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Geometrodynamics of spinning light

Nature Photonics volume 2, pages 748–753 (2008)Cite this article

Abstract

The semiclassical evolution of spinning particles has recently been re-examined in condensed matter physics, high-energy physics, and optics, resulting in the prediction of the intrinsic spin Hall effect associated with the Berry phase. A fundamental origin of this effect is related to the spin–orbit interaction and topological monopoles. Here, we report a unified theory and a direct observation of two mutual phenomena: a spin-dependent deflection (the spin Hall effect) of photons and the precession of the Stokes vector along the coiled ray trajectory of classical geometrical optics. Our measurements are in perfect agreement with theoretical predictions, thereby verifying the dynamical action of the topological Berry-phase monopole in the evolution of light. These results may have promising applications in nano-optics and can be immediately extrapolated to the evolution of massless particles in a variety of physical systems.

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Figure 1: Spin–orbit interaction of photons—the Berry phase and spin Hall effect—on a helical light trajectory.
Figure 2: Representations of the evolution of the wave polarization along a helical ray trajectory.
Figure 3: Experimental setup.
Figure 4: Experimental measurements of Stokes vector precession and the spin Hall effect of light.

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References

  1. Berry, M. V. Quantal phase-factors accompanying adiabatic changes. Proc. R. Soc. A 392, 45–57 (1984).

    Article  ADS  MathSciNet  Google Scholar 

  2. Shapere, A. & Wilczek, F. (eds) Geometric Phases in Physics (World Scientific, 1989).

    MATH  Google Scholar 

  3. Littlejohn, R. G. & Flynn, W. G. Geometric phases in the asymptotic theory of coupled wave-equations. Phys. Rev. A 44, 5239–5256 (1991).

    Article  ADS  MathSciNet  Google Scholar 

  4. Sundaram, G. & Niu, Q. Wave-packet dynamics in slowly perturbed crystals: Gradient corrections and Berry-phase effects. Phys. Rev. B 59, 14915–14925 (1999).

    Article  ADS  Google Scholar 

  5. Fang, Z. et al. The anomalous Hall effect and magnetic monopoles in momentum space. Science 302, 92–95 (2003).

    Article  ADS  Google Scholar 

  6. Murakami, S., Nagaosa, N. & Zhang, S. C. Dissipationless quantum spin current at room temperature. Science 301, 1348–1351 (2003).

    Article  ADS  Google Scholar 

  7. Sinova, J. et al. Universal intrinsic spin Hall effect. Phys. Rev. Lett. 92, 126603 (2004).

    Article  ADS  Google Scholar 

  8. Mathur, H. Thomas precession, spin–orbit interaction and Berry's phase. Phys. Rev. Lett. 67, 3325–3327 (1991).

    Article  ADS  MathSciNet  Google Scholar 

  9. Bialynicki-Birula, I. & Bialynicki-Birula, Z. Berry's phase in the relativistic theory of spinning particles. Phys. Rev. D 35, 2383–2387 (1987).

    Article  ADS  MathSciNet  Google Scholar 

  10. Bérard, A. & Mohrbach, H. Spin Hall effect and Berry phase of spinning particles. Phys. Lett. A 352, 190–195 (2006).

    Article  ADS  MathSciNet  Google Scholar 

  11. 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 

  12. Bliokh, K. Y. & Bliokh, Y. P. Modified geometrical optics of a smoothly inhomogeneous isotropic medium: The anisotropy, Berry phase and the optical Magnus effect. Phys. Rev. E 70, 026605 (2004).

    Article  ADS  Google Scholar 

  13. Bliokh, K. Y. & Bliokh, Y. P. Topological spin transport of photons: the optical Magnus effect and Berry phase. Phys. Lett. A 333, 181–186 (2004).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  15. 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 

  16. Bliokh, K. Y. Geometrical optics of beams with vortices: Berry phase and orbital angular momentum Hall effect. Phys. Rev. Lett. 97, 043901 (2006).

    Article  ADS  Google Scholar 

  17. Duval, C., Horváth, Z. & Horváthy, P. A. Fermat principle for spinning light. Phys. Rev. D 74, 021701(R) (2006).

    Article  ADS  MathSciNet  Google Scholar 

  18. Gosselin, P., Bérard, A. & Mohrbach, H. Spin Hall effect of photons in a static gravitational field. Phys. Rev. D 75, 084035 (2007).

    Article  ADS  Google Scholar 

  19. Bliokh, K. Y., Frolov, D. Y. & Kravtsov, Y. A. Non-Abelian evolution of electromagnetic waves in a weakly anisotropic inhomogeneous medium. Phys. Rev. A 75, 053821 (2007).

