Abstract

We report on the observation of the spin separation of light in the plane of incidence when a linearly polarized beam is reflected or refracted at a planar dielectric interface. Remarkably, the in-plane spin separation reaches hundreds of nanometers, comparable with the transverse spin separation induced by the well-known spin Hall effect of light. The observation is properly explained by considering the in-plane spread of wave-vectors. This study thus offers new insights on the spinoptics and may provide a potential method to control light in optical nanodevices.

© 2011 OSA

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  1. M. Merano, A. Aiello, M. P. van Exter, and J. P. Woerdman, “Observing angular deviations in the specular reflection of a light beam,” Nat. Photonics 3(6), 337–340 (2009).
    [CrossRef]
  2. M. Merano, N. Hermosa, J. P. Woerdman, and A. Aiello, “How orbital angular momentum affects beam shifts in optical reflection,” Phys. Rev. A 82(2), 023817 (2010).
    [CrossRef]
  3. A. Aiello and J. P. Woerdman, “Role of beam propagation in Goos-Hanchen and Imbert-Fedorov shifts,” Opt. Lett. 33(13), 1437–1439 (2008).
    [CrossRef] [PubMed]
  4. K. Y. Bliokh, I. V. Shadrivov, and Y. S. Kivshar, “Goos-Hanchen and Imbert-Fedorov shifts of polarized vortex beams,” Opt. Lett. 34(3), 389–391 (2009).
    [CrossRef] [PubMed]
  5. M. Onoda, S. Murakami, and N. Nagaosa, “Hall effect of light,” Phys. Rev. Lett. 93(8), 083901 (2004).
    [CrossRef] [PubMed]
  6. 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(7), 073903 (2006).
    [CrossRef] [PubMed]
  7. K. Y. Bliokh and Y. P. Bliokh, “Polarization, transverse shifts, and angular momentum conservation laws in partial reflection and refraction of an electromagnetic wave packet,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(6), 066609 (2007).
    [CrossRef] [PubMed]
  8. O. Hosten and P. Kwiat, “Observation of the spin hall effect of light via weak measurements,” Science 319(5864), 787–790 (2008).
    [CrossRef] [PubMed]
  9. Y. Qin, Y. Li, H. Y. He, and Q. H. Gong, “Measurement of spin Hall effect of reflected light,” Opt. Lett. 34(17), 2551–2553 (2009).
    [CrossRef] [PubMed]
  10. Y. Qin, Y. Li, X. B. Feng, Z. P. Liu, H. Y. He, Y. F. Xiao, and Q. H. Gong, “Spin Hall effect of reflected light at the air-uniaxial crystal interface,” Opt. Express 18(16), 16832–16839 (2010).
    [CrossRef] [PubMed]
  11. H. L. Luo, S. C. Wen, W. X. Shu, Z. X. Tang, Y. H. Zou, and D. Y. Fan, “Spin Hall effect of a light beam in left-handed materials,” Phys. Rev. A 80(4), 043810 (2009).
    [CrossRef]
  12. A. V. Dooghin, N. D. Kundikova, V. S. Liberman, and B. Y. Zel’dovich, “Optical Magnus effect,” Phys. Rev. A 45(11), 8204–8208 (1992).
    [CrossRef] [PubMed]
  13. A. Bérard and H. Mohrbach, “Spin Hall effect and Berry phase of spinning particles,” Phys. Lett. A 352(3), 190–195 (2006).
    [CrossRef]
  14. A. Aiello, N. Lindlein, C. Marquardt, and G. Leuchs, “Transverse angular momentum and geometric spin Hall effect of light,” Phys. Rev. Lett. 103(10), 100401 (2009).
    [CrossRef] [PubMed]
  15. K. Y. Bliokh, A. Niv, V. Kleiner, and E. Hasman, “Geometrodynamics of spinning light,” Nat. Photonics 2(12), 748–753 (2008).
    [CrossRef]
  16. 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(3), 030404 (2008).
    [CrossRef] [PubMed]
  17. K. Y. Bliokh and A. S. Desyatnikov, “Spin and orbital Hall effects for diffracting optical beams in gradient-index media,” Phys. Rev. A 79(1), 011807 (2009).
    [CrossRef]
  18. D. Haefner, S. Sukhov, and A. Dogariu, “Spin hall effect of light in spherical geometry,” Phys. Rev. Lett. 102(12), 123903 (2009).
    [CrossRef] [PubMed]
  19. J. M. Menard, A. E. Mattacchione, M. Betz, and H. M. van Driel, “Imaging the spin Hall effect of light inside semiconductors via absorption,” Opt. Lett. 34(15), 2312–2314 (2009).
    [CrossRef] [PubMed]
  20. J. M. Ménard, A. E. Mattacchione, H. M. van Driel, C. Hautmann, and M. Betz, “Ultrafast optical imaging of the spin Hall effect of light in semiconductors,” Phys. Rev. B 82(4), 045303 (2010).
    [CrossRef]
  21. K. Artmann, “Berechnung der seitenversetzung des totalreflektierten strahles,” Ann. Phys. 437(1-2), 87–102 (1948).
    [CrossRef]

