Anomalous-dispersion phase-matching in a hyper-gap crystal

While both birefringent and anomalous-dispersion phase-matching~(ADPM) are possible in homogeneous single crystals, birefringent phase-matching dominates in nonlinear optical applications. Though demonstrated in gases and liquids, ADPM has not been established in solids due to the parasitic photon loss from the material absorption inducing the anomalous dispersion. This absorption bottleneck can be overcome by a crystal with an additional spectral gap in its absorption spectrum, beyond the bandgap, which we term the ``hyper-gap''. Here, we theoretically propose and experimentally demonstrate such a hyper-gap crystal and the ADPM-enabled third harmonic generation inside the hyper-gap. Our results introduce a new class of nonlinear optical materials that do not rely on lattice anisotropy or periodic poling.