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Optical nonlinearities in excess of 500 through sublattice reconstruction

Nature volume 643, pages 669–674 (2025)Cite this article

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Abstract

The ability of materials to respond to stimuli with significant optical nonlinearity is crucial for technological advancement and innovation1,2,3. Although photon-avalanche upconversion nanomaterials with nonlinearities exceeding 60 have been developed, further enhancement remains challenging4,5,6. Here we present a method to increase photon-avalanche nonlinearity beyond 500 by reconstructing the sublattice and extending the avalanche network. We demonstrate that lutetium substitution in the host material induces significant local crystal field distortions. These distortions strengthen cross-relaxation, the key process governing population accumulation. As a result, the optical nonlinearity is significantly amplified, enabling sub-diffraction imaging through single-beam scanning microscopy, achieving lateral and axial resolutions of 33 nm (about 1/32 of λExc) and 80 nm (around 1/13 of λExc), respectively (where λExc is the excitation wavelength). Moreover, our research shows regional differentiation within photon-avalanche nanocrystals, in which photon-avalanche performance varies across different regions at the single-nanoparticle level. This effect, coupled with extreme optical nonlinearity, enables visualization of nanoemitters at resolutions beyond their physical size using simple instrumentation. These advancements open new possibilities for super-resolution imaging, ultra-sensitive sensing, on-chip optical switching and infrared quantum counting.

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Fig. 1: Enhancement of photon-avalanche nonlinearity through sublattice reconstruction.
Fig. 2: Mechanistic investigation of extreme optical nonlinearity through sublattice reconstruction by Lu3+ substitution.
Fig. 3: Enhanced super-resolution imaging through photon avalanching in NaLuF4:Tm(15%) nanocrystals with nonlinearity more than 150.
Fig. 4: Achieving more than 500 optical nonlinearity and observing regional differentiation in nanodiscs with an expanded avalanche network.

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Data availability

Source data are provided with this paper. Source data for Figs. 1–4 and Extended Data Figs. 1–8 are also available at GitHub (https://github.com/Jiaye1998/PA-raw-data.git). All other source data are available from the corresponding authors upon reasonable request.

Code availability

Relevant codes are available at GitHub (https://github.com/Jiaye1998/PA-simulation.git).

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Acknowledgements

This work was supported by the RIE2025 Manufacturing, Trade and Connectivity (MTC) Individual Research Grant (award no. M24N7c0092) and Programmatic Fund (award no. M21J9b0085), National Research Foundation, Prime Minister’s Office, Singapore under the NRF Investigatorship programme (award no. NRF-NRF105-2019-000), and the National Natural Science Foundation of China (62288102, 62375230). We thank X. Zhang for technical assistance with the figure illustration and L. Zhong for XRD Rietveld refinement.

Author information

Author notes

  1. These authors contributed equally: Jiaye Chen, Chang Liu

Authors and Affiliations

  1. Department of Chemistry, National University of Singapore, Singapore, Singapore

    Jiaye Chen & Xiaogang Liu

  2. Institute of Flexible Electronics (IFE, Future Technologies), Xiamen University, Xiamen, China

    Chang Liu & Liangliang Liang

  3. Institute of Sustainability for Chemicals, Energy and Environment (ISCE2), Agency for Science Technology and Research (A*STAR), Singapore, Singapore

    Shibo Xi

  4. Department of Materials Science and Engineering, National University of Singapore, Singapore, Singapore

    Shengdong Tan, Qian He & Xiaogang Liu

  5. Institute of Materials Research and Engineering, Agency for Science Technology and Research, Singapore, Singapore

    Xiaogang Liu

  6. Center for Functional Materials, National University of Singapore Suzhou Research Institute, Suzhou, China

    Xiaogang Liu

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Contributions

J.C., L.L. and X.L. conceived the idea. X.L. and L.L. supervised the project and led the collaborative efforts. J.C. prepared the photon-avalanche samples. L.L., C.L. and J.C. built the optical testing system. J.C. and C.L. carried out the optical measurements and data analysis. J.C., S.X., S.T. and Q.H. analysed the crystal structure. C.L. and L.L. conducted numerical simulations. J.C., L.L. and X.L. wrote the paper. All authors participated in the discussion and analysis of the paper.

Corresponding authors

Correspondence to Liangliang Liang or Xiaogang Liu.

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Nature thanks Artur Bednarkiewicz and Qiuqiang Zhan for their contribution to the peer review of this work.

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Extended data figures and tables

Extended Data Fig. 1 Statistical comparison of optical nonlinearity and photon avalanching thresholds in NaYF4 and NaLuF4 based host.

a, Scanning electron microscopy (SEM) image showing a uniform film prepared for photon avalanching studies, with an inset illustrating the thickness profile of the film, approximately equivalent to two layers of nanocrystals. b, Graph depicting the power-dependent luminescence of Tm3+-activated NaYF4 nanocrystals with different Tm3+ doping concentrations, highlighting the effect of inert shell passivation on reducing optical nonlinearity. c and d, Graphs showing the statistical mean value of optical nonlinearity across samples (c) and the excitation thresholds (d) for initiating photon avalanche in NaYF4:Tm nanocrystals. e, Variation in optical nonlinearity among NaYF4:Tm(15%) nanocrystals with different levels of Lu3+ substitution. f, Relationship between luminescence power-dependence and Tm3+-doping concentration in Tm3+-activated NaLuF4 nanocrystals, indicating photon avalanching behavior. g and h, Graphs showing statistical data on optical nonlinearity (g) and excitation thresholds (h) for photon avalanche luminescence in NaLuF4:Tm(x%) nanocrystals. Error bars represent the standard deviation (s.d.) from five independent measurements, centered at the mean.