    Article  ADS  Google Scholar 

  20. Leyder, C. et al. Observation of the optical spin Hall effect. Nature Phys. 3, 628–631 (2007).

    Article  ADS  Google Scholar 

  21. Kato, Y. K., Myers, R. C., Gossard, A. C. & Awschalom, D. D. Observation of the spin Hall effect in semiconductors. Science 306, 1910–1913 (2004).

    Article  ADS  Google Scholar 

  22. Wunderlich, J., Kaestner, B., Sinova, J. & Jungwirth, T. Experimental observation of the spin-Hall effect in a two-dimensional spin–orbit coupled semiconductor system. Phys. Rev. Lett. 94, 047204 (2005).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  24. Fedorov, F. I. K teorii polnogo otrazheniya. Dokl. Akad. Nauk SSSR 105, 465–468 (1955).

    MathSciNet  Google Scholar 

  25. Imbert, C. Calculation and experimental proof of transverse shift induced by total internal reflection of a circularly polarized-light beam. Phys. Rev. D 5, 787–796 (1972).

    Article  ADS  Google Scholar 

  26. Кravtsov, Y. А. & Оrlov, Y. I. Geometrical Optics of Inhomogeneous Medium (Springer-Verlag, 1990).

    Book  Google Scholar 

  27. Kuratsuji, H. & Iida, S. Deformation of symplectic structure and anomalous commutators in field theories. Phys. Rev. D 37, 441–447 (1988).

    Article  ADS  MathSciNet  Google Scholar 

  28. Rytov, S.М. Dokl. Akad. Nauk. SSSR 18, 263–265 (1938). Reprinted in Markovski, B. & Vinitsky, S. I. (eds) Topological Phases in Quantum Theory (World Scientific, 1989).

    Google Scholar 

  29. Vladimirskii, V. V. Dokl. Akad. Nauk. SSSR 31, 222–224 (1941). Reprinted in Markovski, B. & Vinitsky, S. I. (eds) Topological Phases in Quantum Theory (World Scientific, 1989).

    Google Scholar 

  30. Ross, J. N. The rotation of the polarization in low birefringence monomode optical fibres due to geometric effects. Opt. Quant. Electron. 16, 455–461 (1984).

    Article  ADS  Google Scholar 

  31. Chiao, R. Y. & Wu, Y. S. Manifestations of Berry topological phase for the photon. Phys. Rev. Lett. 57, 933–936 (1986).

    Article  ADS  Google Scholar 

  32. Tomita, A. & Chiao, R. Y. Observation of Berry topological phase by use of an optical fiber. Phys. Rev. Lett. 57, 937–940 (1986).

    Article  ADS  Google Scholar 

  33. Berry, M. V. Interpreting the anholonomy of coiled light. Nature 326, 277–278 (1987).

    Article  ADS  Google Scholar 

  34. Lipson, S. G. Berry's phase in optical interferometry— a simple derivation. Opt. Lett. 15, 154–155 (1990).

    Article  ADS  Google Scholar 

  35. Thouless, D. J., Ao, P. & Niu, Q. Transverse force on a quantized vortex in a superfluid. Phys. Rev. Lett. 76, 3758–3761 (1996).

    Article  ADS  Google Scholar 

  36. Born, M. & Wolf, E. Principles of Optics Ed. 6 (Pergamon, 1980).

    Google Scholar 

  37. Collet, E. Polarized Light (Marcel Dekker, 1993).

    Google Scholar 

  38. Fedoseev, V. G. Spin-independent transverse shift of the centre of gravity of a reflected and of a refracted light beam. Opt. Commun. 193, 9–18 (2001).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We are indebted to P.A. Horváthy, C. Duval and Y.A. Kravtsov for fruitful correspondence. The work by K.B. is supported by the Linkage International Grant of the Australian Research Council.

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Authors and Affiliations

  1. Micro and Nanooptics Laboratory, Faculty of Mechanical Engineering and Russell Berrie Nanotechnology Institute, Technion–Israel Institute of Technology, Haifa, 32000, Israel

    Konstantin Y. Bliokh, Avi Niv, Vladimir Kleiner & Erez Hasman

  2. Institute of Radio Astronomy, 4 Krasnoznamyonnaya St, Kharkov, 61002, Ukraine

    Konstantin Y. Bliokh

  3. Nonlinear Physics Centre, Research School of Physical Sciences and Engineering, Australian National University, Canberra, ACT 0200, Australia

    Konstantin Y. Bliokh

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  1. Konstantin Y. Bliokh
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Correspondence to Konstantin Y. Bliokh.

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Bliokh, K., Niv, A., Kleiner, V. et al. Geometrodynamics of spinning light. Nature Photon 2, 748–753 (2008). https://doi.org/10.1038/nphoton.2008.229

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