Abstract

We report the manipulation of spin-dependent splitting by geometric Doppler effect based on dielectric metasurfaces. The extrapolation of rotational Doppler effect from temporal to spatial coordinate gives the phase change when the local optical axes of dielectric metasurfaces are rotating in space. Therefore, the continuous variation of local optical axes in a certain direction will introduce a phase gradient in the same direction at the beam cross section. This is additive to the phase gradient appeared when breaking the rotational symmetry of linearly polarized cylindrical vector beams, which leads to the deflections of different spin components of light, i.e., photonic spin Hall effect. Hence, it is possible to manipulate the spin-dependent splitting by introducing the geometric Doppler effect. Theoretically and experimentally, we show that the magnitude and orientation of the spin-dependent splitting are both tunable when changing the spatial rotation rate of local optical axes and incident polarization.

© 2015 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Photonic spin Hall effect in dielectric metasurfaces with rotational symmetry breaking

Yachao Liu, Xiaohui Ling, Xunong Yi, Xinxing Zhou, Shizhen Chen, Yougang Ke, Hailu Luo, and Shuangchun Wen
Opt. Lett. 40(5) 756-759 (2015)

Observation of photonic spin Hall effect with phase singularity at dielectric metasurfaces

Ying Li, Yachao Liu, Xiaohui Ling, Xunong Yi, Xinxing Zhou, Yougang Ke, Hailu Luo, Shuangchun Wen, and Dianyuan Fan
Opt. Express 23(2) 1767-1774 (2015)

Manipulating spin-dependent splitting of vector abruptly autofocusing beam by encoding cosine-azimuthal variant phases

Yi Zhang, Peng Li, Sheng Liu, Lei Han, Huachao Cheng, and Jianlin Zhao
Opt. Express 24(25) 28409-28418 (2016)

References

  • View by:
  • |
  • |
  • |

  1. M. Onoda, S. Murakami, and N. Nagaosa, “Hall effect of light,” Phys. Rev. Lett. 93, 083901 (2004).
    [Crossref] [PubMed]
  2. K. Y. Bliokh and Y. P. Bliokh, “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).
    [Crossref] [PubMed]
  3. K. Y. Bliokh, A. Niv, V. Kleiner, and E. Hasman, “Geometrodynamics of spinning light,” Nat. Photonics 2, 748–753 (2008).
    [Crossref]
  4. O. Hosten and P. Kwiat, “Observation of the spin Hall effect of light via weak measurements,” Science 319, 787–790 (2008).
    [Crossref] [PubMed]
  5. H. Luo, X. Zhou, W. Shu, S. Wen, and D. Fan, “Enhanced and switchable spin Hall effect of light near the Brewster angle on reflection,” Phys. Rev. A 84, 043806 (2011).
    [Crossref]
  6. Y. Qin, Y. Li, X. Feng, Y. Xiao, H. Yang, and Q. Gong, “Observation of the in-plane spin separation of light,” Opt. Express 19, 9636–9645 (2011).
    [Crossref] [PubMed]
  7. X. Ling, X. Zhou, H. Luo, and S. Wen, “Steering far-field spin-dependent splitting of light by inhomogeneous anisotropic media,” Phys. Rev. A 86, 053824 (2012).
    [Crossref]
  8. X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin Hall effect at metasurfaces,” Science 334, 1405–1407 (2013).
    [Crossref]
  9. B. A. Garetz and S. Arnold, “Variable frequency shifting of circularly polarized laser radiation via a rotating half-wave retardation plate,” Opt. Commun. 31, 1–3 (1979).
    [Crossref]
  10. G. Nienhuis, “Doppler effect induced by rotating lenses,” Opt. Commun. 132, 8–14 (1996).
    [Crossref]
  11. H. Luo, S. Wen, W. Shu, Z. Tang, Y. Zou, and D. Fan, “Rotational Doppler effect in left-handed materials,” Phys. Rev. A 78, 033805 (2008).
    [Crossref]
  12. S. G. Lipson, “Berry’s phase in optical interferometry: a simple derivation,” Opt. Lett. 15, 154–155 (1990).
    [Crossref] [PubMed]
  13. K. Y. Bliokh, Y. Gorodetski, V. Kleiner, and E. Hasman, “Coriolis effect in optics: unified geometric phase and spin-Hall effect,” Phys. Rev. Lett. 101, 030404 (2008).
    [Crossref] [PubMed]
  14. A. Niv, Y. Gorodetski, V. Kleiner, and E. Hasman, “Topological spin-orbit interaction of light in anisotropic inhomogeneous subwavelength structures,” Opt. Lett. 33, 2910–2912 (2008).
    [Crossref] [PubMed]
  15. E. Karimi, S. Slussarenko, B. Piccirillo, L. Marrucci, and E. Santamato, “Polarization-controlled evolution of light transverse modes and associated pancharatnam geometric phase in orbital angular momentum,” Phys. Rev. A 81, 053813 (2010).
    [Crossref]
  16. A. Aiello and J. P. Woerdman, “Role of beam propagation in Goos-Hänchen and Imbert-Fedorov shifts,” Opt. Lett. 33, 1437–1439 (2008).
    [Crossref] [PubMed]
  17. H. Luo, S. Wen, W. Shu, and D. Fan, “Spin Hall effect of light in photon tunneling,” Phys. Rev. A 82, 043825 (2010).
    [Crossref]
  18. N. Dahan, Y. Gorodetski, K. Frischwasser, V. Kleiner, and E. Hasman, “Geometric Doppler effect: spin-split dispersion of thermal radiation,” Phys. Rev. Lett. 105, 136402 (2010).
    [Crossref]
  19. Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photonics 1, 1–57 (2009).
    [Crossref]
  20. F. Cardano, E. Karimi, S. Slussarenko, L. Marrucci, C. de Lisio, and E. Santamato, “Polarization pattern of vector vortex beams generated by q-plates with different topological charges,” Appl. Opt. 51, C1–C6 (2012).
    [Crossref] [PubMed]
  21. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
    [Crossref] [PubMed]
  22. M. Padgett, J. Courtial, and L. Allen, “Light’s orbital angular momentum,” Phys. Today 57, 35–40 (2004).
    [Crossref]
  23. J. Lin, P. Genevet, M. A. Kats, N. Antoniou, and F. Capasso, “Nanostructured holograms for broadband manipulation of vector beams,” Nano Lett. 13, 4269–4274 (2013).
    [Crossref] [PubMed]
  24. Y. Liu, X. Ling, X. Yi, X. Zhou, H. Luo, and S. Wen, “Realization of polarization evolution on higher-order Poincaré sphere with metasurface,” Appl. Phys. Lett. 104, 191110 (2014).
    [Crossref]
  25. X. Yi, X. Ling, Z. Zhang, X. Zhou, Y. Liu, S. Chen, H. Luo, and S. Wen, “Generation of cylindrical vector vortex beams by two cascaded metasurfaces,” Opt. Express 22, 17207–17215 (2014).
    [Crossref] [PubMed]
  26. P. Genevet, N. Yu, F. Aieta, J. Lin, M. A. Kats, R. Blanchard, M. O. Scully, Z. Gaburro, and F. Capasso, “Ultra-thin plasmonic optical vortex plate based on phase discontinuities,” Appl. Phys. Lett. 100, 013101 (2012).
    [Crossref]
  27. L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K. Cheah, C. Qiu, J. Li, T. Zentgraf, and S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commum. 4, 2808 (2013).
  28. M. Veysi, C. Guclu, and F. Capolino, “Vortex beams with strong longitudinally polarized magnetic field and their generation by using metasurfaces,” J. Opt. Soc. Am. B 32, 345–354 (2015).
    [Crossref]
  29. F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12, 4932–4936 (2012).
    [Crossref] [PubMed]
  30. X. Chen, L. Huang, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, C. Qiu, S. Zhang, and T. Zentgraf, “Dual-polarity plasmonic metalens for visible light,” Nat. Commum. 3, 1198 (2012).
    [Crossref]
  31. N. Shitrit, I. Yulevich, E. Maguid, D. Ozeri, D. Veksler, V. Kleiner, and E. Hasman, “Spin-optical metamaterial route to spin-controlled photonics,” Science 340, 724–726 (2013).
    [Crossref] [PubMed]
  32. D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345, 298–302 (2014).
    [Crossref] [PubMed]
  33. Y. Li, Y. Liu, X. Ling, X. Yi, X. Zhou, Y. Ke, H. Luo, S. Wen, and D. Fan, “Observation of photonic spin Hall effect with phase singularity at dielectric metasurfaces,” Opt. Express 23, 1767–1774 (2015).
    [Crossref] [PubMed]
  34. Y. Liu, X. Ling, X. Yi, X. Zhou, S. Chen, Y. Ke, H. Luo, and S. Wen, “Photonic spin Hall effect in dielectric metasurfaces with rotational symmetry breaking,” Opt. Lett. 40, 756–759 (2015).
    [Crossref] [PubMed]
  35. X. Yi, Y. Liu, X. Ling, X. Zhou, Y. Ke, H. Luo, S. Wen, and D. Fan, “Hybrid-order Poincaré sphere,” Phys. Rev. A 91, 023801 (2015).
    [Crossref]
  36. N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
    [Crossref] [PubMed]
  37. L. Huang, X. Chen, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, “Dispersionless phase discontinuities for controlling light propagation,” Nano Lett. 12, 5750–5755 (2012).
    [Crossref] [PubMed]
  38. X. Ling, X. Yi, X. Zhou, Y. Liu, W. Shu, H. Luo, and S. Wen, “Realization of tunable spin-dependent splitting in intrinsic photonic spin Hall effect,” Appl. Phys. Lett. 105, 151101 (2014).
    [Crossref]
  39. A. Aiello, N. Lindlein, C. Marquardt, and G. Leuchs, “Transverse angular momentum and geometric spin hall effect of light,” Phys. Rev. Lett. 103, 100401 (2009).
    [Crossref] [PubMed]
  40. M. Beresna, M. Gecevičius, P. G. Kazansky, and T. Gertus, “Radially polarized optical vortex converter created by femtosecond laser nanostructuring of glass,” Appl. Phys. Lett. 98, 201101 (2011).
    [Crossref]
  41. D. Hakobyan and E. Brasselet, “Left-handed optical radiation torque,” Nat. Photonics 8, 610–614 (2014).
    [Crossref]
  42. M. Beresna, M. Gecevicius, and P. G. Kazansky, “Ultrafast laser direct writing and nanostructuring in transparent materials,” Adv. Opt. Photonics 6, 293–339 (2014).
    [Crossref]
  43. L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96, 163905 (2006).
    [Crossref] [PubMed]
  44. M. Born and E. Wolf, Principles of Optics (Cambridge University, 1997).