Source Data

Extended Data Fig. 2 Schematic of the optical system for photon avalanche study and beam profiling results.

a, Schematic diagram of the custom-designed optical system used for photon avalanching luminescence measurements. Key components include lenses (L), mirrors (M), a single-mode fiber (SMF), bandpass filters (BP), neutral density filters (ND), longpass filters (LP), beam splitters (BS), and a single-photon avalanche detector (SPAD). BS1 transmits 95% of the incident light while reflecting 5%. A flip mirror allows adjustment between detection using either the SPAD or the spectrometer. b, Image of the laser beam after passing through the single-mode fiber, showing a symmetric Gaussian distribution. c and d, Intensity profiles of the laser beam along the horizontal (X) (c) and vertical (Y) (d) directions. e, Point spread function (PSF) of the excitation focal spot on the sample plane, measured by scanning an 80 nm gold nanoparticle and recording the scattering intensity at each pixel. Image dimensions: 2,000 × 2,000 nm; pixel size: 40 nm; pixel dwell time: 50 ms. f and g, Line profiles of the continuous wave 1,064-nm excitation PSF along the X (f) and Y axis (g) in (e). The focal spot diameter, defined as the distance between points where the intensity falls to 1/e² (approximately 13.5% of the peak intensity), is measured to be 735 nm.

Source Data

Extended Data Fig. 3 Testing of laser power stability and photostability of 27-nm NaLuF4:Tm(15%) nanocrystals.

a, Ten-minute power stability test of the single-mode 1,064 nm laser used for photon avalanche measurements. b, Record of laser power intensity fluctuation as the gradient neutral density filter is rotated by small increments (0.2°) during photon avalanche testing. c, Ten-min photostability of 27-nm NaLuF4:Tm(15%) nanocrystals under two different excitation intensities at three different locations. d, Bidirectional scanning results showing photon avalanching luminescence characteristics of 27-nm NaLuF4:Tm(15%) nanocrystals without hysteresis.

Source Data

Extended Data Fig. 4 Excitation intensity-dependent rising kinetics.

a-c, The excitation intensity-dependent rising kinetics of the 805-nm emission (3H4 → 3H6) in 26-nm NaYF4:Tm(15%) (a), 27-nm NaLuF4:Tm(15%) (b), and 176-nm NaLuF4:Tm(15%) nanocrystals (c). The rise time is defined as the duration required for the luminescence to reach 95% of its maximum steady-state, providing insights into the responsiveness of the nanocrystals to external stimulation. d, the 805-nm emission (3H4 → 3H6) rise times versus excitation intensity in a, b and c.

Source Data

Extended Data Fig. 5 Photon avalanche performance of NaLuF4:Tm(15%) nanodiscs and NaYF4:Tm(15%) nanodiscs.

a-b, TEM (a) and SEM (b) images of monolayer NaLuF4:Tm(15%) nanodiscs, with diameter of ~ 176 nm. c, photon avalanche response of 176-nm NaLuF4:Tm(15%) nanodiscs. d, TEM image of NaYF4:Tm(15%) nanodiscs with a mean diameter of approximately 160 nm. e, Photon avalanche response of 160-nm NaYF4:Tm(15%) nanodiscs.

Source Data

Extended Data Fig. 6 In-depth study of photodarkening of 176-nm NaLuF4:Tm(15%) nanodiscs.

a, Increasing and decreasing excitation power scans for 176-nm NaLuF4:Tm(15%) nanodiscs over a wide power range. The inset shows an enlarged view of the pre-photon avalanche (PA) and PA regions, with the excitation power around 107 kW/cm² highlighted. This range is particularly sensitive for probing the occurrence of photodarkening. b, Experiment to quantitatively determine the photodarkening threshold. Initially, five cycles between 106.2 kW/cm² and 110.6 kW/cm² were conducted to confirm that changes in power density below the photodarkening threshold would not lead to irreversible changes in luminescence intensity. Subsequently, the low-power level was maintained at 106.2 kW/cm², while the high-power level was gradually increased from 108.2 kW/cm² to 373.5 kW/cm². After each power adjustment, a 10-second stabilization period was allowed to measure the luminescence intensity.

Source Data

Extended Data Fig. 7 Energy dispersive spectroscopy (EDS) mappings for 176-nm NaLuF4:Tm(15%) nanodiscs.

a, Scanning transmission electron microscopy-high-angle annular dark-field images of a single NaLuF4:Tm(15%) nanodisc. b, c, Horizontal (b) and vertical (c) line profiles for Tm and Lu elements.

Source Data

Extended Data Fig. 8 Regional differentiation effect measurement in a single 176-nm NaLuF4:Tm(15%) nanodisc.

Mapping of a single 176-nm NaLuF4:Tm(15%) nanodisc with progressively increasing excitation power. Image dimensions: 260 × 260 nm; pixel size: 20 nm; pixel dwell time: 1 ms. Two red concentric dashed-line circles indicate the center region and the edge region, respectively.

Source Data

Supplementary information

Supplementary Information

This file contains Supplementary Materials and Methods, Supplementary Figs. 1–18, Supplementary Tables 1–4 and Supplementary References.

Supplementary Video 1

Real-time automated data collection and analysis process of photon-avalanche luminescence. This process involved testing a film composed of self-assembled monolayer nanoparticles to prove its exceptionally high optical nonlinearity and reliability.

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Chen, J., Liu, C., Xi, S. et al. Optical nonlinearities in excess of 500 through sublattice reconstruction. Nature 643, 669–674 (2025). https://doi.org/10.1038/s41586-025-09164-y

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