Dipole radiation near hyperbolic metamaterials: applicability of effective-medium approximation

We investigate the radiation rate of a dipole in close proximity to a hyperbolic metamaterial and confirm that both the radiation rate and its fraction directed into the metamaterial are greatly increased compared to bulk dielectric or metal. However, we find that the homogenized effective-medium approach greatly overestimates the Purcell factor compared to metal-dielectric subwavelength multilayers with previously reported layer thicknesses.