2015 (4)

2014 (6)

X. Yi, X. Ling, Z. Zhang, X. Zhou, Y. Liu, S. Chen, H. Luo, and S. Wen, “Generation of cylindrical vector vortex beams by two cascaded metasurfaces,” Opt. Express 22, 17207–17215 (2014).
[Crossref] [PubMed]

D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345, 298–302 (2014).
[Crossref] [PubMed]

Y. Liu, X. Ling, X. Yi, X. Zhou, H. Luo, and S. Wen, “Realization of polarization evolution on higher-order Poincaré sphere with metasurface,” Appl. Phys. Lett. 104, 191110 (2014).
[Crossref]

X. Ling, X. Yi, X. Zhou, Y. Liu, W. Shu, H. Luo, and S. Wen, “Realization of tunable spin-dependent splitting in intrinsic photonic spin Hall effect,” Appl. Phys. Lett. 105, 151101 (2014).
[Crossref]

D. Hakobyan and E. Brasselet, “Left-handed optical radiation torque,” Nat. Photonics 8, 610–614 (2014).
[Crossref]

M. Beresna, M. Gecevicius, and P. G. Kazansky, “Ultrafast laser direct writing and nanostructuring in transparent materials,” Adv. Opt. Photonics 6, 293–339 (2014).
[Crossref]

2013 (4)

L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K. Cheah, C. Qiu, J. Li, T. Zentgraf, and S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commum. 4, 2808 (2013).

J. Lin, P. Genevet, M. A. Kats, N. Antoniou, and F. Capasso, “Nanostructured holograms for broadband manipulation of vector beams,” Nano Lett. 13, 4269–4274 (2013).
[Crossref] [PubMed]

N. Shitrit, I. Yulevich, E. Maguid, D. Ozeri, D. Veksler, V. Kleiner, and E. Hasman, “Spin-optical metamaterial route to spin-controlled photonics,” Science 340, 724–726 (2013).
[Crossref] [PubMed]

X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin Hall effect at metasurfaces,” Science 334, 1405–1407 (2013).
[Crossref]

2012 (6)

X. Ling, X. Zhou, H. Luo, and S. Wen, “Steering far-field spin-dependent splitting of light by inhomogeneous anisotropic media,” Phys. Rev. A 86, 053824 (2012).
[Crossref]

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12, 4932–4936 (2012).
[Crossref] [PubMed]

X. Chen, L. Huang, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, C. Qiu, S. Zhang, and T. Zentgraf, “Dual-polarity plasmonic metalens for visible light,” Nat. Commum. 3, 1198 (2012).
[Crossref]

L. Huang, X. Chen, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, “Dispersionless phase discontinuities for controlling light propagation,” Nano Lett. 12, 5750–5755 (2012).
[Crossref] [PubMed]

P. Genevet, N. Yu, F. Aieta, J. Lin, M. A. Kats, R. Blanchard, M. O. Scully, Z. Gaburro, and F. Capasso, “Ultra-thin plasmonic optical vortex plate based on phase discontinuities,” Appl. Phys. Lett. 100, 013101 (2012).
[Crossref]

F. Cardano, E. Karimi, S. Slussarenko, L. Marrucci, C. de Lisio, and E. Santamato, “Polarization pattern of vector vortex beams generated by q-plates with different topological charges,” Appl. Opt. 51, C1–C6 (2012).
[Crossref] [PubMed]

2011 (4)

Y. Qin, Y. Li, X. Feng, Y. Xiao, H. Yang, and Q. Gong, “Observation of the in-plane spin separation of light,” Opt. Express 19, 9636–9645 (2011).
[Crossref] [PubMed]

M. Beresna, M. Gecevičius, P. G. Kazansky, and T. Gertus, “Radially polarized optical vortex converter created by femtosecond laser nanostructuring of glass,” Appl. Phys. Lett. 98, 201101 (2011).
[Crossref]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
[Crossref] [PubMed]

H. Luo, X. Zhou, W. Shu, S. Wen, and D. Fan, “Enhanced and switchable spin Hall effect of light near the Brewster angle on reflection,” Phys. Rev. A 84, 043806 (2011).
[Crossref]

2010 (3)

E. Karimi, S. Slussarenko, B. Piccirillo, L. Marrucci, and E. Santamato, “Polarization-controlled evolution of light transverse modes and associated pancharatnam geometric phase in orbital angular momentum,” Phys. Rev. A 81, 053813 (2010).
[Crossref]

H. Luo, S. Wen, W. Shu, and D. Fan, “Spin Hall effect of light in photon tunneling,” Phys. Rev. A 82, 043825 (2010).
[Crossref]

N. Dahan, Y. Gorodetski, K. Frischwasser, V. Kleiner, and E. Hasman, “Geometric Doppler effect: spin-split dispersion of thermal radiation,” Phys. Rev. Lett. 105, 136402 (2010).
[Crossref]

2009 (2)

Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photonics 1, 1–57 (2009).
[Crossref]

A. Aiello, N. Lindlein, C. Marquardt, and G. Leuchs, “Transverse angular momentum and geometric spin hall effect of light,” Phys. Rev. Lett. 103, 100401 (2009).
[Crossref] [PubMed]

2008 (6)

H. Luo, S. Wen, W. Shu, Z. Tang, Y. Zou, and D. Fan, “Rotational Doppler effect in left-handed materials,” Phys. Rev. A 78, 033805 (2008).
[Crossref]

K. Y. Bliokh, Y. Gorodetski, V. Kleiner, and E. Hasman, “Coriolis effect in optics: unified geometric phase and spin-Hall effect,” Phys. Rev. Lett. 101, 030404 (2008).
[Crossref] [PubMed]

K. Y. Bliokh, A. Niv, V. Kleiner, and E. Hasman, “Geometrodynamics of spinning light,” Nat. Photonics 2, 748–753 (2008).
[Crossref]

O. Hosten and P. Kwiat, “Observation of the spin Hall effect of light via weak measurements,” Science 319, 787–790 (2008).
[Crossref] [PubMed]

A. Aiello and J. P. Woerdman, “Role of beam propagation in Goos-Hänchen and Imbert-Fedorov shifts,” Opt. Lett. 33, 1437–1439 (2008).
[Crossref] [PubMed]

A. Niv, Y. Gorodetski, V. Kleiner, and E. Hasman, “Topological spin-orbit interaction of light in anisotropic inhomogeneous subwavelength structures,” Opt. Lett. 33, 2910–2912 (2008).
[Crossref] [PubMed]

2006 (2)

K. Y. Bliokh and Y. P. Bliokh, “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).
[Crossref] [PubMed]

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96, 163905 (2006).
[Crossref] [PubMed]

2004 (2)

M. Onoda, S. Murakami, and N. Nagaosa, “Hall effect of light,” Phys. Rev. Lett. 93, 083901 (2004).
[Crossref] [PubMed]

M. Padgett, J. Courtial, and L. Allen, “Light’s orbital angular momentum,” Phys. Today 57, 35–40 (2004).
[Crossref]

1996 (1)

G. Nienhuis, “Doppler effect induced by rotating lenses,” Opt. Commun. 132, 8–14 (1996).
[Crossref]

1992 (1)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[Crossref] [PubMed]

1990 (1)

1979 (1)

B. A. Garetz and S. Arnold, “Variable frequency shifting of circularly polarized laser radiation via a rotating half-wave retardation plate,” Opt. Commun. 31, 1–3 (1979).
[Crossref]

Aiello, A.

