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Picophotonic localization metrology beyond thermal fluctuations


Despite recent tremendous progress in optical imaging and metrology1,2,3,4,5,6, there remains a substantial resolution gap between atomic-scale transmission electron microscopy and optical techniques. Is optical imaging and metrology of nanostructures exhibiting Brownian motion possible with such resolution, beyond thermal fluctuations? Here we report on an experiment in which the average position of a nanowire with a thermal oscillation amplitude of 150 pm is resolved in single-shot measurements with subatomic precision of 92 pm, using light at a wavelength of λ = 488 nm, providing an example of such sub-Brownian metrology with λ/5,300 precision. To localize the nanowire, we employ a deep-learning analysis of the scattering of topologically structured light, which is highly sensitive to the nanowire’s position. This non-invasive metrology with absolute errors down to a fraction of the typical size of an atom, opens a range of opportunities to study picometre-scale phenomena with light.

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Fig. 1: Measuring nanowire displacement via scattering of topologically structured light.
Fig. 2: Optical measurements of nanowire displacement.
Fig. 3: Sensitivity of scattered fields to small nanowire displacements.

Data availability

For the purpose of open access, the authors have applied a Creative Commons attribution (CC BY) license to any author accepted manuscript version arising.

The data from this paper can be obtained from the University of Southampton ePrints research repository:


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This work was supported by the Engineering and Physical Sciences Research Council, UK (grant number EP/T02643X/1; N.I.Z., K.F.M., J.-Y.O.), the Ministry of Education, Singapore (MOE2016-T3-1-006; N.I.Z.), the National Research Foundation Singapore (NRF-CRP23-2019-0006) and the China Scholarship Council (201806160012; T.L.).

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The project was conceived by T.L., J.-Y.O., K.F.M. and N.I.Z. Experimental work and neural network programming were undertaken by T.L., C.-H.C., J.-Y.O., J.X. and E.A.C. All co-authors contributed to analysis of data. The manuscript was written by T.L., K.F.M. and N.I.Z. and cross-edited by other co-authors. Work was supervised by K.F.M. and N.I.Z.

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Correspondence to Nikolay I. Zheludev.

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Nature Materials thanks Konstantinos Makris, Zeev Zalevsky and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary discussion sections 1–5 and Fig. 1.

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Liu, T., Chi, CH., Ou, JY. et al. Picophotonic localization metrology beyond thermal fluctuations. Nat. Mater. (2023).

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