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From transverse angular momentum to photonic wheels

Nature Photonics volume 9, pages 789–795 (2015)Cite this article

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Abstract

Scientists have known for more than a century that light possesses both linear and angular momenta along the direction of propagation. However, only recent advances in optics have led to the notion of spinning electromagnetic fields capable of carrying angular momenta transverse to the direction of motion. Such fields enable numerous applications in nano-optics, biosensing and near-field microscopy, including three-dimensional control over atoms, molecules and nanostructures, and allowing for the realization of chiral nanophotonic interfaces and plasmonic devices. Here, we report on recent developments of optics with light carrying transverse spin. We present both the underlying principles and the latest achievements, and also highlight new capabilities and future applications emerging from this young yet already advanced field of research.

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Figure 1: Comparison of electric-field configurations that generate longitudinal and transverse SAM.
Figure 2: Common field distributions with transverse SAM densities.
Figure 3: Near-fields of a transversely spinning dipole.
Figure 4: Examples of nanoprobing techniques for measuring transversely spinning (electric) fields.

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References

  1. Marcuvitz, N. Waveguide Handbook 1st edn (McGraw-Hill 1951).

    Google Scholar 

  2. Novotny, L. & Hecht, B. Principles of Nano-optics 2nd edn (Cambridge Univ. Press, 2013).

    Google Scholar 

  3. Richards, B. & Wolf, E. Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system. Proc. R. Soc. Lond. A 253, 358–379 (1959).

    Article  ADS  Google Scholar 

  4. Barnett, S. M. Optical angular-momentum flux. J. Opt. B 4, S7 (2002).

    Article  ADS  Google Scholar 

  5. Berry, M. V. Optical currents. J. Opt. A 11, 094001 (2009).

    Article  ADS  Google Scholar 

  6. Bliokh, K. Y., Alonso, M. A., Ostrovskaya, E. A. & Aiello, A. Angular momenta and spin-orbit interaction of nonparaxial light in free space. Phys. Rev. A 82, 063825 (2010).

    Article  ADS  Google Scholar 

  7. Cameron, R. P., Barnett, S. M. & Yao, A. M. Optical helicity, optical spin and related quantities in electromagnetic theory. New J. Phys. 14, 053050 (2012).

    Article  ADS  Google Scholar 

  8. Liberman, V. S. & Zel'dovich, B. Y. Spin-orbit interaction of a photon in an inhomogeneous medium. Phys. Rev. A 46, 5199–5207 (1992).

    Article  ADS  Google Scholar 

  9. Onoda, M., Murakami, S. & Nagaosa, N. Hall effect of light. Phys. Rev. Lett. 93, 083901 (2004).

    Article  ADS  Google Scholar 

  10. Bliokh, K. Y. & Bliokh, Y. P. Conservation of angular momentum, transverse shift, and spin Hall effect in reflection and refraction of an electromagnetic wave packet. Phys. Rev. Lett. 96, 073903 (2006).

    Article  ADS  Google Scholar 

  11. Bliokh, K. Y. & Bliokh, Y. P. Polarization, transverse shifts, and angular momentum conservation laws in partial reflection and refraction of an electromagnetic wave packet. Phys. Rev. E 75, 066609 (2007).

    Article  ADS  Google Scholar 

  12. Hosten, O. & Kwiat, P. Observation of the spin Hall effect of light via weak measurements. Science 319, 787–790 (2008).

    Article  ADS  Google Scholar 

  13. Aiello, A. & Woerdman, J. P. Role of beam propagation in Goos–Hänchen and Imbert–Fedorov shifts. Opt. Lett. 33, 1437–1439 (2008).

    Article  ADS  Google Scholar 

  14. Bliokh, K. Y., Niv, A., Kleiner, V. & Hasman, E. Geometrodynamics of spinning light. Nature Photon. 2, 748–753 (2008).

    Article  ADS  Google Scholar 

  15. Fedoseyev, V. G. Transformation of the orbital angular momentum at the reflection and transmission of a light beam on a plane interface. J. Phys. A 41, 505202 (2008).

    Article  MathSciNet  Google Scholar 

  16. Bliokh, K. Y., Shadrivov, I. V. & Kivshar, Y. S. Goos–Hänchen and Imbert–Fedorov shifts of polarized vortex beams. Opt. Lett. 34, 389–391 (2009).