A. Aiello, N. Lindlein, C. Marquardt, and G. Leuchs, “Transverse angular momentum and geometric spin hall effect of light,” Phys. Rev. Lett. 103, 100401 (2009).
[Crossref] [PubMed]

A. Aiello and J. P. Woerdman, “Role of beam propagation in Goos-Hänchen and Imbert-Fedorov shifts,” Opt. Lett. 33, 1437–1439 (2008).
[Crossref] [PubMed]

Aieta, F.

P. Genevet, N. Yu, F. Aieta, J. Lin, M. A. Kats, R. Blanchard, M. O. Scully, Z. Gaburro, and F. Capasso, “Ultra-thin plasmonic optical vortex plate based on phase discontinuities,” Appl. Phys. Lett. 100, 013101 (2012).
[Crossref]

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12, 4932–4936 (2012).
[Crossref] [PubMed]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
[Crossref] [PubMed]

Allen, L.

M. Padgett, J. Courtial, and L. Allen, “Light’s orbital angular momentum,” Phys. Today 57, 35–40 (2004).
[Crossref]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[Crossref] [PubMed]

Antoniou, N.

J. Lin, P. Genevet, M. A. Kats, N. Antoniou, and F. Capasso, “Nanostructured holograms for broadband manipulation of vector beams,” Nano Lett. 13, 4269–4274 (2013).
[Crossref] [PubMed]

Arnold, S.

B. A. Garetz and S. Arnold, “Variable frequency shifting of circularly polarized laser radiation via a rotating half-wave retardation plate,” Opt. Commun. 31, 1–3 (1979).
[Crossref]

Bai, B.

L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K. Cheah, C. Qiu, J. Li, T. Zentgraf, and S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commum. 4, 2808 (2013).

X. Chen, L. Huang, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, C. Qiu, S. Zhang, and T. Zentgraf, “Dual-polarity plasmonic metalens for visible light,” Nat. Commum. 3, 1198 (2012).
[Crossref]

L. Huang, X. Chen, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, “Dispersionless phase discontinuities for controlling light propagation,” Nano Lett. 12, 5750–5755 (2012).
[Crossref] [PubMed]

Beijersbergen, M. W.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[Crossref] [PubMed]

Beresna, M.

M. Beresna, M. Gecevicius, and P. G. Kazansky, “Ultrafast laser direct writing and nanostructuring in transparent materials,” Adv. Opt. Photonics 6, 293–339 (2014).
[Crossref]

M. Beresna, M. Gecevičius, P. G. Kazansky, and T. Gertus, “Radially polarized optical vortex converter created by femtosecond laser nanostructuring of glass,” Appl. Phys. Lett. 98, 201101 (2011).
[Crossref]

Blanchard, R.

P. Genevet, N. Yu, F. Aieta, J. Lin, M. A. Kats, R. Blanchard, M. O. Scully, Z. Gaburro, and F. Capasso, “Ultra-thin plasmonic optical vortex plate based on phase discontinuities,” Appl. Phys. Lett. 100, 013101 (2012).
[Crossref]

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12, 4932–4936 (2012).
[Crossref] [PubMed]

Bliokh, K. Y.

K. Y. Bliokh, A. Niv, V. Kleiner, and E. Hasman, “Geometrodynamics of spinning light,” Nat. Photonics 2, 748–753 (2008).
[Crossref]

K. Y. Bliokh, Y. Gorodetski, V. Kleiner, and E. Hasman, “Coriolis effect in optics: unified geometric phase and spin-Hall effect,” Phys. Rev. Lett. 101, 030404 (2008).
[Crossref] [PubMed]

K. Y. Bliokh and Y. P. Bliokh, “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).
[Crossref] [PubMed]

Bliokh, Y. P.

K. Y. Bliokh and Y. P. Bliokh, “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).
[Crossref] [PubMed]

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1997).

Brasselet, E.

D. Hakobyan and E. Brasselet, “Left-handed optical radiation torque,” Nat. Photonics 8, 610–614 (2014).
[Crossref]

Brongersma, M. L.

D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345, 298–302 (2014).
[Crossref] [PubMed]

Capasso, F.

J. Lin, P. Genevet, M. A. Kats, N. Antoniou, and F. Capasso, “Nanostructured holograms for broadband manipulation of vector beams,” Nano Lett. 13, 4269–4274 (2013).
[Crossref] [PubMed]

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12, 4932–4936 (2012).
[Crossref] [PubMed]

P. Genevet, N. Yu, F. Aieta, J. Lin, M. A. Kats, R. Blanchard, M. O. Scully, Z. Gaburro, and F. Capasso, “Ultra-thin plasmonic optical vortex plate based on phase discontinuities,” Appl. Phys. Lett. 100, 013101 (2012).
[Crossref]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
[Crossref] [PubMed]

Capolino, F.

Cardano, F.

Cheah, K.

L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K. Cheah, C. Qiu, J. Li, T. Zentgraf, and S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commum. 4, 2808 (2013).

Chen, S.

Chen, X.

L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K. Cheah, C. Qiu, J. Li, T. Zentgraf, and S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commum. 4, 2808 (2013).

X. Chen, L. Huang, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, C. Qiu, S. Zhang, and T. Zentgraf, “Dual-polarity plasmonic metalens for visible light,” Nat. Commum. 3, 1198 (2012).
[Crossref]

L. Huang, X. Chen, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, “Dispersionless phase discontinuities for controlling light propagation,” Nano Lett. 12, 5750–5755 (2012).
[Crossref] [PubMed]

Courtial, J.

M. Padgett, J. Courtial, and L. Allen, “Light’s orbital angular momentum,” Phys. Today 57, 35–40 (2004).
[Crossref]

Dahan, N.

N. Dahan, Y. Gorodetski, K. Frischwasser, V. Kleiner, and E. Hasman, “Geometric Doppler effect: spin-split dispersion of thermal radiation,” Phys. Rev. Lett. 105, 136402 (2010).
[Crossref]

de Lisio, C.

Fan, D.

Y. Li, Y. Liu, X. Ling, X. Yi, X. Zhou, Y. Ke, H. Luo, S. Wen, and D. Fan, “Observation of photonic spin Hall effect with phase singularity at dielectric metasurfaces,” Opt. Express 23, 1767–1774 (2015).
[Crossref] [PubMed]

X. Yi, Y. Liu, X. Ling, X. Zhou, Y. Ke, H. Luo, S. Wen, and D. Fan, “Hybrid-order Poincaré sphere,” Phys. Rev. A 91, 023801 (2015).
[Crossref]

H. Luo, X. Zhou, W. Shu, S. Wen, and D. Fan, “Enhanced and switchable spin Hall effect of light near the Brewster angle on reflection,” Phys. Rev. A 84, 043806 (2011).
[Crossref]

H. Luo, S. Wen, W. Shu, and D. Fan, “Spin Hall effect of light in photon tunneling,” Phys. Rev. A 82, 043825 (2010).
[Crossref]

H. Luo, S. Wen, W. Shu, Z. Tang, Y. Zou, and D. Fan, “Rotational Doppler effect in left-handed materials,” Phys. Rev. A 78, 033805 (2008).
[Crossref]

Fan, P.

D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345, 298–302 (2014).
[Crossref] [PubMed]

Feng, X.

Frischwasser, K.

N. Dahan, Y. Gorodetski, K. Frischwasser, V. Kleiner, and E. Hasman, “Geometric Doppler effect: spin-split dispersion of thermal radiation,” Phys. Rev. Lett. 105, 136402 (2010).
[Crossref]

Gaburro, Z.

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12, 4932–4936 (2012).
[Crossref] [PubMed]

P. Genevet, N. Yu, F. Aieta, J. Lin, M. A. Kats, R. Blanchard, M. O. Scully, Z. Gaburro, and F. Capasso, “Ultra-thin plasmonic optical vortex plate based on phase discontinuities,” Appl. Phys. Lett. 100, 013101 (2012).
[Crossref]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
[Crossref] [PubMed]

Garetz, B. A.

