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.

没有反演对称性的高质量晶体是通过三波混合实现光频率转换的常规平台。在块状晶体中，有效的波混合依赖于相位匹配配置，而在微米和纳米级，则需要共振机制来增强非线性的光-物质相互作用。这些策略通常会导致特定波长的性能和窄带应用。由光学非线性晶体的随机组装构成的无序光子材料，可以在随机准相位匹配状态下实现宽带可调性，并且不需要高质量的材料。在这里，我们通过钛酸钡纳米晶体的自下而上组装实现的几微米的Mie共振球中的随机准相位匹配，实现了共振和无序的结合。测得的二次谐波产生揭示了宽带和共振波混合的组合，其中三重共振驱动并增强了二次谐波产生，而无序使相位匹配条件保持松弛。除了块状晶体的相干长度以外，我们的纳米晶体组件为微尺度的定制相位匹配提供了新的机会。它们可以调整以实现从近紫外到红外范围的频率转换，成本低并且可以覆盖大表面积。超过块状晶体的相干长度。它们可以调整以实现从近紫外到红外范围的频率转换，成本低并且可以覆盖大表面积。超过块状晶体的相干长度。它们可以调整以实现从近紫外到红外范围的频率转换，成本低并且可以覆盖大表面积。