Avalanche phenomena use steeply nonlinear dynamics to generate disproportionately large responses from small perturbations, and are found in a multitude of events and materials1. Photon avalanching enables technologies such as optical phase-conjugate imaging2, infrared quantum counting3 and efficient upconverted lasing4,5,6. However, the photon-avalanching mechanism underlying these optical applications has been observed only in bulk materials and aggregates6,7, limiting its utility and impact. Here we report the realization of photon avalanching at room temperature in single nanostructures—small, Tm3+-doped upconverting nanocrystals—and demonstrate their use in super-resolution imaging in near-infrared spectral windows of maximal biological transparency. Avalanching nanoparticles (ANPs) can be pumped by continuous-wave lasers, and exhibit all of the defining features of photon avalanching, including clear excitation-power thresholds, exceptionally long rise time at threshold, and a dominant excited-state absorption that is more than 10,000 times larger than ground-state absorption. Beyond the avalanching threshold, ANP emission scales nonlinearly with the 26th power of the pump intensity, owing to induced positive optical feedback in each nanocrystal. This enables the experimental realization of photon-avalanche single-beam super-resolution imaging7 with sub-70-nanometre spatial resolution, achieved by using only simple scanning confocal microscopy and without any computational analysis. Pairing their steep nonlinearity with existing super-resolution techniques and computational methods8,9,10, ANPs enable imaging with higher resolution and at excitation intensities about 100 times lower than other probes. The low photon-avalanching threshold and excellent photostability of ANPs also suggest their utility in a diverse array of applications, including sub-wavelength imaging7,11,12 and optical and environmental sensing13,14,15.
This is a preview of subscription content
Subscription info for Chinese customers
We have a dedicated website for our Chinese customers. Please go to naturechina.com to subscribe to this journal.
Get time limited or full article access on ReadCube.
All prices are NET prices.
The code for modelling the PA behaviour using the differential rate equations described in the Supplementary Information are freely available at https://github.com/nawhgnahc/Photon_Avalanche_DRE_calculation.git.
Turcotte, D. L. Self-organized criticality. Rep. Prog. Phys. 62, 1377–1429 (1999).
Ni, H. & Rand, S. C. Avalanche phase conjugation. Opt. Lett. 17, 1222–1224 (1992).
Chivian, J. S., Case, W. E. & Eden, D. D. The photon avalanche: a new phenomenon in Pr3+‐based infrared quantum counters. Appl. Phys. Lett. 35, 124–125 (1979).
Lenth, W. & Macfarlane, R. M. Excitation mechanisms for upconversion lasers. J. Lumin. 45, 346–350 (1990).
Joubert, M.-F. Photon avalanche upconversion in rare earth laser materials. Opt. Mater. 11, 181–203 (1999).
Auzel, F. Upconversion and anti-Stokes processes with f and d ions in solids. Chem. Rev. 104, 139–174 (2004).
Bednarkiewicz, A., Chan, E. M., Kotulska, A., Marciniak, L. & Prorok, K. Photon avalanche in lanthanide doped nanoparticles for biomedical applications: super-resolution imaging. Nanoscale Horiz. 4, 881–889 (2019).
Thompson, M. A., Lew, M. D. & Moerner, W. E. Extending microscopic resolution with single-molecule imaging and active control. Annu. Rev. Biophys. 41, 321–342 (2012).
Gustafsson, M. G. L. Nonlinear structured-illumination microscopy: wide-field fluorescence imaging with theoretically unlimited resolution. Proc. Natl Acad. Sci. USA 102, 13081 (2005).
Heintzmann, R. & Huser, T. Super-resolution structured illumination microscopy. Chem. Rev. 117, 13890–13908 (2017).
Denkova, D. et al. 3D sub-diffraction imaging in a conventional confocal configuration by exploiting super-linear emitters. Nat. Commun. 10, 3695 (2019).
Liu, Y. et al. Super-resolution mapping of single nanoparticles inside tumor spheroids. Small 16, 1905572 (2020).
Marciniak, L., Bednarkiewicz, A. & Elzbieciak, K. NIR–NIR photon avalanche based luminescent thermometry with Nd3+ doped nanoparticles. J. Mater. Chem. C 6, 7568–7575 (2018).
Pickel, A. D. et al. Apparent self-heating of individual upconverting nanoparticle thermometers. Nat. Commun. 9, 4907 (2018).
Lay, A. et al. Optically robust and biocompatible mechanosensitive upconverting nanoparticles. ACS Cent. Sci. 5, 1211–1222 (2019).
Xie, P. & Gosnell, T. R. Room-temperature upconversion fiber laser tunable in the red, orange, green, and blue spectral regions. Opt. Lett. 20, 1014–1016 (1995).
Guy, S., Joubert, M. F. & Jacquier, B. Photon avalanche and the mean-field approximation. Phys. Rev. B 55, 8240–8248 (1997).