B. A. Garetz and S. Arnold, “Variable frequency shifting of circularly polarized laser radiation via a rotating half-wave retardation plate,” Opt. Commun. 31, 1–3 (1979).
[Crossref]

Gecevicius, M.

M. Beresna, M. Gecevicius, and P. G. Kazansky, “Ultrafast laser direct writing and nanostructuring in transparent materials,” Adv. Opt. Photonics 6, 293–339 (2014).
[Crossref]

M. Beresna, M. Gecevičius, P. G. Kazansky, and T. Gertus, “Radially polarized optical vortex converter created by femtosecond laser nanostructuring of glass,” Appl. Phys. Lett. 98, 201101 (2011).
[Crossref]

Genevet, P.

J. Lin, P. Genevet, M. A. Kats, N. Antoniou, and F. Capasso, “Nanostructured holograms for broadband manipulation of vector beams,” Nano Lett. 13, 4269–4274 (2013).
[Crossref] [PubMed]

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12, 4932–4936 (2012).
[Crossref] [PubMed]

P. Genevet, N. Yu, F. Aieta, J. Lin, M. A. Kats, R. Blanchard, M. O. Scully, Z. Gaburro, and F. Capasso, “Ultra-thin plasmonic optical vortex plate based on phase discontinuities,” Appl. Phys. Lett. 100, 013101 (2012).
[Crossref]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
[Crossref] [PubMed]

Gertus, T.

M. Beresna, M. Gecevičius, P. G. Kazansky, and T. Gertus, “Radially polarized optical vortex converter created by femtosecond laser nanostructuring of glass,” Appl. Phys. Lett. 98, 201101 (2011).
[Crossref]

Gong, Q.

Gorodetski, Y.

N. Dahan, Y. Gorodetski, K. Frischwasser, V. Kleiner, and E. Hasman, “Geometric Doppler effect: spin-split dispersion of thermal radiation,” Phys. Rev. Lett. 105, 136402 (2010).
[Crossref]

A. Niv, Y. Gorodetski, V. Kleiner, and E. Hasman, “Topological spin-orbit interaction of light in anisotropic inhomogeneous subwavelength structures,” Opt. Lett. 33, 2910–2912 (2008).
[Crossref] [PubMed]

K. Y. Bliokh, Y. Gorodetski, V. Kleiner, and E. Hasman, “Coriolis effect in optics: unified geometric phase and spin-Hall effect,” Phys. Rev. Lett. 101, 030404 (2008).
[Crossref] [PubMed]

Guclu, C.

Hakobyan, D.

D. Hakobyan and E. Brasselet, “Left-handed optical radiation torque,” Nat. Photonics 8, 610–614 (2014).
[Crossref]

Hasman, E.

D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345, 298–302 (2014).
[Crossref] [PubMed]

N. Shitrit, I. Yulevich, E. Maguid, D. Ozeri, D. Veksler, V. Kleiner, and E. Hasman, “Spin-optical metamaterial route to spin-controlled photonics,” Science 340, 724–726 (2013).
[Crossref] [PubMed]

N. Dahan, Y. Gorodetski, K. Frischwasser, V. Kleiner, and E. Hasman, “Geometric Doppler effect: spin-split dispersion of thermal radiation,” Phys. Rev. Lett. 105, 136402 (2010).
[Crossref]

A. Niv, Y. Gorodetski, V. Kleiner, and E. Hasman, “Topological spin-orbit interaction of light in anisotropic inhomogeneous subwavelength structures,” Opt. Lett. 33, 2910–2912 (2008).
[Crossref] [PubMed]

K. Y. Bliokh, A. Niv, V. Kleiner, and E. Hasman, “Geometrodynamics of spinning light,” Nat. Photonics 2, 748–753 (2008).
[Crossref]

K. Y. Bliokh, Y. Gorodetski, V. Kleiner, and E. Hasman, “Coriolis effect in optics: unified geometric phase and spin-Hall effect,” Phys. Rev. Lett. 101, 030404 (2008).
[Crossref] [PubMed]

Hosten, O.

O. Hosten and P. Kwiat, “Observation of the spin Hall effect of light via weak measurements,” Science 319, 787–790 (2008).
[Crossref] [PubMed]

Huang, L.

L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K. Cheah, C. Qiu, J. Li, T. Zentgraf, and S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commum. 4, 2808 (2013).

X. Chen, L. Huang, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, C. Qiu, S. Zhang, and T. Zentgraf, “Dual-polarity plasmonic metalens for visible light,” Nat. Commum. 3, 1198 (2012).
[Crossref]

L. Huang, X. Chen, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, “Dispersionless phase discontinuities for controlling light propagation,” Nano Lett. 12, 5750–5755 (2012).
[Crossref] [PubMed]

Jin, G.

L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K. Cheah, C. Qiu, J. Li, T. Zentgraf, and S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commum. 4, 2808 (2013).

X. Chen, L. Huang, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, C. Qiu, S. Zhang, and T. Zentgraf, “Dual-polarity plasmonic metalens for visible light,” Nat. Commum. 3, 1198 (2012).
[Crossref]

L. Huang, X. Chen, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, “Dispersionless phase discontinuities for controlling light propagation,” Nano Lett. 12, 5750–5755 (2012).
[Crossref] [PubMed]

Karimi, E.

F. Cardano, E. Karimi, S. Slussarenko, L. Marrucci, C. de Lisio, and E. Santamato, “Polarization pattern of vector vortex beams generated by q-plates with different topological charges,” Appl. Opt. 51, C1–C6 (2012).
[Crossref] [PubMed]

E. Karimi, S. Slussarenko, B. Piccirillo, L. Marrucci, and E. Santamato, “Polarization-controlled evolution of light transverse modes and associated pancharatnam geometric phase in orbital angular momentum,” Phys. Rev. A 81, 053813 (2010).
[Crossref]

Kats, M. A.

J. Lin, P. Genevet, M. A. Kats, N. Antoniou, and F. Capasso, “Nanostructured holograms for broadband manipulation of vector beams,” Nano Lett. 13, 4269–4274 (2013).
[Crossref] [PubMed]

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12, 4932–4936 (2012).
[Crossref] [PubMed]

P. Genevet, N. Yu, F. Aieta, J. Lin, M. A. Kats, R. Blanchard, M. O. Scully, Z. Gaburro, and F. Capasso, “Ultra-thin plasmonic optical vortex plate based on phase discontinuities,” Appl. Phys. Lett. 100, 013101 (2012).
[Crossref]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
[Crossref] [PubMed]

Kazansky, P. G.

M. Beresna, M. Gecevicius, and P. G. Kazansky, “Ultrafast laser direct writing and nanostructuring in transparent materials,” Adv. Opt. Photonics 6, 293–339 (2014).
[Crossref]

M. Beresna, M. Gecevičius, P. G. Kazansky, and T. Gertus, “Radially polarized optical vortex converter created by femtosecond laser nanostructuring of glass,” Appl. Phys. Lett. 98, 201101 (2011).
[Crossref]

Ke, Y.

Kleiner, V.

N. Shitrit, I. Yulevich, E. Maguid, D. Ozeri, D. Veksler, V. Kleiner, and E. Hasman, “Spin-optical metamaterial route to spin-controlled photonics,” Science 340, 724–726 (2013).
[Crossref] [PubMed]

N. Dahan, Y. Gorodetski, K. Frischwasser, V. Kleiner, and E. Hasman, “Geometric Doppler effect: spin-split dispersion of thermal radiation,” Phys. Rev. Lett. 105, 136402 (2010).
[Crossref]

A. Niv, Y. Gorodetski, V. Kleiner, and E. Hasman, “Topological spin-orbit interaction of light in anisotropic inhomogeneous subwavelength structures,” Opt. Lett. 33, 2910–2912 (2008).
[Crossref] [PubMed]

K. Y. Bliokh, A. Niv, V. Kleiner, and E. Hasman, “Geometrodynamics of spinning light,” Nat. Photonics 2, 748–753 (2008).
[Crossref]

K. Y. Bliokh, Y. Gorodetski, V. Kleiner, and E. Hasman, “Coriolis effect in optics: unified geometric phase and spin-Hall effect,” Phys. Rev. Lett. 101, 030404 (2008).
[Crossref] [PubMed]

Kwiat, P.

O. Hosten and P. Kwiat, “Observation of the spin Hall effect of light via weak measurements,” Science 319, 787–790 (2008).
[Crossref] [PubMed]

Leuchs, G.