2010 (3)

M. Merano, N. Hermosa, J. P. Woerdman, and A. Aiello, “How orbital angular momentum affects beam shifts in optical reflection,” Phys. Rev. A 82(2), 023817 (2010).
[CrossRef]

Y. Qin, Y. Li, X. B. Feng, Z. P. Liu, H. Y. He, Y. F. Xiao, and Q. H. Gong, “Spin Hall effect of reflected light at the air-uniaxial crystal interface,” Opt. Express 18(16), 16832–16839 (2010).
[CrossRef] [PubMed]

J. M. Ménard, A. E. Mattacchione, H. M. van Driel, C. Hautmann, and M. Betz, “Ultrafast optical imaging of the spin Hall effect of light in semiconductors,” Phys. Rev. B 82(4), 045303 (2010).
[CrossRef]

2009 (8)

H. L. Luo, S. C. Wen, W. X. Shu, Z. X. Tang, Y. H. Zou, and D. Y. Fan, “Spin Hall effect of a light beam in left-handed materials,” Phys. Rev. A 80(4), 043810 (2009).
[CrossRef]

Y. Qin, Y. Li, H. Y. He, and Q. H. Gong, “Measurement of spin Hall effect of reflected light,” Opt. Lett. 34(17), 2551–2553 (2009).
[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(10), 100401 (2009).
[CrossRef] [PubMed]

K. Y. Bliokh and A. S. Desyatnikov, “Spin and orbital Hall effects for diffracting optical beams in gradient-index media,” Phys. Rev. A 79(1), 011807 (2009).
[CrossRef]

D. Haefner, S. Sukhov, and A. Dogariu, “Spin hall effect of light in spherical geometry,” Phys. Rev. Lett. 102(12), 123903 (2009).
[CrossRef] [PubMed]

J. M. Menard, A. E. Mattacchione, M. Betz, and H. M. van Driel, “Imaging the spin Hall effect of light inside semiconductors via absorption,” Opt. Lett. 34(15), 2312–2314 (2009).
[CrossRef] [PubMed]

K. Y. Bliokh, I. V. Shadrivov, and Y. S. Kivshar, “Goos-Hanchen and Imbert-Fedorov shifts of polarized vortex beams,” Opt. Lett. 34(3), 389–391 (2009).
[CrossRef] [PubMed]

M. Merano, A. Aiello, M. P. van Exter, and J. P. Woerdman, “Observing angular deviations in the specular reflection of a light beam,” Nat. Photonics 3(6), 337–340 (2009).
[CrossRef]

2008 (4)

O. Hosten and P. Kwiat, “Observation of the spin hall effect of light via weak measurements,” Science 319(5864), 787–790 (2008).
[CrossRef] [PubMed]

A. Aiello and J. P. Woerdman, “Role of beam propagation in Goos-Hanchen and Imbert-Fedorov shifts,” Opt. Lett. 33(13), 1437–1439 (2008).
[CrossRef] [PubMed]

K. Y. Bliokh, A. Niv, V. Kleiner, and E. Hasman, “Geometrodynamics of spinning light,” Nat. Photonics 2(12), 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(3), 030404 (2008).
[CrossRef] [PubMed]

2007 (1)

K. Y. Bliokh and Y. P. Bliokh, “Polarization, transverse shifts, and angular momentum conservation laws in partial reflection and refraction of an electromagnetic wave packet,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(6), 066609 (2007).
[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(7), 073903 (2006).
[CrossRef] [PubMed]

A. Bérard and H. Mohrbach, “Spin Hall effect and Berry phase of spinning particles,” Phys. Lett. A 352(3), 190–195 (2006).
[CrossRef]

2004 (1)

M. Onoda, S. Murakami, and N. Nagaosa, “Hall effect of light,” Phys. Rev. Lett. 93(8), 083901 (2004).
[CrossRef] [PubMed]

1992 (1)

A. V. Dooghin, N. D. Kundikova, V. S. Liberman, and B. Y. Zel’dovich, “Optical Magnus effect,” Phys. Rev. A 45(11), 8204–8208 (1992).
[CrossRef] [PubMed]

1948 (1)

K. Artmann, “Berechnung der seitenversetzung des totalreflektierten strahles,” Ann. Phys. 437(1-2), 87–102 (1948).
[CrossRef]

Aiello, A.

