Singularity-driven Second and Third Harmonic Generation in a {epsilon}-near-zero nanolayer

We show a new path to {epsilon}~0 materials without resorting to metal-based metamaterial composites. A medium that can be modeled using Lorentz oscillators usually displays {epsilon}=0 crossing points, e.g. {epsilon}=0 at {lambda}~7{mu}m and 20{mu}m for SiO2 and CaF2, respectively. We show that a Lorentz medium yields a singularity-driven enhancement of the electric field followed by dramatic lowering of thresholds for a plethora of nonlinear optical phenomena. We illustrate the remarkable enhancement of second and third harmonic generation in a layer of {epsilon}~0 material 20nm thick, and discuss the role of nonlinear surface sources.