Abstract
Far-field optical imaging techniques allow the determination of the position of point-like emitters and scatterers1,2,3. Although the optical wavelength sets a fundamental limit to the image resolution of unknown objects, the position of an individual emitter can in principle be estimated from the image with arbitrary precision. This is used, for example, in the determination of the position of stars4 or in optical super-resolution microscopy5. Furthermore, precise position determination is an experimental prerequisite for the manipulation and measurement of individual quantum systems, such as atoms, ions and solid-state-based quantum emitters6,7,8. Here we demonstrate that spin–orbit coupling of light in the emission of elliptically polarized emitters can lead to systematic, wavelength-scale errors in the estimation of the emitter’s position. Imaging a single trapped atom as well as a single sub-wavelength-diameter gold nanoparticle, we demonstrate a shift between the emitters’ measured and actual positions, which is comparable to the optical wavelength. For certain settings, the expected shift can become arbitrarily large. Beyond optical imaging techniques, our findings could be relevant for the localization of objects using any type of wave that carries orbital angular momentum relative to the emitter’s position with a component orthogonal to the direction of observation.
This is a preview of subscription content, access via your institution
Access options
Access Nature and 54 other Nature Portfolio journals
Get Nature+, our best-value online-access subscription
$29.99 / 30 days
cancel any time
Subscribe to this journal
Receive 12 print issues and online access
$209.00 per year
only $17.42 per issue
Rent or buy this article
Prices vary by article type
from$1.95
to$39.95
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
Data availability
The data that support the findings of this study are available from the authors upon reasonable request. Contact persons are G.A. for the ion experiment, and J.V. or A.R. for the nanoparticle experiment.
References
Boas, D. A., Pitris, C. & Ramanujam, N. Handbook of Biomedical Optics (CRC Press, Boca Raton, 2011).
Kovalevsky, J. & Seidelmann, P. K. Fundamentals of Astrometry (Cambridge Univ. Press, Cambridge, 2004).
Novotny, L. & Hecht, B. Principles of Nano-Optics (Cambridge Univ. Press, Cambridge, 2006).
Anderson, J. & King, I. R. Toward high-precision astrometry with WFPC2. I. Deriving an accurate point-spread function. Publ. Astron. Soc. Pac. 112, 1360–1382 (2000).
Hell, S. W. Far-field optical nanoscopy. Science 316, 1153–1158 (2007).
Alberti, A. et al. Super-resolution microscopy of single atoms in optical lattices. New J. Phys. 18, 053010 (2016).
Wong-Campos, J. D., Johnson, K. G., Neyenhuis, B., Mizrahi, J. & Monroe, C. High-resolution adaptive imaging of a single atom. Nat. Photon. 10, 606–610 (2016).
Sapienza, L., Davanço, M., Badolato, A. & Srinivasan, K. Nanoscale optical positioning of single quantum dots for bright and pure single-photon emission. Nat. Commun. 6, 7833 (2015).
Thompson, R. E., Larson, D. R. & Webb, W. W. Precise nanometer localization analysis for individual fluorescent probes. Biophys. J. 82, 2775–2783 (2002).
Enderlein, J., Toprak, E. & Selvin, P. R. Polarization effect on position accuracy of fluorophore localization. Opt. Express 14, 8111–8120 (2006).
Engelhardt, J. et al. Molecular orientation affects localization accuracy in superresolution far-field fluorescence microscopy. Nano Lett. 11, 209–213 (2011).
Backlund, M. P. et al. Simultaneous, accurate measurement of the 3D position and orientation of single molecules. Proc. Natl Acad. Sci. USA 109, 19087–19092 (2012).
Lew, M. D. & Moerner, W. E. Azimuthal polarization filtering for accurate, precise, and robust single-molecule localization microscopy. Nano Lett. 14, 6407–6413 (2014).
Backlund, M. P. et al. Removing orientation-induced localization biases in single-molecule microscopy using a broadband metasurface mask. Nat. Photon. 10, 459–464 (2016).
Mortensen, K. I., Churchman, L. S., Spudich, J. A. & Flyvbjerg, H. Optimized localization analysis for single-molecule tracking and super-resolution microscopy. Nat. Methods 7, 377–381 (2010).
Quirin, S., Pavani, S. R. P. & Piestun, R. Optimal 3D single-molecule localization for superresolution microscopy with aberrations and engineered point spread functions. Proc. Natl Acad. Sci. USA 109, 675–679 (2012).
Stallinga, S. & Rieger, B. Position and orientation estimation of fixed dipole emitters using an effective Hermite point spread function model. Opt. Express 20, 5896–5921 (2012).
Wertz, E., Isaacoff, B. P., Flynn, J. D. & Biteen, J. S. Single-molecule super-resolution microscopy reveals how light couples to a plasmonic nanoantenna on the nanometer scale. Nano Lett. 15, 2662–2670 (2015).
Raab, M., Vietz, C., Stefani, F. D., Acuna, G. P. & Tinnefeld, P. Shifting molecular localization by plasmonic coupling in a single-molecule mirage. Nat. Commun. 8, 13966 (2017).
Moe, G. & Happer, G. Conservation of angular momentum for light propagating in a transparent anisotropic medium. J. Phys. B At. Mol. Phys. 10, 1191–1208 (1977).
Schwartz, C. & Dogariu, A. Conservation of angular momentum of light in single scattering. Opt. Express 14, 8425–8433 (2006).