M. Merano, N. Hermosa, J. P. Woerdman, and A. Aiello, “How orbital angular momentum affects beam shifts in optical reflection,” Phys. Rev. A 82(2), 023817 (2010).
[CrossRef]

M. Merano, A. Aiello, M. P. van Exter, and J. P. Woerdman, “Observing angular deviations in the specular reflection of a light beam,” Nat. Photonics 3(6), 337–340 (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(10), 100401 (2009).
[CrossRef] [PubMed]

A. Aiello and J. P. Woerdman, “Role of beam propagation in Goos-Hanchen and Imbert-Fedorov shifts,” Opt. Lett. 33(13), 1437–1439 (2008).
[CrossRef] [PubMed]

Artmann, K.

K. Artmann, “Berechnung der seitenversetzung des totalreflektierten strahles,” Ann. Phys. 437(1-2), 87–102 (1948).
[CrossRef]

Bérard, A.

A. Bérard and H. Mohrbach, “Spin Hall effect and Berry phase of spinning particles,” Phys. Lett. A 352(3), 190–195 (2006).
[CrossRef]

Betz, M.

J. M. Ménard, A. E. Mattacchione, H. M. van Driel, C. Hautmann, and M. Betz, “Ultrafast optical imaging of the spin Hall effect of light in semiconductors,” Phys. Rev. B 82(4), 045303 (2010).
[CrossRef]

J. M. Menard, A. E. Mattacchione, M. Betz, and H. M. van Driel, “Imaging the spin Hall effect of light inside semiconductors via absorption,” Opt. Lett. 34(15), 2312–2314 (2009).
[CrossRef] [PubMed]

Bliokh, K. Y.

K. Y. Bliokh and A. S. Desyatnikov, “Spin and orbital Hall effects for diffracting optical beams in gradient-index media,” Phys. Rev. A 79(1), 011807 (2009).
[CrossRef]

K. Y. Bliokh, I. V. Shadrivov, and Y. S. Kivshar, “Goos-Hanchen and Imbert-Fedorov shifts of polarized vortex beams,” Opt. Lett. 34(3), 389–391 (2009).
[CrossRef] [PubMed]

K. Y. Bliokh, A. Niv, V. Kleiner, and E. Hasman, “Geometrodynamics of spinning light,” Nat. Photonics 2(12), 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(3), 030404 (2008).
[CrossRef] [PubMed]

K. Y. Bliokh and Y. P. Bliokh, “Polarization, transverse shifts, and angular momentum conservation laws in partial reflection and refraction of an electromagnetic wave packet,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(6), 066609 (2007).
[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(7), 073903 (2006).
[CrossRef] [PubMed]

Bliokh, Y. P.

K. Y. Bliokh and Y. P. Bliokh, “Polarization, transverse shifts, and angular momentum conservation laws in partial reflection and refraction of an electromagnetic wave packet,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(6), 066609 (2007).
[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(7), 073903 (2006).
[CrossRef] [PubMed]

Desyatnikov, A. S.

K. Y. Bliokh and A. S. Desyatnikov, “Spin and orbital Hall effects for diffracting optical beams in gradient-index media,” Phys. Rev. A 79(1), 011807 (2009).
[CrossRef]

Dogariu, A.

D. Haefner, S. Sukhov, and A. Dogariu, “Spin hall effect of light in spherical geometry,” Phys. Rev. Lett. 102(12), 123903 (2009).
[CrossRef] [PubMed]

Dooghin, A. V.

A. V. Dooghin, N. D. Kundikova, V. S. Liberman, and B. Y. Zel’dovich, “Optical Magnus effect,” Phys. Rev. A 45(11), 8204–8208 (1992).
[CrossRef] [PubMed]

Fan, D. Y.

H. L. Luo, S. C. Wen, W. X. Shu, Z. X. Tang, Y. H. Zou, and D. Y. Fan, “Spin Hall effect of a light beam in left-handed materials,” Phys. Rev. A 80(4), 043810 (2009).
[CrossRef]

Feng, X. B.

Gong, Q. H.

Gorodetski, Y.

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(3), 030404 (2008).
[CrossRef] [PubMed]

Haefner, D.

D. Haefner, S. Sukhov, and A. Dogariu, “Spin hall effect of light in spherical geometry,” Phys. Rev. Lett. 102(12), 123903 (2009).
[CrossRef] [PubMed]

Hasman, E.

K. Y. Bliokh, A. Niv, V. Kleiner, and E. Hasman, “Geometrodynamics of spinning light,” Nat. Photonics 2(12), 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(3), 030404 (2008).
[CrossRef] [PubMed]

Hautmann, C.

J. M. Ménard, A. E. Mattacchione, H. M. van Driel, C. Hautmann, and M. Betz, “Ultrafast optical imaging of the spin Hall effect of light in semiconductors,” Phys. Rev. B 82(4), 045303 (2010).
[CrossRef]

He, H. Y.