Deng, H., Yang, S., Xiao, S., Gong, H.-M. & Wang, Q.-Q. Controlled synthesis and upconverted avalanche luminescence of cerium(III) and neodymium(III) orthovanadate nanocrystals with high uniformity of size and shape. J. Am. Chem. Soc. 130, 2032–2040 (2008).
Wang, Q.-Q. et al. Highly efficient avalanche multiphoton luminescence from coupled Au nanowires in the visible region. Nano Lett. 7, 723–728 (2007).
Ma, Z. et al. Origin of the avalanche-like photoluminescence from metallic nanowires. Sci. Rep. 6, 18857 (2016).
Liu, Y. et al. Amplified stimulated emission in upconversion nanoparticles for super-resolution nanoscopy. Nature 543, 229–233 (2017).
Levy, E. S. et al. Energy-looping nanoparticles: harnessing excited-state absorption for deep-tissue imaging. ACS Nano 10, 8423–8433 (2016).
Fernandez-Bravo, A. et al. Continuous-wave upconverting nanoparticle microlasers. Nat. Nanotechnol. 13, 572–577 (2018).
Si, X., Li, Z., Qu-Quan, W., Hong, D. & Shi-He, Y. Energy transfer and avalanche upconversion of NdxY1 − xVO4 nanocrystals. Chin. Phys. Lett. 26, 124209 (2009).
Bednarkiewicz, A. & Strek, W. Laser-induced hot emission in Nd3+/Yb3+:YAG nanocrystallite ceramics. J. Phys. D 35, 2503–2507 (2002).
Dwivedi, Y., Bahadur, A. & Rai, S. B. Optical avalanche in Ho:Yb:Gd2O3 nanocrystals. J. Appl. Phys. 110, 043103 (2011).
Wang, G., Peng, Q. & Li, Y. Luminescence tuning of upconversion nanocrystals. Chemistry 16, 4923–4931 (2010).
Zhou, B., Shi, B., Jin, D. & Liu, X. Controlling upconversion nanocrystals for emerging applications. Nat. Nanotechnol. 10, 924–936 (2015).
Tian, B. et al. Low irradiance multiphoton imaging with alloyed lanthanide nanocrystals. Nat. Commun. 9, 3082 (2018).
Tajon, C. A. et al. Photostable and efficient upconverting nanocrystal-based chemical sensors. Opt. Mater. 84, 345–353 (2018).
Bünzli, J.-C. G. & Piguet, C. Taking advantage of luminescent lanthanide ions. Chem. Soc. Rev. 34, 1048–1077 (2005).
Gnach, A., Lipinski, T., Bednarkiewicz, A., Rybka, J. & Capobianco, J. A. Upconverting nanoparticles: assessing the toxicity. Chem. Soc. Rev. 44, 1561–1584 (2015).
Gargas, D. J. et al. Engineering bright sub-10-nm upconverting nanocrystals for single-molecule imaging. Nat. Nanotechnol. 9, 300 (2014).
Fischer, S., Bronstein, N. D., Swabeck, J. K., Chan, E. M. & Alivisatos, A. P. Precise tuning of surface quenching for luminescence enhancement in core–shell lanthanide-doped nanocrystals. Nano Lett. 16, 7241–7247 (2016).
Johnson, N. J. J. et al. Direct evidence for coupled surface and concentration quenching dynamics in lanthanide-doped nanocrystals. J. Am. Chem. Soc. 139, 3275–3282 (2017).
Liu, Q. et al. Single upconversion nanoparticle imaging at sub-10 W cm−2 irradiance. Nat. Photon. 12, 548–553 (2018).
Chen, X. et al. Confining energy migration in upconversion nanoparticles towards deep ultraviolet lasing. Nat. Commun. 7, 10304 (2016).
Wang, F. et al. Tuning upconversion through energy migration in core–shell nanoparticles. Nat. Mater. 10, 968–973 (2011).
Gamelin, D. R., Lüthi, S. R. & Güdel, H. U. The role of laser heating in the intrinsic optical bistability of Yb3+-doped bromide lattices. J. Phys. Chem. B 104, 11045–11057 (2000).
Butcher, J. C. Numerical Methods for Ordinary Differential Equations (Wiley, 2016).
Goldner, P. & Pelle, F. Photon avalanche fluorescence and lasers. Opt. Mater. 5, 239–249 (1996).
Joubert, M. F., Guy, S. & Jacquier, B. Model of the photon-avalanche effect. Phys. Rev. B 48, 10031–10037 (1993).
Hong, G. et al. Through-skull fluorescence imaging of the brain in a new near-infrared window. Nat. Photon. 8, 723–730 (2014).
Ostrowski, A. D. et al. Controlled synthesis and single-particle imaging of bright, sub-10 nm lanthanide-doped upconverting nanocrystals. ACS Nano 6, 2686–2692 (2012).
Hossan, M. Y. et al. Explaining the nanoscale effect in the upconversion dynamics of β-NaYF4:Yb3+, Er3+ core and core–shell nanocrystals. J. Phys. Chem. C 121, 16592–16606 (2017).
