Singularity-driven Second and Third Harmonic Generation in a ε-near-zero nanolayer

We show a new path to ε~0 materials without resorting to metal-based metamaterial composites. A medium that can be modeled using Lorentz oscillators usually displays ε=0 crossing points, e.g. ε=0 at λ~7μm and 20μm 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 ε~0 material 20nm thick, and discuss the role of nonlinear surface sources.

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