Focus: How to Locate a Nanoparticle with Sub-angstrom Precision

Physics 11, 115
Laser tricks allow nanoparticle position measurements with a record 0.6-angstrom uncertainty, which will be useful in future nanotech devices.
J. Eismann/MPL
Nanoparticle ruler. In this measurement technique, red laser light coming from above is focused onto a spherical nanoparticle. The polarization of the light in this example is azimuthal, meaning that the electric field vectors (arrows) form a circle around the center of the beam. Here, the particle is right-of-center, leading to asymmetric transverse scattering (purple surfaces) that is stronger on the right of the image. Analysis of the scattering intensity pattern provides a measure of the particle’s distance from the beam’s center.Nanoparticle ruler. In this measurement technique, red laser light coming from above is focused onto a spherical nanoparticle. The polarization of the light in this example is azimuthal, meaning that the electric field vectors (arrows) form a circle ... Show more

Tiny components only nanometers across will be a major part of next-generation communications devices. Now researchers have developed a visible-light method for locating such objects with a record precision of less than one angstrom. The method is based on hitting the nano-object with laser light that has a carefully structured polarization pattern and then observing the scattered light. Beyond nanotech, the technique could lead to systems for stabilizing positioning systems in microscopes and related technologies.

Common wisdom has it that if you are using light to measure the position of something, the light’s wavelength is an important limitation. But there are exceptions. Two years ago, a team led by Peter Banzer of the Max Planck Institute for the Science of Light (MPL) in Germany reported that they could, in principle, use visible light with a distictive polarization to measure angstrom-scale displacements of a roughly 100-nanometer sphere, even though the wavelength was several hundred nanometers (nm) [1]. Their experiment was based on extending a theory developed in the 1980s by the late Milton Kerker at Clarkson College of Technology, New York.

Kerker showed that ordinary, plane-polarized light scattering from a particle much smaller than the wavelength could create significant observable effects. He worked out the interactions of the electric and magnetic components of a light beam with a tiny, nonconducting sphere made of a material that responds similarly to magnetic and electric fields. He found that the light could scatter in a highly asymmetric pattern, for example, all forward and none backward. Expanding on Kerker’s ideas, Banzer and his colleagues added a twist: their laser beam was tightly focused and radially polarized, meaning that the electric field lines pointed in the radial direction in the beam cross section, like spokes in a wheel. They showed in preliminary experiments that the asymmetric scattering pattern perpendicular to the beam (transverse Kerker scattering) is altered by small displacements of the nanoparticle [1].

In their latest work, the team developed a theoretical model that allowed them to choose the best wavelength and polarization pattern for the effect and to demonstrate sub-angstrom precision. In the experiment, they tightly focused a laser beam onto a 156-nm-diameter silicon sphere covered with a thin shell of silicon dioxide. They then used a CCD camera to image the intensity pattern of light that was deflected outward by the sphere into a ring-shaped region. When they moved the sphere off-center by a few nanometers, the circularly symmetric pattern became asymmetric. This asymmetry was maximized using a wavelength of about 640 nm for radially polarized light and about 545 nm for azimuthal polarization (where the electric field lines form circles in the beam’s cross section), numbers that agreed with the team’s theoretical predictions. They also found that using azimuthal polarization made the technique more sensitive to displacement than radial polarization.

To study the limits of the technique, the team moved the particle in steps of 2 nm throughout a 40 nm by 40 nm area around the center of the beam and observed the changes in the light scattering pattern. However, the expected location measurement accuracy, less than an angstrom, was much better than the precision of their positioning device. Furthermore, the experiment was conducted at room temperature, causing thermal jitter of up to 4 nm.

The solution to these problems was to take many measurements and to compare pairs of scattering intensity patterns made at different locations by subtracting one image from another. The large number of pixels in each image, along with the large number of images, provided enough data to measure a difference in particle position (between a pair of images) of as little as 3 angstroms, with a measurement precision of 0.6 angstroms.

Team member Martin Neugebauer of MPL says that even higher precision is possible. “We only used a normal CCD camera; if you had a very good detector and lots of light, you could drive the precision up and measure even smaller displacements,” he says.

The new method is "a brilliant example" of determining position with precision smaller than the light's wavelength, says optical physicist Lorenzo Marrucci of the University of Naples, Federico II. He is also impressed with the system’s potential to track rapid motion of a particle. “There could be a huge number of applications in the developing field of nanomechanics," he says.

This research is published in Physical Review Letters.

–Phil Dooley

Phil Dooley is a freelance science communicator in Canberra, Australia.


  1. M. Neugebauer, P. Woźniak, A. Bag, G. Leuchs, and P. Banzer, “Polarization-controlled directional scattering for nanoscopic position sensing,” Nat. Commun. 7, 11286 (2016).

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