Nonlinear optics in a high-index of refraction material.

Nonlinear response in a material increases with its index of refraction as $n^4$. Commonly, $n \sim$ 1 so that diffraction, dispersion, and chromatic walk-off limit nonlinear scattering. Ferroelectric crystals with a periodic 3D polarization structure overcome some of these constraints through versatile Cherenkov and quasi-phase-matching mechanisms. Three-dimensional self-structuring can also lead to a giant broadband refraction \cite{DiMei2018}. We here perform second-harmonic-generation experiments in KTN:Li with $n>26$. Enhanced response causes wavelength conversion to occur in the form of bulk Cherenkov radiation without diffraction and chromatic walk-off, even in the presence of strong wave-vector mismatch and highly focused beams. The process occurs with an arbitrarily wide spectral acceptance, more than 100 nm in the near infrared spectrum, an ultra-wide angular acceptance, up to $\pm 40^{\circ}$, with no polarization selectivity, and can be tuned to allow bulk supercontinuum generation. Results pave the way to highly efficient versatile and adaptable nonlinear optical devices with the promise of single-photon-to-single-photon nonlinear optics.