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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.

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Fig. 1: Bottom-up assembly of BaTiO3 disordered microspheres.
Fig. 2: Linear optical characterization of the assembled microspheres.
Fig. 3: Simulation and visualization of the linear quasi-normal modes of the microspheres.
Fig. 4: SHG from the assembled microspheres and observation of RQPM.
Fig. 5: Numerical comparison of the SHG scaling between the disordered microspheres and BaTiO3 crystalline structures.
Fig. 6: Wavelength-dependent Mie driven SHG from the assembled microspheres.

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

Code availability

The codes that support the findings of this study are available from the corresponding author upon reasonable request.


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We acknowledge discussions with M. Lehner, C. Renaut, V. Vogler-Neuling and L. Pattelli. We acknowledge support from the FIRST—Center for Micro and Nanoscience of ETHZ and from the Scientific Center of Optical and Electron Microscopy (ScopeM) of ETHZ. The project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement no. 800487 (SECOONDO) and from the European Research Council under the grant agreement no. 714837 (Chi2-nano-oxides). We thank the Swiss National Science Foundation (SNF) grant 150609.

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Authors and Affiliations



R.S. and R.G. conceived the work. R.S., M.Z. and L.I. developed the assembly method. R.S., A.M., F.K. and M.R.E. realized the structures, performed the FIB cuts and the SEM characterization. A.M., J.S.M. and F.T. performed the simulations. R.S., A.M. and J.S.M. developed the theory. R.S., A.M., J.S.M. and R.G. analysed the data. R.S. wrote the first draft of the manuscript. All authors discussed the results and contributed to the writing of the manuscript.

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Correspondence to Romolo Savo.

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Supplementary Discussion, Figs. 1–15 and Table 1.

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Savo, R., Morandi, A., Müller, J.S. et al. Broadband Mie driven random quasi-phase-matching. Nat. Photonics 14, 740–747 (2020).

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