Wavelength-scale errors in optical localization due to spin–orbit coupling of light


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.

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Fig. 1: Polarization-dependent displacement.
Fig. 2: Experimental set-ups.
Fig. 3: Apparent displacement of the emitters.

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.


  1. 1.

    Boas, D. A., Pitris, C. & Ramanujam, N. Handbook of Biomedical Optics (CRC Press, Boca Raton, 2011).

  2. 2.

    Kovalevsky, J. & Seidelmann, P. K. Fundamentals of Astrometry (Cambridge Univ. Press, Cambridge, 2004).

  3. 3.

    Novotny, L. & Hecht, B. Principles of Nano-Optics (Cambridge Univ. Press, Cambridge, 2006).

  4. 4.

    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).

    ADS  Article  Google Scholar 

  5. 5.

    Hell, S. W. Far-field optical nanoscopy. Science 316, 1153–1158 (2007).

    ADS  Article  Google Scholar 

  6. 6.

    Alberti, A. et al. Super-resolution microscopy of single atoms in optical lattices. New J. Phys. 18, 053010 (2016).

    ADS  Article  Google Scholar 

  7. 7.

    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).

    ADS  Article  Google Scholar 

  8. 8.

    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).

    ADS  Article  Google Scholar 

  9. 9.

    Thompson, R. E., Larson, D. R. & Webb, W. W. Precise nanometer localization analysis for individual fluorescent probes. Biophys. J. 82, 2775–2783 (2002).

    Article  Google Scholar 

  10. 10.

    Enderlein, J., Toprak, E. & Selvin, P. R. Polarization effect on position accuracy of fluorophore localization. Opt. Express 14, 8111–8120 (2006).

    ADS  Article  Google Scholar 

  11. 11.

    Engelhardt, J. et al. Molecular orientation affects localization accuracy in superresolution far-field fluorescence microscopy. Nano Lett. 11, 209–213 (2011).

    ADS  Article  Google Scholar 

  12. 12.

    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).

    ADS  Article  Google Scholar 

  13. 13.

    Lew, M. D. & Moerner, W. E. Azimuthal polarization filtering for accurate, precise, and robust single-molecule localization microscopy. Nano Lett. 14, 6407–6413 (2014).

    ADS  Article  Google Scholar 

  14. 14.

    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).

    ADS  Article  Google Scholar 

  15. 15.

    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).

    Article  Google Scholar 

  16. 16.

    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).

    ADS  Article  Google Scholar 

  17. 17.

    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).

    ADS  Article  Google Scholar 

  18. 18.

    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).

    ADS  Article  Google Scholar 

  19. 19.

    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).

    ADS  Article  Google Scholar 

  20. 20.

    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).

    ADS  Article  Google Scholar 

  21. 21.

    Schwartz, C. & Dogariu, A. Conservation of angular momentum of light in single scattering. Opt. Express 14, 8425–8433 (2006).

    ADS  Article  Google Scholar 

  22. 22.

    Bliokh, K. Y., Rodrguez-Fortuno, F. J., Nori, F. & Zayats, A. V. Spin–orbit interactions of light. Nat. Photon. 9, 796–808 (2016).

    ADS  Article  Google Scholar 

  23. 23.

    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).

    ADS  Article  Google Scholar 

  24. 24.

    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).

    ADS  Article  Google Scholar 

  25. 25.

    Lodahl, P. et al. Chiral quantum optics. Nature 541, 473–480 (2017).

    ADS  Article  Google Scholar 

  26. 26.

    Li, X. & Arnoldus, H. F. Macroscopic far-field observation of the sub-wavelength near-field dipole vortex. Phys. Lett. A 374, 1063–1067 (2010).

    ADS  Article  Google Scholar 

  27. 27.

    Darwin, C. G. Notes on the theory of radiation. Proc. Roy. Soc. A 136, 36–52 (1932).

    ADS  Article  Google Scholar 

  28. 28.

    Bekshaev, A. Y., Bliokh, K. Y. & Nori, F. Transverse spin and momentum in two-wave interference. Phys. Rev. X 5, 011039 (2015).

    Google Scholar 

  29. 29.

    Berry, M. V. Optical currents. J. Opt. A: Pure Appl. Opt. 11, 094001 (2009).

    ADS  Article  Google Scholar 

  30. 30.

    Knee, G. C., Combes, J., Ferrie, C. & Gauger, E. M. Weak-value amplification: state of play. Quantum Meas. Quantum Metrol. 3, 32–37 (2016).

    Google Scholar 

  31. 31.

    Stallinga, S. & Rieger, B. Accuracy of the Gaussian point spread function model in 2D localization microscopy. Opt. Express 18, 24461–24476 (2010).

    ADS  Article  Google Scholar 

  32. 32.

    Howes, P. D., Chandrawati, R. & Stevens, M. M. Colloidal nanoparticles as advanced biological sensors. Science 346, 1247390 (2014).

    Article  Google Scholar 

  33. 33.

    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).

    ADS  Article  Google Scholar 

  34. 34.

    Petersen, J., Volz, J. & Rauschenbeutel, A. Chiral nanophotonic waveguide interface based on spin–orbit interaction of light. Science 346, 67–71 (2014).

    ADS  Article  Google Scholar 

  35. 35.

    Yildiz, A. et al. Myosin V walks hand-over-hand: single fluorophore imaging with 1.5-nm localization. Science 300, 2061–2065 (2003).

    ADS  Article  Google Scholar 

  36. 36.

    Small, A. R. & Parthasarathy, R. Superresolution localization methods. Annu. Rev. Phys. Chem. 65, 107–125 (2014).

    ADS  Article  Google Scholar 

  37. 37.

    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).

    ADS  Article  Google Scholar 

  38. 38.

    Lee, J.-S. & Pottier, E. Polarimetric Radar Imaging: From Basics to Applications (CRC Press, Boca Raton, 2009).

  39. 39.

    Hayes, M. P. & Gough, P. T. Synthetic aperture sonar: a review of current status. IEEE J. Ocean. Eng. 34, 207–224 (2009).

    ADS  Article  Google Scholar 

  40. 40.

    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).

    ADS  Article  Google Scholar 

  41. 41.

    Bialynicki-Birula, I. & Bialynicka-Birula, Z. Gravitational waves carrying orbital angular momentum. New J. Phys. 18, 023022 (2016).

    ADS  Article  Google Scholar 

  42. 42.

    James, D. Quantum dynamics of cold trapped ions with application to quantum computation. Appl. Phys. B 66, 181–190 (1998).

    ADS  Article  Google Scholar 

  43. 43.

    Bobroff, N. Position measurement with a resolution and noise-limited instrument. Rev. Sci. Instrum. 57, 1152–1157 (1986).

    ADS  Article  Google Scholar 

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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.

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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.

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Correspondence to G. Araneda or J. Volz or A. Rauschenbeutel.

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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

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