A. Aiello, N. Lindlein, C. Marquardt, and G. Leuchs, “Transverse angular momentum and geometric spin hall effect of light,” Phys. Rev. Lett. 103, 100401 (2009).
[Crossref] [PubMed]

Li, G.

L. Huang, X. Chen, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, “Dispersionless phase discontinuities for controlling light propagation,” Nano Lett. 12, 5750–5755 (2012).
[Crossref] [PubMed]

X. Chen, L. Huang, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, C. Qiu, S. Zhang, and T. Zentgraf, “Dual-polarity plasmonic metalens for visible light,” Nat. Commum. 3, 1198 (2012).
[Crossref]

Li, J.

L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K. Cheah, C. Qiu, J. Li, T. Zentgraf, and S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commum. 4, 2808 (2013).

Li, Y.

Lin, D.

D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345, 298–302 (2014).
[Crossref] [PubMed]

Lin, J.

J. Lin, P. Genevet, M. A. Kats, N. Antoniou, and F. Capasso, “Nanostructured holograms for broadband manipulation of vector beams,” Nano Lett. 13, 4269–4274 (2013).
[Crossref] [PubMed]

P. Genevet, N. Yu, F. Aieta, J. Lin, M. A. Kats, R. Blanchard, M. O. Scully, Z. Gaburro, and F. Capasso, “Ultra-thin plasmonic optical vortex plate based on phase discontinuities,” Appl. Phys. Lett. 100, 013101 (2012).
[Crossref]

Lindlein, N.

A. Aiello, N. Lindlein, C. Marquardt, and G. Leuchs, “Transverse angular momentum and geometric spin hall effect of light,” Phys. Rev. Lett. 103, 100401 (2009).
[Crossref] [PubMed]

Ling, X.

Y. Li, Y. Liu, X. Ling, X. Yi, X. Zhou, Y. Ke, H. Luo, S. Wen, and D. Fan, “Observation of photonic spin Hall effect with phase singularity at dielectric metasurfaces,” Opt. Express 23, 1767–1774 (2015).
[Crossref] [PubMed]

X. Yi, Y. Liu, X. Ling, X. Zhou, Y. Ke, H. Luo, S. Wen, and D. Fan, “Hybrid-order Poincaré sphere,” Phys. Rev. A 91, 023801 (2015).
[Crossref]

Y. Liu, X. Ling, X. Yi, X. Zhou, S. Chen, Y. Ke, H. Luo, and S. Wen, “Photonic spin Hall effect in dielectric metasurfaces with rotational symmetry breaking,” Opt. Lett. 40, 756–759 (2015).
[Crossref] [PubMed]

X. Ling, X. Yi, X. Zhou, Y. Liu, W. Shu, H. Luo, and S. Wen, “Realization of tunable spin-dependent splitting in intrinsic photonic spin Hall effect,” Appl. Phys. Lett. 105, 151101 (2014).
[Crossref]

Y. Liu, X. Ling, X. Yi, X. Zhou, H. Luo, and S. Wen, “Realization of polarization evolution on higher-order Poincaré sphere with metasurface,” Appl. Phys. Lett. 104, 191110 (2014).
[Crossref]

X. Yi, X. Ling, Z. Zhang, X. Zhou, Y. Liu, S. Chen, H. Luo, and S. Wen, “Generation of cylindrical vector vortex beams by two cascaded metasurfaces,” Opt. Express 22, 17207–17215 (2014).
[Crossref] [PubMed]

X. Ling, X. Zhou, H. Luo, and S. Wen, “Steering far-field spin-dependent splitting of light by inhomogeneous anisotropic media,” Phys. Rev. A 86, 053824 (2012).
[Crossref]

Lipson, S. G.

Liu, Y.

Y. Liu, X. Ling, X. Yi, X. Zhou, S. Chen, Y. Ke, H. Luo, and S. Wen, “Photonic spin Hall effect in dielectric metasurfaces with rotational symmetry breaking,” Opt. Lett. 40, 756–759 (2015).
[Crossref] [PubMed]

X. Yi, Y. Liu, X. Ling, X. Zhou, Y. Ke, H. Luo, S. Wen, and D. Fan, “Hybrid-order Poincaré sphere,” Phys. Rev. A 91, 023801 (2015).
[Crossref]

Y. Li, Y. Liu, X. Ling, X. Yi, X. Zhou, Y. Ke, H. Luo, S. Wen, and D. Fan, “Observation of photonic spin Hall effect with phase singularity at dielectric metasurfaces,” Opt. Express 23, 1767–1774 (2015).
[Crossref] [PubMed]

Y. Liu, X. Ling, X. Yi, X. Zhou, H. Luo, and S. Wen, “Realization of polarization evolution on higher-order Poincaré sphere with metasurface,” Appl. Phys. Lett. 104, 191110 (2014).
[Crossref]

X. Yi, X. Ling, Z. Zhang, X. Zhou, Y. Liu, S. Chen, H. Luo, and S. Wen, “Generation of cylindrical vector vortex beams by two cascaded metasurfaces,” Opt. Express 22, 17207–17215 (2014).
[Crossref] [PubMed]

X. Ling, X. Yi, X. Zhou, Y. Liu, W. Shu, H. Luo, and S. Wen, “Realization of tunable spin-dependent splitting in intrinsic photonic spin Hall effect,” Appl. Phys. Lett. 105, 151101 (2014).
[Crossref]

Luo, H.

Y. Liu, X. Ling, X. Yi, X. Zhou, S. Chen, Y. Ke, H. Luo, and S. Wen, “Photonic spin Hall effect in dielectric metasurfaces with rotational symmetry breaking,” Opt. Lett. 40, 756–759 (2015).
[Crossref] [PubMed]

Y. Li, Y. Liu, X. Ling, X. Yi, X. Zhou, Y. Ke, H. Luo, S. Wen, and D. Fan, “Observation of photonic spin Hall effect with phase singularity at dielectric metasurfaces,” Opt. Express 23, 1767–1774 (2015).
[Crossref] [PubMed]

X. Yi, Y. Liu, X. Ling, X. Zhou, Y. Ke, H. Luo, S. Wen, and D. Fan, “Hybrid-order Poincaré sphere,” Phys. Rev. A 91, 023801 (2015).
[Crossref]

Y. Liu, X. Ling, X. Yi, X. Zhou, H. Luo, and S. Wen, “Realization of polarization evolution on higher-order Poincaré sphere with metasurface,” Appl. Phys. Lett. 104, 191110 (2014).
[Crossref]

X. Yi, X. Ling, Z. Zhang, X. Zhou, Y. Liu, S. Chen, H. Luo, and S. Wen, “Generation of cylindrical vector vortex beams by two cascaded metasurfaces,” Opt. Express 22, 17207–17215 (2014).
[Crossref] [PubMed]

X. Ling, X. Yi, X. Zhou, Y. Liu, W. Shu, H. Luo, and S. Wen, “Realization of tunable spin-dependent splitting in intrinsic photonic spin Hall effect,” Appl. Phys. Lett. 105, 151101 (2014).
[Crossref]

X. Ling, X. Zhou, H. Luo, and S. Wen, “Steering far-field spin-dependent splitting of light by inhomogeneous anisotropic media,” Phys. Rev. A 86, 053824 (2012).
[Crossref]

H. Luo, X. Zhou, W. Shu, S. Wen, and D. Fan, “Enhanced and switchable spin Hall effect of light near the Brewster angle on reflection,” Phys. Rev. A 84, 043806 (2011).
[Crossref]

H. Luo, S. Wen, W. Shu, and D. Fan, “Spin Hall effect of light in photon tunneling,” Phys. Rev. A 82, 043825 (2010).
[Crossref]

H. Luo, S. Wen, W. Shu, Z. Tang, Y. Zou, and D. Fan, “Rotational Doppler effect in left-handed materials,” Phys. Rev. A 78, 033805 (2008).
[Crossref]

Maguid, E.

N. Shitrit, I. Yulevich, E. Maguid, D. Ozeri, D. Veksler, V. Kleiner, and E. Hasman, “Spin-optical metamaterial route to spin-controlled photonics,” Science 340, 724–726 (2013).
[Crossref] [PubMed]

Manzo, C.

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96, 163905 (2006).
[Crossref] [PubMed]

Marquardt, C.

A. Aiello, N. Lindlein, C. Marquardt, and G. Leuchs, “Transverse angular momentum and geometric spin hall effect of light,” Phys. Rev. Lett. 103, 100401 (2009).
[Crossref] [PubMed]

Marrucci, L.