Bliokh, K. Y., Rodrguez-Fortuno, F. J., Nori, F. & Zayats, A. V. Spin–orbit interactions of light. Nat. Photon. 9, 796–808 (2016).
Bliokh, K. Y., Gorodetski, Y., Kleiner, V. & Hasman, E. Coriolis effect in optics: unified geometric phase and spin-Hall effect. Phys. Rev. Lett. 101, 030404 (2008).
Rodríguez-Herrera, O. G., Lara, D., Bliokh, K. Y., Ostrovskaya, E. A. & Dainty, C. Optical nanoprobing via spin–orbit interaction of light. Phys. Rev. Lett. 104, 253601 (2010).
Lodahl, P. et al. Chiral quantum optics. Nature 541, 473–480 (2017).
Li, X. & Arnoldus, H. F. Macroscopic far-field observation of the sub-wavelength near-field dipole vortex. Phys. Lett. A 374, 1063–1067 (2010).
Darwin, C. G. Notes on the theory of radiation. Proc. Roy. Soc. A 136, 36–52 (1932).
Bekshaev, A. Y., Bliokh, K. Y. & Nori, F. Transverse spin and momentum in two-wave interference. Phys. Rev. X 5, 011039 (2015).
Berry, M. V. Optical currents. J. Opt. A: Pure Appl. Opt. 11, 094001 (2009).
Knee, G. C., Combes, J., Ferrie, C. & Gauger, E. M. Weak-value amplification: state of play. Quantum Meas. Quantum Metrol. 3, 32–37 (2016).
Stallinga, S. & Rieger, B. Accuracy of the Gaussian point spread function model in 2D localization microscopy. Opt. Express 18, 24461–24476 (2010).
Howes, P. D., Chandrawati, R. & Stevens, M. M. Colloidal nanoparticles as advanced biological sensors. Science 346, 1247390 (2014).
Zhang, P., Lee, S., Yu, H., Fang, N. & Kang, S. H. Super-resolution of fluorescence-free plasmonic nanoparticles using enhanced dark-field illumination based on wavelength-modulation. Sci. Rep. 5, 11447 (2015).
Petersen, J., Volz, J. & Rauschenbeutel, A. Chiral nanophotonic waveguide interface based on spin–orbit interaction of light. Science 346, 67–71 (2014).
Yildiz, A. et al. Myosin V walks hand-over-hand: single fluorophore imaging with 1.5-nm localization. Science 300, 2061–2065 (2003).
Small, A. R. & Parthasarathy, R. Superresolution localization methods. Annu. Rev. Phys. Chem. 65, 107–125 (2014).
Bakr, W. S., Gillen, J. I., Peng, A., Folling, S. & Greiner, M. A quantum gas microscope for detecting single atoms in a Hubbard-regime optical lattice. Nature 462, 74–77 (2009).
Lee, J.-S. & Pottier, E. Polarimetric Radar Imaging: From Basics to Applications (CRC Press, Boca Raton, 2009).
Hayes, M. P. & Gough, P. T. Synthetic aperture sonar: a review of current status. IEEE J. Ocean. Eng. 34, 207–224 (2009).
Abbott, B. P. et al. Search for post-merger gravitational waves from the remnant of the binary neutron star merger GW170817. Astrophys. J. Lett. 851, L16 (2017).
Bialynicki-Birula, I. & Bialynicka-Birula, Z. Gravitational waves carrying orbital angular momentum. New J. Phys. 18, 023022 (2016).
James, D. Quantum dynamics of cold trapped ions with application to quantum computation. Appl. Phys. B 66, 181–190 (1998).
Bobroff, N. Position measurement with a resolution and noise-limited instrument. Rev. Sci. Instrum. 57, 1152–1157 (1986).
Acknowledgements
The authors thank P. Obšil for experimental support, and J. Enderlein, M. Hush and A. Jesacher for helpful discussions. This work was supported by the Austrian Science Fund (FWF, SINPHONIA project P23022, SFB FoQuS F4001, SFB NextLite F4908), by the European Research Council through project CRYTERION #227959, by the Institut für Quanteninformation GmbH and by the Australian Research Council through project CE170100012.
Author information
Authors and Affiliations
Contributions
J.V. and A.R. proposed the concept. All authors contributed to the design and the setting up of the experiments (atom experiment: G.A., Y.C., D.B.H. and R.B.; nanoparticle experiment: S.W., J.V. and A.R.). G.A. and D.B.H. performed the atom experiment and analysed the data. S.W. performed the nanoparticle experiment and analysed the data. All authors contributed to the writing of the manuscript.
Corresponding authors
Ethics declarations
Competing interests
The authors declare no competing interests.
Additional information
Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary information
Supplementary Information
Supplementary notes, figures and references
Rights and permissions
About this article
Cite this article
Araneda, G., Walser, S., Colombe, Y. et al. Wavelength-scale errors in optical localization due to spin–orbit coupling of light. Nature Phys 15, 17–21 (2019). https://doi.org/10.1038/s41567-018-0301-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1038/s41567-018-0301-y
This article is cited by
-
Dynamical and topological properties of the spin angular momenta in general electromagnetic fields
Communications Physics (2023)
-
Photoelectronic mapping of the spin–orbit interaction of intense light fields
Nature Photonics (2021)
-
Atomic scale displacements detected by optical image cross-correlation analysis and 3D printed marker arrays
Scientific Reports (2021)
-
Fabrication of optical nanofibre-based cavities using focussed ion-beam milling: a review
Applied Physics B (2020)