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Nonlinear response in a material increases with its index of refraction as$n^4$. Commonly, $n \sim$ 1 so that diffraction, dispersion, and chromaticwalk-off limit nonlinear scattering. Ferroelectric crystals with a periodic 3Dpolarization structure overcome some of these constraints through versatileCherenkov and quasi-phase-matching mechanisms. Three-dimensionalself-structuring can also lead to a giant optical refraction. Here, we performsecond-harmonic-generation experiments in KTN:Li in conditions of giantbroadband refraction. Enhanced response causes wavelength conversion to occurin the form of bulk Cherenkov radiation without diffraction and chromaticwalk-off, even in the presence of strong wave-vector mismatch and highlyfocused beams. The process occurs with a wide spectral acceptance of more than100 nm in the near infrared spectrum, an ultra-wide angular acceptance of up to$\pm 40^{\circ}$, with no polarization selectivity, and can be tuned to allowbulk supercontinuum generation. Results pave the way to highly efficient andadaptable nonlinear optical devices with the promise ofsingle-photon-to-single-photon nonlinear optics.

Constraint-free wavelength conversion supported by giant optical refraction in a 3D perovskite supercrystal