F. Cardano, E. Karimi, S. Slussarenko, L. Marrucci, C. de Lisio, and E. Santamato, “Polarization pattern of vector vortex beams generated by q-plates with different topological charges,” Appl. Opt. 51, C1–C6 (2012).
[Crossref] [PubMed]

E. Karimi, S. Slussarenko, B. Piccirillo, L. Marrucci, and E. Santamato, “Polarization-controlled evolution of light transverse modes and associated pancharatnam geometric phase in orbital angular momentum,” Phys. Rev. A 81, 053813 (2010).
[Crossref]

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96, 163905 (2006).
[Crossref] [PubMed]

Mühlenbernd, H.

L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K. Cheah, C. Qiu, J. Li, T. Zentgraf, and S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commum. 4, 2808 (2013).

X. Chen, L. Huang, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, C. Qiu, S. Zhang, and T. Zentgraf, “Dual-polarity plasmonic metalens for visible light,” Nat. Commum. 3, 1198 (2012).
[Crossref]

L. Huang, X. Chen, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, “Dispersionless phase discontinuities for controlling light propagation,” Nano Lett. 12, 5750–5755 (2012).
[Crossref] [PubMed]

Murakami, S.

M. Onoda, S. Murakami, and N. Nagaosa, “Hall effect of light,” Phys. Rev. Lett. 93, 083901 (2004).
[Crossref] [PubMed]

Nagaosa, N.

M. Onoda, S. Murakami, and N. Nagaosa, “Hall effect of light,” Phys. Rev. Lett. 93, 083901 (2004).
[Crossref] [PubMed]

Nienhuis, G.

G. Nienhuis, “Doppler effect induced by rotating lenses,” Opt. Commun. 132, 8–14 (1996).
[Crossref]

Niv, A.

Onoda, M.

M. Onoda, S. Murakami, and N. Nagaosa, “Hall effect of light,” Phys. Rev. Lett. 93, 083901 (2004).
[Crossref] [PubMed]

Ozeri, D.

N. Shitrit, I. Yulevich, E. Maguid, D. Ozeri, D. Veksler, V. Kleiner, and E. Hasman, “Spin-optical metamaterial route to spin-controlled photonics,” Science 340, 724–726 (2013).
[Crossref] [PubMed]

Padgett, M.

M. Padgett, J. Courtial, and L. Allen, “Light’s orbital angular momentum,” Phys. Today 57, 35–40 (2004).
[Crossref]

Paparo, D.

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96, 163905 (2006).
[Crossref] [PubMed]

Piccirillo, B.

E. Karimi, S. Slussarenko, B. Piccirillo, L. Marrucci, and E. Santamato, “Polarization-controlled evolution of light transverse modes and associated pancharatnam geometric phase in orbital angular momentum,” Phys. Rev. A 81, 053813 (2010).
[Crossref]

Qin, Y.

Qiu, C.

L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K. Cheah, C. Qiu, J. Li, T. Zentgraf, and S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commum. 4, 2808 (2013).

X. Chen, L. Huang, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, C. Qiu, S. Zhang, and T. Zentgraf, “Dual-polarity plasmonic metalens for visible light,” Nat. Commum. 3, 1198 (2012).
[Crossref]

Rho, J.

X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin Hall effect at metasurfaces,” Science 334, 1405–1407 (2013).
[Crossref]

Santamato, E.

F. Cardano, E. Karimi, S. Slussarenko, L. Marrucci, C. de Lisio, and E. Santamato, “Polarization pattern of vector vortex beams generated by q-plates with different topological charges,” Appl. Opt. 51, C1–C6 (2012).
[Crossref] [PubMed]

E. Karimi, S. Slussarenko, B. Piccirillo, L. Marrucci, and E. Santamato, “Polarization-controlled evolution of light transverse modes and associated pancharatnam geometric phase in orbital angular momentum,” Phys. Rev. A 81, 053813 (2010).
[Crossref]

Scully, M. O.

P. Genevet, N. Yu, F. Aieta, J. Lin, M. A. Kats, R. Blanchard, M. O. Scully, Z. Gaburro, and F. Capasso, “Ultra-thin plasmonic optical vortex plate based on phase discontinuities,” Appl. Phys. Lett. 100, 013101 (2012).
[Crossref]

Shitrit, N.

N. Shitrit, I. Yulevich, E. Maguid, D. Ozeri, D. Veksler, V. Kleiner, and E. Hasman, “Spin-optical metamaterial route to spin-controlled photonics,” Science 340, 724–726 (2013).
[Crossref] [PubMed]

Shu, W.

X. Ling, X. Yi, X. Zhou, Y. Liu, W. Shu, H. Luo, and S. Wen, “Realization of tunable spin-dependent splitting in intrinsic photonic spin Hall effect,” Appl. Phys. Lett. 105, 151101 (2014).
[Crossref]

H. Luo, X. Zhou, W. Shu, S. Wen, and D. Fan, “Enhanced and switchable spin Hall effect of light near the Brewster angle on reflection,” Phys. Rev. A 84, 043806 (2011).
[Crossref]

H. Luo, S. Wen, W. Shu, and D. Fan, “Spin Hall effect of light in photon tunneling,” Phys. Rev. A 82, 043825 (2010).
[Crossref]

H. Luo, S. Wen, W. Shu, Z. Tang, Y. Zou, and D. Fan, “Rotational Doppler effect in left-handed materials,” Phys. Rev. A 78, 033805 (2008).
[Crossref]

Slussarenko, S.

F. Cardano, E. Karimi, S. Slussarenko, L. Marrucci, C. de Lisio, and E. Santamato, “Polarization pattern of vector vortex beams generated by q-plates with different topological charges,” Appl. Opt. 51, C1–C6 (2012).
[Crossref] [PubMed]

E. Karimi, S. Slussarenko, B. Piccirillo, L. Marrucci, and E. Santamato, “Polarization-controlled evolution of light transverse modes and associated pancharatnam geometric phase in orbital angular momentum,” Phys. Rev. A 81, 053813 (2010).
[Crossref]

Spreeuw, R. J. C.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[Crossref] [PubMed]

Tan, Q.

L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K. Cheah, C. Qiu, J. Li, T. Zentgraf, and S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commum. 4, 2808 (2013).

X. Chen, L. Huang, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, C. Qiu, S. Zhang, and T. Zentgraf, “Dual-polarity plasmonic metalens for visible light,” Nat. Commum. 3, 1198 (2012).
[Crossref]

L. Huang, X. Chen, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, “Dispersionless phase discontinuities for controlling light propagation,” Nano Lett. 12, 5750–5755 (2012).
[Crossref] [PubMed]

Tang, Z.

H. Luo, S. Wen, W. Shu, Z. Tang, Y. Zou, and D. Fan, “Rotational Doppler effect in left-handed materials,” Phys. Rev. A 78, 033805 (2008).
[Crossref]

Tetienne, J.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
[Crossref] [PubMed]

Veksler, D.

N. Shitrit, I. Yulevich, E. Maguid, D. Ozeri, D. Veksler, V. Kleiner, and E. Hasman, “Spin-optical metamaterial route to spin-controlled photonics,” Science 340, 724–726 (2013).
[Crossref] [PubMed]

Veysi, M.

Wang, Y.

X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin Hall effect at metasurfaces,” Science 334, 1405–1407 (2013).
[Crossref]

Wen, S.

Y. Liu, X. Ling, X. Yi, X. Zhou, S. Chen, Y. Ke, H. Luo, and S. Wen, “Photonic spin Hall effect in dielectric metasurfaces with rotational symmetry breaking,” Opt. Lett. 40, 756–759 (2015).
[Crossref] [PubMed]

X. Yi, Y. Liu, X. Ling, X. Zhou, Y. Ke, H. Luo, S. Wen, and D. Fan, “Hybrid-order Poincaré sphere,” Phys. Rev. A 91, 023801 (2015).
[Crossref]

Y. Li, Y. Liu, X. Ling, X. Yi, X. Zhou, Y. Ke, H. Luo, S. Wen, and D. Fan, “Observation of photonic spin Hall effect with phase singularity at dielectric metasurfaces,” Opt. Express 23, 1767–1774 (2015).
[Crossref] [PubMed]

Y. Liu, X. Ling, X. Yi, X. Zhou, H. Luo, and S. Wen, “Realization of polarization evolution on higher-order Poincaré sphere with metasurface,” Appl. Phys. Lett. 104, 191110 (2014).
[Crossref]

X. Yi, X. Ling, Z. Zhang, X. Zhou, Y. Liu, S. Chen, H. Luo, and S. Wen, “Generation of cylindrical vector vortex beams by two cascaded metasurfaces,” Opt. Express 22, 17207–17215 (2014).
[Crossref] [PubMed]

X. Ling, X. Yi, X. Zhou, Y. Liu, W. Shu, H. Luo, and S. Wen, “Realization of tunable spin-dependent splitting in intrinsic photonic spin Hall effect,” Appl. Phys. Lett. 105, 151101 (2014).
[Crossref]

X. Ling, X. Zhou, H. Luo, and S. Wen, “Steering far-field spin-dependent splitting of light by inhomogeneous anisotropic media,” Phys. Rev. A 86, 053824 (2012).
[Crossref]

H. Luo, X. Zhou, W. Shu, S. Wen, and D. Fan, “Enhanced and switchable spin Hall effect of light near the Brewster angle on reflection,” Phys. Rev. A 84, 043806 (2011).
[Crossref]

H. Luo, S. Wen, W. Shu, and D. Fan, “Spin Hall effect of light in photon tunneling,” Phys. Rev. A 82, 043825 (2010).
[Crossref]

H. Luo, S. Wen, W. Shu, Z. Tang, Y. Zou, and D. Fan, “Rotational Doppler effect in left-handed materials,” Phys. Rev. A 78, 033805 (2008).
[Crossref]

Woerdman, J. P.