Teitelboim, A. et al. Energy transfer networks within upconverting nanoparticles are complex systems with collective, robust, and history-dependent dynamics. J. Phys. Chem. C 123, 2678–2689 (2019).
Chan, E. M., Gargas, D. J., Schuck, P. J. & Milliron, D. J. Concentrating and recycling energy in lanthanide codopants for efficient and spectrally pure emission: the case of NaYF4:Er3+/Tm3+ upconverting nanocrystals. J. Phys. Chem. B 116, 10561–10570 (2012).
Corle, T. R. & Kino, G. S. Confocal Scanning Optical Microscopy and Related Imaging Systems (Academic Press, 1996).
Chen, C. et al. Multi-photon near-infrared emission saturation nanoscopy using upconversion nanoparticles. Nat. Commun. 9, 3290 (2018).
Pichaandi, J., Boyer, J.-C., Delaney, K. R. & van Veggel, F. C. J. M. Two-photon upconversion laser (scanning and wide-field) microscopy using Ln3+-doped NaYF4 upconverting nanocrystals: a critical evaluation of their performance and potential in bioimaging. J. Phys. Chem. C 115, 19054–19064 (2011).
Auzel, F., Chen, Y. & Meichenin, D. Room temperature photon avalanche up-conversion in Er-doped ZBLAN glass. J. Lumin. 60-61, 692–694 (1994).
Auzel, F. & Chen, Y. Photon avalanche luminescence of Er3+ ions in LiYF4 crystal. J. Lumin. 65, 45–56 (1995).
Gomes, A. S. L., Maciel, G. S., de Araújo, R. E., Acioli, L. H. & de Araújo, C. B. Diode pumped avalanche upconversion in Pr3+-doped fibers. Opt. Commun. 103, 361–364 (1993).
Martín, I. R. et al. Room temperature photon avalanche upconversion in Tm3+-doped fluoroindate glasses. J. Phys. Condens. Matter 12, 1507–1516 (2000).
Li, Y. et al. BiOCl:Er3+ nanosheets with tunable thickness for photon avalanche phosphors. ACS Appl. Nano Mater. 2, 7652–7660 (2019).
Garfield, D. J. et al. Enrichment of molecular antenna triplets amplifies upconverting nanoparticle emission. Nat. Photon. 12, 402–407 (2018).
Liu, Y. et al. Controlled assembly of upconverting nanoparticles for low-threshold microlasers and their imaging in scattering media. ACS Nano 14, 1508–1519 (2020).
Fernandez-Bravo, A. et al. Ultralow-threshold, continuous-wave upconverting lasing from subwavelength plasmons. Nat. Mater. 18, 1172–1176 (2019).
Kilbane, J. D. et al. Far-field optical nanothermometry using individual sub-50 nm upconverting nanoparticles. Nanoscale 8, 11611–11616 (2016).
Zhai, Y. et al. Near infrared neuromorphic computing via upconversion-mediated optogenetics. Nano Energy 67, 104262 (2020).
Bradac, C. et al. Room-temperature spontaneous superradiance from single diamond nanocrystals. Nat. Commun. 8, 1205 (2017).
Asenjo-Garcia, A., Kimble, H. J. & Chang, D. E. Optical waveguiding by atomic entanglement in multilevel atom arrays. Proc. Natl Acad. Sci. USA 116, 25503 (2019)
P.J.S., Y.D.S., S.H.N. and C.L. gratefully acknowledge support from the Global Research Laboratory (GRL) Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science and ICT (number 2016911815), and KRICT (KK2061-23, SKO1930-20). Y.D.S. acknowledges the Industrial Strategic Technology Development Program (number 10077582) funded by the Ministry of Trade, Industry, and Energy (MOTIE), Korea. E.Z.X. gratefully acknowledges support from the NSF Graduate Research Fellowship Program. Y.L. was supported by a China Scholarship Council fellowship. A.T. was supported by the Weizmann Institute of Science − National Postdoctoral Award Program for Advancing Women in Science. Work at the Molecular Foundry was supported by the Office of Science, Office of Basic Energy Sciences, of the US Department of Energy under contract number DE-AC02-05CH11231. K.Y. acknowledges support from Programmable Quantum Materials, an Energy Frontier Research Center funded by the US Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES), under award DE-SC0019443. A.B. acknowledges financial support from NCN, Poland, grant number UMO-2018/31/B/ST5/01827.
The authors declare no competing interests.
Peer review information Nature thanks Xueyuan Chen, Andries Meijerink and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
About this article
Cite this article
Lee, C., Xu, E.Z., Liu, Y. et al. Giant nonlinear optical responses from photon-avalanching nanoparticles. Nature 589, 230–235 (2021). https://doi.org/10.1038/s41586-020-03092-9
Journal of Biological Physics (2022)
Continuous-wave near-infrared stimulated-emission depletion microscopy using downshifting lanthanide nanoparticles
Nature Nanotechnology (2021)
Insights on the continuous representations of piecewise-smooth nonlinear systems: limits of applicability and effectiveness
Nonlinear Dynamics (2021)