    Article  ADS  Google Scholar 

  17. Bliokh, K. Y., Aiello, A. & Alonso, M. A. Spin-orbit Interactions of Light in Isotropic Media Ch. 8, 174–245 (Cambridge Univ. Press, 2012).

    Google Scholar 

  18. Altland, A. & Simons, B. Condensed Matter Field Theory 2nd edn (Cambridge Univ. Press, 1996).

    MATH  Google Scholar 

  19. Aiello, A., Lindlein, N., Marquardt, C. & Leuchs, G. Transverse angular momentum and geometric spin Hall effect of light. Phys. Rev. Lett. 103, 100401 (2009).

    Article  ADS  Google Scholar 

  20. Aiello, A., Marquardt, C. & Leuchs, G. Transverse angular momentum of photons. Phys. Rev. A 81, 053838 (2010).

    Article  ADS  Google Scholar 

  21. Bekshaev, A. Y. Oblique section of a paraxial light beam: criteria for azimuthal energy flow and orbital angular momentum. J. Opt. A 11, 094003 (2009).

    Article  ADS  Google Scholar 

  22. Bekshaev, A., Bliokh, K. Y. & Soskin, M. Internal flows and energy circulation in light beams. J. Opt. 13, 053001 (2011).

    Article  ADS  Google Scholar 

  23. Huard, S. & Vigoureux, J. M. Mise en evidence de la polarisation d'une onde de surface par absorption atomique. Opt. Commun. 25, 5–8 (1978).

    Article  ADS  Google Scholar 

  24. Risset, C.-A. A complete basis of evanescent plane waves. Opt. Commun. 104, 7–12 (1993).

    Article  ADS  Google Scholar 

  25. Józefowski, L., Fiutowski, J., Kawalec, T. & Rubahn, H.-G. Direct measurement of the evanescent-wave polarization state. J. Opt. Soc. Am. B 24, 624–628 (2007).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  27. Kim, K.-Y., Lee, I.-M., Kim, J., Jung, J. & Lee, B. Time reversal and the spin angular momentum of transverse-electric and transverse-magnetic surface modes. Phys. Rev. A 86, 063805 (2012).

    Article  ADS  Google Scholar 

  28. Neugebauer, M. et al. Experimental demonstration of the geometric spin Hall effect of light in highly focused vector beams in Conference on Lasers and Electro-Optics QW1E.4 (OSA, 2012).

    Google Scholar 

  29. Banzer, P. et al. The photonic wheel-demonstration of a state of light with purely transverse angular momentum. J. Eur. Opt. Soc. Rap. Publ. 8, 13032 (2013).

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Google Scholar 

  32. Mueller, J. P. B. & Capasso, F. Asymmetric surface plasmon polariton emission by a dipole emitter near a metal surface. Phys. Rev. B 88, 121410 (2013).

    Article  ADS  Google Scholar 

  33. Junge, C., O'Shea, D., Volz, J. & Rauschenbeutel, A. Strong coupling between single atoms and nontransversal photons. Phys. Rev. Lett. 110, 213604 (2013).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  35. O'Connor, D., Ginzburg, P., Rodríguez-Fortuño, F. J., Wurtz, G. A. & Zayats, A. V. Spin–orbit coupling in surface plasmon scattering by nanostructures. Nature Commun. 5, 5327 (2014).

    Article  ADS  Google Scholar 

  36. Rodríguez-Fortuño, F. J. et al. Near-field interference for the unidirectional excitation of electromagnetic guided modes. Science 340, 328–330 (2013).

    Article  ADS  Google Scholar 

  37. Rodríguez-Fortuño, F. J. et al. Universal method for the synthesis of arbitrary polarization states radiated by a nanoantenna. Las. Photon. Rev. 8, L27–L31 (2014).

    Article  Google Scholar 

  38. Neugebauer, M., Bauer, T., Banzer, P. & Leuchs, G. Polarization tailored light driven directional optical nanobeacon. Nano Lett. 14, 2546–2551 (2014).

    Article  ADS  Google Scholar 

  39. Bauer, T., Orlov, S., Peschel, U., Banzer, P. & Leuchs, G. Nanointerferometric amplitude and phase reconstruction of tightly focused vector beams. Nature Photon. 8, 23–27 (2014).

    Article  ADS  Google Scholar 

  40. 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 

  41. Canaguier-Durand, A., Cuche, A., Genet, C. & Ebbesen, T. W. Force and torque on an electric dipole by spinning light fields. Phys. Rev. A 88, 033831 (2013).

