Optical density of states near planar ENZ materials.

We study the local density of optical states (LDOS) for lossy dielectric substrates whose electric permittivity has a vanishing real part, approaching zero from the positive side of the real axis. A criterion for evaluating the threshold height above (below) which radiative (non-radiative) processes dominate for a dipole emitter is established. We focus on the case of a vertical dipole above the -near-zero (ENZ) substrate and show that, in the lossless case, complete LDOS cancellation originates from radiative modes in its near field. We evaluate the performance of commercially available ENZ materials and quantify the limits of such cancellation effects with the intrinsic losses of the substrate.