Hyper-gap optical materials

Optical materials largely refer to transparent insulators and semiconductors for guiding, diffracting, and nonlinearly generating light at photon energies below the electronic bandgaps. Here we propose that a solid can be equally lossless above the fundamental bandgap inside an energy interval dubbed the hyper-gap, in a class of crystals consisting of well-isolated conduction and valence bands. The optics within the hyper-gap can completely defy the conventional rules and limits, including the low-loss negative permittivity unavailable in existing metals for plasmonic metamaterials, the anomalous-dispersion phase-matching in isotropic bulks without birefringence nor periodic patterns for nonlinear optics, as well as the negative group-velocity dispersion from the visible to the deep-ultraviolet unattainable in known dielectrics for ultrafast optics.