A. Aiello and J. P. Woerdman, “Role of beam propagation in Goos-Hänchen and Imbert-Fedorov shifts,” Opt. Lett. 33, 1437–1439 (2008).
[Crossref] [PubMed]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[Crossref] [PubMed]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1997).

Xiao, Y.

Yang, H.

Ye, Z.

X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin Hall effect at metasurfaces,” Science 334, 1405–1407 (2013).
[Crossref]

Yi, X.

Y. Liu, X. Ling, X. Yi, X. Zhou, S. Chen, Y. Ke, H. Luo, and S. Wen, “Photonic spin Hall effect in dielectric metasurfaces with rotational symmetry breaking,” Opt. Lett. 40, 756–759 (2015).
[Crossref] [PubMed]

Y. Li, Y. Liu, X. Ling, X. Yi, X. Zhou, Y. Ke, H. Luo, S. Wen, and D. Fan, “Observation of photonic spin Hall effect with phase singularity at dielectric metasurfaces,” Opt. Express 23, 1767–1774 (2015).
[Crossref] [PubMed]

X. Yi, Y. Liu, X. Ling, X. Zhou, Y. Ke, H. Luo, S. Wen, and D. Fan, “Hybrid-order Poincaré sphere,” Phys. Rev. A 91, 023801 (2015).
[Crossref]

Y. Liu, X. Ling, X. Yi, X. Zhou, H. Luo, and S. Wen, “Realization of polarization evolution on higher-order Poincaré sphere with metasurface,” Appl. Phys. Lett. 104, 191110 (2014).
[Crossref]

X. Yi, X. Ling, Z. Zhang, X. Zhou, Y. Liu, S. Chen, H. Luo, and S. Wen, “Generation of cylindrical vector vortex beams by two cascaded metasurfaces,” Opt. Express 22, 17207–17215 (2014).
[Crossref] [PubMed]

X. Ling, X. Yi, X. Zhou, Y. Liu, W. Shu, H. Luo, and S. Wen, “Realization of tunable spin-dependent splitting in intrinsic photonic spin Hall effect,” Appl. Phys. Lett. 105, 151101 (2014).
[Crossref]

Yin, X.

X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin Hall effect at metasurfaces,” Science 334, 1405–1407 (2013).
[Crossref]

Yu, N.

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12, 4932–4936 (2012).
[Crossref] [PubMed]

P. Genevet, N. Yu, F. Aieta, J. Lin, M. A. Kats, R. Blanchard, M. O. Scully, Z. Gaburro, and F. Capasso, “Ultra-thin plasmonic optical vortex plate based on phase discontinuities,” Appl. Phys. Lett. 100, 013101 (2012).
[Crossref]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
[Crossref] [PubMed]

Yulevich, I.

N. Shitrit, I. Yulevich, E. Maguid, D. Ozeri, D. Veksler, V. Kleiner, and E. Hasman, “Spin-optical metamaterial route to spin-controlled photonics,” Science 340, 724–726 (2013).
[Crossref] [PubMed]

Zentgraf, T.

L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K. Cheah, C. Qiu, J. Li, T. Zentgraf, and S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commum. 4, 2808 (2013).

X. Chen, L. Huang, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, C. Qiu, S. Zhang, and T. Zentgraf, “Dual-polarity plasmonic metalens for visible light,” Nat. Commum. 3, 1198 (2012).
[Crossref]

L. Huang, X. Chen, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, “Dispersionless phase discontinuities for controlling light propagation,” Nano Lett. 12, 5750–5755 (2012).
[Crossref] [PubMed]

Zhan, Q.

Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photonics 1, 1–57 (2009).
[Crossref]

Zhang, H.

L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K. Cheah, C. Qiu, J. Li, T. Zentgraf, and S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commum. 4, 2808 (2013).

Zhang, S.

L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K. Cheah, C. Qiu, J. Li, T. Zentgraf, and S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commum. 4, 2808 (2013).

X. Chen, L. Huang, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, C. Qiu, S. Zhang, and T. Zentgraf, “Dual-polarity plasmonic metalens for visible light,” Nat. Commum. 3, 1198 (2012).
[Crossref]

L. Huang, X. Chen, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, “Dispersionless phase discontinuities for controlling light propagation,” Nano Lett. 12, 5750–5755 (2012).
[Crossref] [PubMed]

Zhang, X.

X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin Hall effect at metasurfaces,” Science 334, 1405–1407 (2013).
[Crossref]

Zhang, Z.

Zhou, X.

X. Yi, Y. Liu, X. Ling, X. Zhou, Y. Ke, H. Luo, S. Wen, and D. Fan, “Hybrid-order Poincaré sphere,” Phys. Rev. A 91, 023801 (2015).
[Crossref]

Y. Li, Y. Liu, X. Ling, X. Yi, X. Zhou, Y. Ke, H. Luo, S. Wen, and D. Fan, “Observation of photonic spin Hall effect with phase singularity at dielectric metasurfaces,” Opt. Express 23, 1767–1774 (2015).
[Crossref] [PubMed]

Y. Liu, X. Ling, X. Yi, X. Zhou, S. Chen, Y. Ke, H. Luo, and S. Wen, “Photonic spin Hall effect in dielectric metasurfaces with rotational symmetry breaking,” Opt. Lett. 40, 756–759 (2015).
[Crossref] [PubMed]

X. Ling, X. Yi, X. Zhou, Y. Liu, W. Shu, H. Luo, and S. Wen, “Realization of tunable spin-dependent splitting in intrinsic photonic spin Hall effect,” Appl. Phys. Lett. 105, 151101 (2014).
[Crossref]

Y. Liu, X. Ling, X. Yi, X. Zhou, H. Luo, and S. Wen, “Realization of polarization evolution on higher-order Poincaré sphere with metasurface,” Appl. Phys. Lett. 104, 191110 (2014).
[Crossref]

X. Yi, X. Ling, Z. Zhang, X. Zhou, Y. Liu, S. Chen, H. Luo, and S. Wen, “Generation of cylindrical vector vortex beams by two cascaded metasurfaces,” Opt. Express 22, 17207–17215 (2014).
[Crossref] [PubMed]

X. Ling, X. Zhou, H. Luo, and S. Wen, “Steering far-field spin-dependent splitting of light by inhomogeneous anisotropic media,” Phys. Rev. A 86, 053824 (2012).
[Crossref]

H. Luo, X. Zhou, W. Shu, S. Wen, and D. Fan, “Enhanced and switchable spin Hall effect of light near the Brewster angle on reflection,” Phys. Rev. A 84, 043806 (2011).
[Crossref]

Zou, Y.

