Multiple Scattering and Random Quasi-Phase-Matching in Disordered Assemblies of LiNbO₃ Nanocubes

Nonlinear disordered photonic media (NDPM), composed of a random configuration of noncentrosymmetric crystals, offer a versatile platform to tailor nonlinear optical effects. The second-harmonic generation (SHG) and its random quasi-phase-matching (RQPM) in the multiple scattering regime are still poorly explored. In this work, we bottom-up assemble NDPM in two different geometries by using LiNbO₃ nanocubes as building blocks and investigate both the multiple scattering and the nonlinear properties. We produce disordered slabs with a continuously variable thickness and microspheres with different diameters, which display a remarkable strong light scattering, evidenced by a subwavelength transport mean free path (). We first provide explicit evidence that the SHG power scales linearly with both the thickness of the slab and the volume of the microspheres. These observations generalize the characteristic linear scaling of RQPM power with the volume to the multiple scattering regime and to different sample geometries. Our structures represent a promising platform to investigate the interplay between disorder and optical nonlinear effects.