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.
We theoretically demonstrate negative refraction and sub-wavelength resolution below the diffraction limit in the UV and extreme UV ranges using semiconductors. The metal-like re-sponse of typical semiconductors such as GaAs or GaP makes it possible
to achieve negative refraction and super-guiding in resonant semiconductor/dielectric multilayer stacks, similar to what has been demonstrated in metallo-dielectric photonic band gap structures. The exploita-tion of this basic property in semiconductors raises the possibility of new, yet-untapped ap-plications in the UV and soft x-ray ranges.