H. Luo, S. Wen, W. Shu, Z. Tang, Y. Zou, and D. Fan, “Rotational Doppler effect in left-handed materials,” Phys. Rev. A 78, 033805 (2008).
[Crossref]

Adv. Opt. Photonics (2)

Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photonics 1, 1–57 (2009).
[Crossref]

M. Beresna, M. Gecevicius, and P. G. Kazansky, “Ultrafast laser direct writing and nanostructuring in transparent materials,” Adv. Opt. Photonics 6, 293–339 (2014).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (4)

M. Beresna, M. Gecevičius, P. G. Kazansky, and T. Gertus, “Radially polarized optical vortex converter created by femtosecond laser nanostructuring of glass,” Appl. Phys. Lett. 98, 201101 (2011).
[Crossref]

P. Genevet, N. Yu, F. Aieta, J. Lin, M. A. Kats, R. Blanchard, M. O. Scully, Z. Gaburro, and F. Capasso, “Ultra-thin plasmonic optical vortex plate based on phase discontinuities,” Appl. Phys. Lett. 100, 013101 (2012).
[Crossref]

X. Ling, X. Yi, X. Zhou, Y. Liu, W. Shu, H. Luo, and S. Wen, “Realization of tunable spin-dependent splitting in intrinsic photonic spin Hall effect,” Appl. Phys. Lett. 105, 151101 (2014).
[Crossref]

Y. Liu, X. Ling, X. Yi, X. Zhou, H. Luo, and S. Wen, “Realization of polarization evolution on higher-order Poincaré sphere with metasurface,” Appl. Phys. Lett. 104, 191110 (2014).
[Crossref]

J. Opt. Soc. Am. B (1)

Nano Lett. (3)

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12, 4932–4936 (2012).
[Crossref] [PubMed]

J. Lin, P. Genevet, M. A. Kats, N. Antoniou, and F. Capasso, “Nanostructured holograms for broadband manipulation of vector beams,” Nano Lett. 13, 4269–4274 (2013).
[Crossref] [PubMed]

L. Huang, X. Chen, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, “Dispersionless phase discontinuities for controlling light propagation,” Nano Lett. 12, 5750–5755 (2012).
[Crossref] [PubMed]

Nat. Commum. (2)

L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K. Cheah, C. Qiu, J. Li, T. Zentgraf, and S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commum. 4, 2808 (2013).

X. Chen, L. Huang, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, C. Qiu, S. Zhang, and T. Zentgraf, “Dual-polarity plasmonic metalens for visible light,” Nat. Commum. 3, 1198 (2012).
[Crossref]

Nat. Photonics (2)

K. Y. Bliokh, A. Niv, V. Kleiner, and E. Hasman, “Geometrodynamics of spinning light,” Nat. Photonics 2, 748–753 (2008).
[Crossref]

D. Hakobyan and E. Brasselet, “Left-handed optical radiation torque,” Nat. Photonics 8, 610–614 (2014).
[Crossref]

Opt. Commun. (2)

B. A. Garetz and S. Arnold, “Variable frequency shifting of circularly polarized laser radiation via a rotating half-wave retardation plate,” Opt. Commun. 31, 1–3 (1979).
[Crossref]

G. Nienhuis, “Doppler effect induced by rotating lenses,” Opt. Commun. 132, 8–14 (1996).
[Crossref]

Opt. Express (3)

Opt. Lett. (4)

Phys. Rev. A (7)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[Crossref] [PubMed]

X. Yi, Y. Liu, X. Ling, X. Zhou, Y. Ke, H. Luo, S. Wen, and D. Fan, “Hybrid-order Poincaré sphere,” Phys. Rev. A 91, 023801 (2015).
[Crossref]

H. Luo, S. Wen, W. Shu, Z. Tang, Y. Zou, and D. Fan, “Rotational Doppler effect in left-handed materials,” Phys. Rev. A 78, 033805 (2008).
[Crossref]

H. Luo, X. Zhou, W. Shu, S. Wen, and D. Fan, “Enhanced and switchable spin Hall effect of light near the Brewster angle on reflection,” Phys. Rev. A 84, 043806 (2011).
[Crossref]

X. Ling, X. Zhou, H. Luo, and S. Wen, “Steering far-field spin-dependent splitting of light by inhomogeneous anisotropic media,” Phys. Rev. A 86, 053824 (2012).
[Crossref]

E. Karimi, S. Slussarenko, B. Piccirillo, L. Marrucci, and E. Santamato, “Polarization-controlled evolution of light transverse modes and associated pancharatnam geometric phase in orbital angular momentum,” Phys. Rev. A 81, 053813 (2010).
[Crossref]

H. Luo, S. Wen, W. Shu, and D. Fan, “Spin Hall effect of light in photon tunneling,” Phys. Rev. A 82, 043825 (2010).
[Crossref]

Phys. Rev. Lett. (6)

N. Dahan, Y. Gorodetski, K. Frischwasser, V. Kleiner, and E. Hasman, “Geometric Doppler effect: spin-split dispersion of thermal radiation,” Phys. Rev. Lett. 105, 136402 (2010).
[Crossref]

K. Y. Bliokh, Y. Gorodetski, V. Kleiner, and E. Hasman, “Coriolis effect in optics: unified geometric phase and spin-Hall effect,” Phys. Rev. Lett. 101, 030404 (2008).
[Crossref] [PubMed]

M. Onoda, S. Murakami, and N. Nagaosa, “Hall effect of light,” Phys. Rev. Lett. 93, 083901 (2004).
[Crossref] [PubMed]

K. Y. Bliokh and Y. P. Bliokh, “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).
[Crossref] [PubMed]

A. Aiello, N. Lindlein, C. Marquardt, and G. Leuchs, “Transverse angular momentum and geometric spin hall effect of light,” Phys. Rev. Lett. 103, 100401 (2009).
[Crossref] [PubMed]

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96, 163905 (2006).
[Crossref] [PubMed]

Phys. Today (1)

M. Padgett, J. Courtial, and L. Allen, “Light’s orbital angular momentum,” Phys. Today 57, 35–40 (2004).
[Crossref]

Science (5)

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
[Crossref] [PubMed]

O. Hosten and P. Kwiat, “Observation of the spin Hall effect of light via weak measurements,” Science 319, 787–790 (2008).
[Crossref] [PubMed]

X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin Hall effect at metasurfaces,” Science 334, 1405–1407 (2013).
[Crossref]

N. Shitrit, I. Yulevich, E. Maguid, D. Ozeri, D. Veksler, V. Kleiner, and E. Hasman, “Spin-optical metamaterial route to spin-controlled photonics,” Science 340, 724–726 (2013).
[Crossref] [PubMed]

D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345, 298–302 (2014).
[Crossref] [PubMed]

Other (1)

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1997).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1

(a) Schematic illustration of the polarization state variation when a circularly polarized beam passes through the metasurface (q = 1). The instantaneous electric field vectors (E) of input and output circularly polarized beams demonstrate that an m = 0 order mode is transformed into the mode m = 2 in this process. (b) The hybrid-order Poincaré sphere showing the evolution of polarization state corresponding to the process depicted in Fig. 1(a). (c),(d) The OAM addition and subtraction. An vortex beam l = 4 would be converted to the vortex l = 5 or 3, when a left- or right-circularly polarized beam impinged upon the metasurface with q = 1/2, respectively.

Fig. 2
Fig. 2

The experiment setup applied to realize the manipulation of spin-dependent splitting based on the geometric Doppler effect. Insets (a) and (b) are the schematic pictures of metasurface with rotational symmetry and with rotational asymmetry respectively. Inset (c) is the example of phase plot (l = 3) applied in our experiments to generate the CVBs.

Fig. 3
Fig. 3

The interference results of vortex beams with Gaussian reference beams, where the vortex beams are generated by metasurfaces (a–c) or by phase-only SLM (d–f). By comparison, it is shown that the metasurfaces can modify the phase front of beam as the geometric Doppler effect predicted.

Fig. 4
Fig. 4

The OAM transformation under the control of geometric Doppler effect. With different sign of input vortexes (generated by SLM), the vortex phases are modulated either constructively or destructively. The first row is the interference results obtained after vortex beams with topological charge l = −1 passing through three different metasurfaces (q = 1/2, 1, and 3/2, respectively), which show that the generated phases are superposed to the original dynamic phases of vortex beams. Oppositely, the second row shows subtractive results when we refer to an incident vortex beam with l = 1.

Fig. 5
Fig. 5

The spin-dependent splitting observed when a linearly polarized CVB passed through the rotationally asymmetric metasurfaces. Red and blue represent the left- and right-circular polarizations, respectively. The results show a larger splitting when the absolute value of m − 2q is increasing, and that the splitting orientation would be inverted when the sign of m − 2q is reversed. Therefore, it is realizable to manipulate the spin-dependent splitting by changing the metasurfaces with different q.

Fig. 6
Fig. 6

The intensity splitting observed in our experiments, which demonstrates a directly measurable intensity splitting when breaking the rotational symmetry of linearly polarized CVBs and that the magnitude of splitting is tunable according to the absolute value of m − 2q.

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

δ Φ = ( J J 0 ) Ω d t ,
t ζ , Ω Ω ζ .
θ ( r , ϕ ) = q ϕ + α 0 ,
Ω ζ = θ / ζ = ( q ϕ + α 0 ) / ζ = q .
δ Φ = ( J J 0 ) Ω d t = ± 2 e z q d ϕ = ± 2 q ϕ .
0 Ψ = d ( σ m ϕ ) / d ϕ = σ m ,
Δ k = 0 Ψ + ζ Φ = ± ( m ± 2 q ) .
d = Δ k k z = ± λ 0 2 π ( m ± 2 q ) z ,

Metrics