Picophotonic localization metrology beyond thermal fluctuations

Abstract

Despite recent tremendous progress in optical imaging and metrology^1-6, 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.

Fig. 1. Measuring nanowire displacement via scattering of topologically structured light.

Incident light scattered from the nanowire is imaged in transmission through a high-numerical-aperture microscope objective (not shown) focused in a plane located at a distance λ behind the membrane. Deeply subwavelength lateral (x direction) displacements of the wire, controlled by application of a d.c. bias between the wire and the adjacent edge of the supporting membrane, are quantified via a deep-learning-enabled analysis of single-shot scattering patterns.

Fig. 2. Optical measurements of nanowire displacement.

a,b, Optically measured versus actual values of nanowire displacement for plane-wave (a) and topologically structured superoscillatory (b) illumination. Dotted lines above and below the ideal correlation diagonals are plotted at ±1 s.d. Dashed vertical lines denote minimum nanowire displacements that can be measured with accuracy exceeding 90% (relative error, <10%).

Fig. 3. Sensitivity of scattered fields to small nanowire displacements.

a,b, Intensity (a) and phase profiles (b) of the superoscillatory field in the xz plane (light propagating in the +z direction, wavelength λ = 488 nm). The sample—a nanowire in the gap between two semi-infinite sections of membrane—lies in the z = 0 plane (its cross-sectional profile being shown in green in a and grey in b). c, Relative change in scattered light intensity resulting from a λ/1,000 displacement of the sample in the x direction along a cross-sectional line through the scattering pattern in the sampling plane (line PQ in Fig. 1) as a function of the initial position x₀ of the sample relative to the symmetry axis of the light field. d, Corresponding plot of relative change in scattered light intensity for plane-wave illumination of the same sample structure. (Further details of numerical simulations are given in Supplementary Information, section 3).