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Deep-subwavelength features of photonic skyrmions in a confined electromagnetic field with orbital angular momentum

Nature Physics volume 15, pages 650–654 (2019)Cite this article

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Abstract

In magnetic materials, skyrmions are nanoscale regions where the orientation of the electron spin changes in a vortex-type manner1,2,3,4. Electromagnetic waves carry both spin and orbital angular momenta5,6. Here we show that spin–orbit coupling7,8,9,10,11,12 in a focused vector beam results in a skyrmion-like structure of local photonic spin. While diffraction limits the spatial size of intensity variations, the direction of the electromagnetic field, which defines the polarization and local photonic spin state, is not subject to this limitation. We demonstrate that the local spin direction in the skyrmion-like structure varies on the deep-subwavelength scale down to 1/60 of the light wavelength, which corresponds to a length scale of about 10 nm. The application of photonic skyrmions may range from high-resolution imaging and precision metrology to quantum technologies and data storage where the local spin state of the field, not its intensity, can be applied to achieve deep-subwavelength optical patterns.

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Fig. 1: Spin vector structure of the evanescent field vortex forming the Neel-type photonic skyrmion.
Fig. 2: Energy flux and local spin vector orientation in an evanescent vortex.
Fig. 3: Local spin structure of a plasmonic vortex.
Fig. 4: Deep-subwavelength features in the local photonic spin structure.

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The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

References

  1. Rossler, U. K., Bogdanov, A. N. & Pfleiderer, C. Spontaneous skyrmion ground states in magnetic metals. Nature 442, 797–801 (2006).

    Article  ADS  Google Scholar 

  2. Muhlbauer, S. et al. Skyrmion lattice in a chiral magnet. Science 323, 915–919 (2009).

    Article  ADS  Google Scholar 

  3. Yu, X. Z. et al. Real-space observation of a two-dimensional skyrmion crystal. Nature 465, 901–904 (2010).

    Article  ADS  Google Scholar 

  4. Heinze, S. et al. Spontaneous atomic-scale magnetic skyrmion lattice in two dimensions. Nat. Phys. 7, 713–718 (2011).

    Article  Google Scholar 

  5. Poynting, J. H. The wave motion of a revolving shaft, and a suggestion as to the angular momentum in a beam of circularly polarised light. Proc. R. Soc. Lond. A 82, 560–567 (1909).

    Article  ADS  Google Scholar 

  6. Allen, L., Beijersbergen, M. W., Spreeuw, R. J. C. & Woerdman, J. P. Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes. Phys. Rev. A 45, 8185–8189 (1992).

    Article  ADS  Google Scholar 

  7. Bliokh, K. Y., Rodriguez-Fortuno, F. J., Nori, F. & Zayats, A. V. Spin–orbit interactions of light. Nat. Photon. 9, 796–808 (2015).

    Article  ADS  Google Scholar 

  8. Milione, G., Sztul, H. I., Nolan, D. A. & Alfano, R. R. Higher-order Poincare sphere, Stokes parameters, and the angular momentum of light. Phys. Rev. Lett. 107, 053601 (2011).

    Article  ADS  Google Scholar 

  9. Zhao, Y., Edgar, J. S., Jeffries, G. D. M., McGloin, D. & Chiu, D. T. Spin-to-orbital angular momentum conversion in a strongly focused optical beam. Phys. Rev. Lett. 99, 073901 (2007).

    Article  ADS  Google Scholar 

  10. Vuong, L. T., Adam, A. J. L., Brok, J. M., Planken, P. C. M. & Urbach, H. P. Electromagnetic spin–orbit interactions via scattering of subwavelength apertures. Phys. Rev. Lett. 104, 083903 (2010).

    Article  ADS  Google Scholar 

  11. Bliokh, K. Y. et al. Spin-to-orbital angular momentum conversion in focusing, scattering, and imaging systems. Opt. Express 19, 26132–26149 (2011).

    Article  ADS  Google Scholar 

  12. Cardano, F., Karimi, E., Marrucci, L., de Lisio, C. & Santamato, E. Generation and dynamics of optical beams with polarization singularities. Opt. Express 21, 8815–8820 (2013).

    Article  ADS  Google Scholar 

  13. Marrucci, L. Generation of helical modes of light by spin-to-orbital angular momentum conversion in inhomogeneous liquid crystals. Mol. Cryst. Liq. Cryst. 488, 148–162 (2008).

    Article  Google Scholar 

  14. Tischler, N. et al. Experimental control of optical helicity in nanophotonics. Light Sci. Appl. 3, e183 (2014).

    Article  Google Scholar 

  15. Hao, X., Kuang, C., Wang, T. & Liu, X. Phase encoding for sharper focus of the azimuthally polarized beam. Opt. Lett. 35, 3928–3930 (2010).

    Article  ADS  Google Scholar 

  16. Padgett, M. & Bowman, R. Tweezers with a twist. Nat. Photon. 5, 343–348 (2011).

    Article  ADS  Google Scholar 

  17. Du, L. et al. Broadband chirality-coded meta-aperture for photon-spin resolving. Nat. Commun. 6, 10051 (2015).

    Article  ADS  Google Scholar 

  18. Bliokh, K. Y. & Nori, F. Transverse spin of a surface polariton. Phys. Rev. A 85, 061801 (2012).

    Article  ADS  Google Scholar 

  19. Bliokh, K. Y., Bekshaev, A. Y. & Nori, F. Extraordinary momentum and spin in evanescent waves. Nat. Commun. 5, 3300 (2014).

