Broadband Mie driven random quasi-phase-matching

High-quality crystals without inversion symmetry are the conventional platform to achieve optical frequency conversion via three-wave mixing. In bulk crystals, efficient wave mixing relies on phase-matching configurations, while at the micro- and nanoscale it requires resonant mechanisms that enhance the nonlinear light-matter interaction. These strategies commonly result in wavelength-specific performances and narrowband applications. Disordered photonic materials, made up of a random assembly of optical nonlinear crystals, enable a broadband tunability in the random quasi-phase-matching regime and do not require high-quality materials. Here, we combine resonances and disorder by implementing random quasi-phase-matching in Mie resonant spheres of a few micrometres realized by the bottom-up assembly of barium titanate nanocrystals. The measured second-harmonic generation reveals a combination of broadband and resonant wave mixing, in which Mie resonances drive and enhance the second-harmonic generation, while the disorder keeps the phase-matching conditions relaxed. Our nanocrystal assemblies provide new opportunities for tailored phase matching at the microscale, beyond the coherence length of the bulk crystal. They can be adapted to achieve frequency conversion from the near-ultraviolet to the infrared ranges, are low cost and can cover large surface areas. Enhanced second-harmonic generation is achieved through random quasi-phase-matching in three-dimensional Mie resonant disordered microspheres realized by the bottom-up assembly of barium titanate nanocrystals.