipole Mie resonances in the spheres. In addition, the model predicts a redshift of the electric resonance with increasing particle loading. Interestingly, when the particle loading exceeds the percolation threshold of 33\%, the model predicts that the electric resonance overlaps with the magnetic resonance, resulting in a negative refractive index. 
Brian A Slovick
physics.optics