  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.

Optics