    Article  ADS  Google Scholar 

  42. Canaguier-Durand, A. & Genet, C. Transverse spinning of a sphere in a plasmonic field. Phys. Rev. A 89, 033841 (2014).

    Article  ADS  Google Scholar 

  43. Canaguier-Durand, A. & Genet, C. Chiral near fields generated from plasmonic optical lattices. Phys. Rev. A 90, 023842 (2014).

    Article  ADS  Google Scholar 

  44. Mathevet, R. & Rikken, G. L. J. A. Magnetic circular dichroism as a local probe of the polarization of a focused Gaussian beam. Opt. Mater. Express 4, 2574–85 (2014).

    Article  ADS  Google Scholar 

  45. Yang, N. & Cohen, A. E. Local geometry of electromagnetic fields and its role in molecular multipole transitions. J. Phys. Chem. B 115, 5304–5311 (2011).

    Article  Google Scholar 

  46. Dennis, M. R., O'Holleran, K. & Padgett, M. J. Singular optics: Optical vortices and polarization singularities. Prog. Opt. 53, 293–363 (2009).

    Article  ADS  Google Scholar 

  47. Freund, I., Soskin, M. S. & Mokhun, A. I. Elliptic critical points in paraxial optical fields. Opt. Commun. 208, 223–253 (2002).

    Article  ADS  Google Scholar 

  48. 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 

  49. 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 

  50. Cameron, R. P. & Barnett, S. M. Electric–magnetic symmetry and Noether's theorem. New J. Phys. 14, 123019 (2012).

    Article  ADS  MathSciNet  Google Scholar 

  51. Bliokh, K. Y., Bekshaev, A. Y. & Nori, F. Dual electromagnetism: Helicity, spin, momentum and angular momentum. New J. Phys. 15, 033026 (2013).

    Article  ADS  Google Scholar 

  52. Lipkin, D. M. Existence of a new conservation law in electromagnetic theory. J. Math. Phys. 5, 696–700 (1964).

    Article  ADS  MathSciNet  Google Scholar 

  53. Bliokh, K. Y., Dressel, J. & Nori, F. Conservation of the spin and orbital angular momenta in electromagnetism. New J. Phys. 16, 093037 (2014).

    Article  ADS  Google Scholar 

  54. O'Neil, A. T., MacVicar, I., Allen, L. & Padgett, M. J. Intrinsic and extrinsic nature of the orbital angular momentum of a light beam. Phys. Rev. Lett. 88, 053601 (2002).

    Article  ADS  Google Scholar 

  55. Garcés-Chávez, V. et al. Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle. Phys. Rev. Lett. 91, 093602 (2003).

    Article  ADS  Google Scholar 

  56. Piccirillo, B. & Santamato, E. Light angular momentum flux and forces in birefringent inhomogeneous media. Phys. Rev. E 69, 056613 (2004).

    Article  ADS  Google Scholar 

  57. Berry, M. V. Paraxial beams of spinning light in Singular Optics (ed. Soskin, M. S.) 3487, 6–11 (SPIE, 1998).

    Google Scholar 

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

    Article  ADS  Google Scholar 

  59. Bialynicki-Birula, I. & Bialynicka-Birula, Z. Canonical separation of angular momentum of light into its orbital and spin parts. J. Opt. 13, 064014 (2011).

    Article  ADS  Google Scholar 

  60. Leader, E. & Lorc, C. The angular momentum controversy: What's it all about and does it matter? Phys. Rep. 541, 163–248 (2014).

    Article  ADS  MathSciNet  Google Scholar 

  61. Uehara, M. On the helicity of an elliptically polarized electromagnetic wave. Am. J. Phys. 56, 942–943 (1988).

    Article  ADS  Google Scholar 

  62. Axelrod, D., Burghardt, T. P. & Thompson, N. L. Total internal reflection fluorescence. Ann. Rev. Biophys. Bioeng. 13, 247–268 (1984).

    Article  Google Scholar 

  63. Kawalec, T., Józefowskia, L., Fiutowski, J., Kasprowicz, M. & Dohnalik, T. Spectroscopic measurements of the evanescent wave polarization state. Opt. Commun. 274, 341–346 (2007).

    Article  ADS  Google Scholar 

  64. Aiello, A. & Banzer, P. Transverse spin of light for all wavefields. Preprint at http://arxiv.org/abs/1502.05350 (2015).