    Article  ADS  Google Scholar 

  20. Bliokh, K. Y., Smirnova, D. & Nori, F. Quantum spin Hall effect of light. Science 348, 1448–1451 (2015).

    Article  ADS  MathSciNet  Google Scholar 

  21. Aiello, A., Banzer, P., Neugebaueru, M. & Leuchs, G. From transverse angular momentum to photonic wheels. Nat. Photon. 9, 789–795 (2015).

    Article  ADS  Google Scholar 

  22. Padgett, M., Courtial, J. & Allen, L. Light’s orbital angular momentum. Phys. Today 57, 35–40 (2004).

    Article  ADS  Google Scholar 

  23. Kezsmarki, I. et al. Neel-type skyrmion lattice with confined orientation in the polar magnetic semiconductor GaV4S8. Nat. Mater. 14, 1116 (2015).

    Article  ADS  Google Scholar 

  24. Barnes, W. L., Dereux, A. & Ebbesen, T. W. Surface plasmon subwavelength optics. Nature 424, 824–830 (2003).

    Article  ADS  Google Scholar 

  25. Kim, H. et al. Synthesis and dynamic switching of surface plasmon vortices with plasmonic vortex lens. Nano Lett. 10, 529–536 (2010).

    Article  ADS  Google Scholar 

  26. Lindfors, K. et al. Local polarization of tightly focused unpolarized light. Nat. Photon. 1, 228–231 (2007).

    Article  ADS  Google Scholar 

  27. Wang, X.-L. et al. Optical orbital angular momentum from the curl of polarization. Phys. Rev. Lett. 105, 253602 (2010).

    Article  ADS  Google Scholar 

  28. Bauer, T., Orlov, S., Peschel, U., Banzer, P. & Leuchs, G. Nanointerferometric amplitude and phase reconstruction of tightly focused vector beams. Nat. Photon. 8, 24–28 (2014).

    Article  ADS  Google Scholar 

  29. Neugebauer, M., Bauer, T., Aiello, A. & Banzer, P. Measuring the transverse spin density of light. Phys. Rev. Lett. 114, 063901 (2015).

    Article  ADS  Google Scholar 

  30. Yang, A. P., Du, L. P., Meng, F. F. & Yuan, X. C. Optical transverse spin coupling through a plasmonic nanoparticle for particle-identification and field-mapping. Nanoscale 10, 9286–9291 (2018).

    Article  Google Scholar 

  31. Zhan, Q. Cylindrical vector beams: from mathematical concepts to applications. Adv. Opt. Photon. 1, 1–57 (2009).

    Article  Google Scholar 

  32. Tsesses, S. et al. Optical skyrmion lattice in evanescent electromagnetic fields. Science 361, 993–996 (2018).

    Article  ADS  MathSciNet  Google Scholar 

  33. Ishimaru, A. Electromagnetic Wave Propagation, Radiation, and Scattering: From Fundamentals to Applications 2nd edn (Wiley-IEEE Press, 2017).

  34. Wolf, E. Electromagnetic diffraction in optical systems - I. An integral representation of the image field. Proc. R. Soc. Lond. A 253, 349–357 (1959).

    Article  ADS  MathSciNet  Google Scholar 

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Acknowledgements

This work was supported, in part, by the National Natural Science Foundation of China grants 61622504, 61427819, 61490712 and 11504244, the National Key Basic Research Program of China (973) grant 2015CB352004, the leadership of Guangdong province program grant 00201505, the Natural Science Foundation of Guangdong Province grant 2016A030312010, the Science and Technology Innovation Commission of Shenzhen grants KQTD2015071016560101, KQTD2017033011044403 and ZDSYS201703031605029, the EPSRC (UK) and the ERC iCOMM project (789340). A.V.Z. acknowledges support from the Royal Society and the Wolfson Foundation. L.D. acknowledges the support given by the Guangdong Special Support Program. L.D. thanks S. Peng for assistance with the theoretical analysis.

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Authors and Affiliations

  1. Nanophotonics Research Centre, Shenzhen Key Laboratory of Micro-Scale Optical Information Technology, Shenzhen University, Guangdong Sheng, China

    Luping Du, Aiping Yang & Xiaocong Yuan

  2. Department of Physics and London Centre for Nanotechnology, King’s College London, London, UK

    Anatoly V. Zayats

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  1. Luping Du
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Contributions

L.D. and A.V.Z. developed the concept. L.D. carried out the analytical and numerical modelling. L.D. and X.Y. designed the experiment. A.Y. performed the experiments. L.D., X.Y. and A.V.Z. wrote the manuscript. L.D., X.Y. and A.V.Z. supervised the work. All the authors discussed the results and commented on the manuscript.

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Correspondence to Luping Du, Anatoly V. Zayats or Xiaocong Yuan.

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Du, L., Yang, A., Zayats, A.V. et al. Deep-subwavelength features of photonic skyrmions in a confined electromagnetic field with orbital angular momentum. Nat. Phys. 15, 650–654 (2019). https://doi.org/10.1038/s41567-019-0487-7

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