  65. Mandel, L. & Wolf, E. Optical Coherence and Quantum Optics (Cambridge Univ. Press, 1995).

    Book  Google Scholar 

  66. Winnerl, S., Hubrich, R., Mittendorff, M., Schneider, H. & Helm, M. Universal phase relation between longitudinal and transverse fields observed in focused terahertz beams. New J. Phys. 14, 103049 (2012).

    Article  ADS  Google Scholar 

  67. le Feber, B., Rotenberg, N. & Kuipers, L. Nanophotonic control of circular dipole emission. Nature Commun. 6, 6695 (2015).

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  69. Lee, S.-Y. et al. Role of magnetic induction currents in nanoslit excitation of surface plasmon polaritons. Phys. Rev. Lett. 108, 213907 (2012).

    Article  ADS  Google Scholar 

  70. Rodríguez-Fortuño, F. J., Barber-Sanz, I., Puerto, D., Griol, A. & Martinez, A. Resolving light handedness with an on-chip silicon microdisk. ACS Photonics 1, 762–767 (2014).

    Article  Google Scholar 

  71. Lefier, Y. & Grosjean, T. Unidirectional sub-diffraction waveguiding based on optical spin-orbit coupling in subwavelength plasmonic waveguides. Opt. Lett. 40, 2890–2893 (2015).

    Article  ADS  Google Scholar 

  72. Pichler, H., Ramos, T., Daley, A. J. & Zoller, P. Quantum optics of chiral spin networks. Phys. Rev. A 91, 042116 (2015).

    Article  ADS  Google Scholar 

  73. Mitsch, R., Sayrin, C., Albrecht, B., Schneeweiss, P. & Rauschenbeutel, A. Quantum state-controlled directional spontaneous emission of photons into a nanophotonic waveguide. Nature Commun. 5, 5713 (2014).

    Article  ADS  Google Scholar 

  74. Söllner, I. et al. Deterministic photon–emitter coupling in chiral photonic circuits. Nature Nanotechnol. 10, 775–778 (2015).

    Article  ADS  Google Scholar 

  75. Rotenberg, N. & Kuipers, L. Mapping nanoscale light fields. Nature Photon. 8, 919–926 (2014).

    Article  ADS  Google Scholar 

  76. Lee, K. G. et al. Vector field microscopic imaging of light. Nature Photon. 1, 53–56 (2007).

    Article  ADS  Google Scholar 

  77. 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).

    Article  ADS  Google Scholar 

  78. Neugebauer, M. et al. Geometric spin Hall effect of light in tightly focused polarization-tailored light beams. Phys. Rev. A 89, 013840 (2014).

    Article  ADS  Google Scholar 

  79. Lin, J. et al. Polarization-controlled tunable directional coupling of surface plasmon polaritons. Science 340, 331–334 (2013).

    Article  ADS  Google Scholar 

  80. Shitrit, N. et al. Spin-optical metamaterial route to spin-controlled photonics. Science 340, 724–726 (2013).

    Article  ADS  MathSciNet  Google Scholar 

  81. Kapitanova, P. V. et al. Photonic spin Hall effect in hyperbolic metamaterials for polarization-controlled routing of subwavelength modes. Nature Commun. 5, 3226 (2014).

    Article  ADS  Google Scholar 

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Acknowledgements

P.B. acknowledges a Feodor Lynen fellowship awarded by the Alexander von Humboldt Foundation and financial support by the Canada Excellence Research Chair (CERC) in Quantum Nonlinear Optics.

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Authors and Affiliations

  1. Max Planck Institute for the Science of Light, Guenther-Scharowsky-Str. 1, Erlangen, D-91058, Germany

    Andrea Aiello, Peter Banzer, Martin Neugebauer & Gerd Leuchs

  2. Institute of Optics, Information and Photonics, University Erlangen-Nuremberg, Staudtstr. 7/B2, Erlangen, D-91058, Germany

    Andrea Aiello, Peter Banzer, Martin Neugebauer & Gerd Leuchs

  3. Department of Physics, University of Ottawa, 25 Templeton, Ottawa, K1N 6N5, Ontario, Canada

    Peter Banzer & Gerd Leuchs

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Correspondence to Peter Banzer.

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Aiello, A., Banzer, P., Neugebauer, M. et al. From transverse angular momentum to photonic wheels. Nature Photon 9, 789–795 (2015). https://doi.org/10.1038/nphoton.2015.203

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