Hermosa, N.

M. Merano, N. Hermosa, J. P. Woerdman, and A. Aiello, “How orbital angular momentum affects beam shifts in optical reflection,” Phys. Rev. A 82(2), 023817 (2010).
[CrossRef]

Hosten, O.

O. Hosten and P. Kwiat, “Observation of the spin hall effect of light via weak measurements,” Science 319(5864), 787–790 (2008).
[CrossRef] [PubMed]

Kivshar, Y. S.

Kleiner, V.

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(3), 030404 (2008).
[CrossRef] [PubMed]

K. Y. Bliokh, A. Niv, V. Kleiner, and E. Hasman, “Geometrodynamics of spinning light,” Nat. Photonics 2(12), 748–753 (2008).
[CrossRef]

Kundikova, N. D.

A. V. Dooghin, N. D. Kundikova, V. S. Liberman, and B. Y. Zel’dovich, “Optical Magnus effect,” Phys. Rev. A 45(11), 8204–8208 (1992).
[CrossRef] [PubMed]

Kwiat, P.

O. Hosten and P. Kwiat, “Observation of the spin hall effect of light via weak measurements,” Science 319(5864), 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(10), 100401 (2009).
[CrossRef] [PubMed]

Li, Y.

Liberman, V. S.

A. V. Dooghin, N. D. Kundikova, V. S. Liberman, and B. Y. Zel’dovich, “Optical Magnus effect,” Phys. Rev. A 45(11), 8204–8208 (1992).
[CrossRef] [PubMed]

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(10), 100401 (2009).
[CrossRef] [PubMed]

Liu, Z. P.

Luo, H. L.

H. L. Luo, S. C. Wen, W. X. Shu, Z. X. Tang, Y. H. Zou, and D. Y. Fan, “Spin Hall effect of a light beam in left-handed materials,” Phys. Rev. A 80(4), 043810 (2009).
[CrossRef]

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(10), 100401 (2009).
[CrossRef] [PubMed]

Mattacchione, A. E.

J. M. Ménard, A. E. Mattacchione, H. M. van Driel, C. Hautmann, and M. Betz, “Ultrafast optical imaging of the spin Hall effect of light in semiconductors,” Phys. Rev. B 82(4), 045303 (2010).
[CrossRef]

J. M. Menard, A. E. Mattacchione, M. Betz, and H. M. van Driel, “Imaging the spin Hall effect of light inside semiconductors via absorption,” Opt. Lett. 34(15), 2312–2314 (2009).
[CrossRef] [PubMed]

Menard, J. M.

Ménard, J. M.

J. M. Ménard, A. E. Mattacchione, H. M. van Driel, C. Hautmann, and M. Betz, “Ultrafast optical imaging of the spin Hall effect of light in semiconductors,” Phys. Rev. B 82(4), 045303 (2010).
[CrossRef]

Merano, M.

M. Merano, N. Hermosa, J. P. Woerdman, and A. Aiello, “How orbital angular momentum affects beam shifts in optical reflection,” Phys. Rev. A 82(2), 023817 (2010).
[CrossRef]

M. Merano, A. Aiello, M. P. van Exter, and J. P. Woerdman, “Observing angular deviations in the specular reflection of a light beam,” Nat. Photonics 3(6), 337–340 (2009).
[CrossRef]

Mohrbach, H.

A. Bérard and H. Mohrbach, “Spin Hall effect and Berry phase of spinning particles,” Phys. Lett. A 352(3), 190–195 (2006).
[CrossRef]

Murakami, S.

M. Onoda, S. Murakami, and N. Nagaosa, “Hall effect of light,” Phys. Rev. Lett. 93(8), 083901 (2004).
[CrossRef] [PubMed]

Nagaosa, N.

M. Onoda, S. Murakami, and N. Nagaosa, “Hall effect of light,” Phys. Rev. Lett. 93(8), 083901 (2004).
[CrossRef] [PubMed]

Niv, A.

K. Y. Bliokh, A. Niv, V. Kleiner, and E. Hasman, “Geometrodynamics of spinning light,” Nat. Photonics 2(12), 748–753 (2008).
[CrossRef]

Onoda, M.

M. Onoda, S. Murakami, and N. Nagaosa, “Hall effect of light,” Phys. Rev. Lett. 93(8), 083901 (2004).
[CrossRef] [PubMed]

Qin, Y.

Shadrivov, I. V.

Shu, W. X.

H. L. Luo, S. C. Wen, W. X. Shu, Z. X. Tang, Y. H. Zou, and D. Y. Fan, “Spin Hall effect of a light beam in left-handed materials,” Phys. Rev. A 80(4), 043810 (2009).
[CrossRef]

Sukhov, S.

D. Haefner, S. Sukhov, and A. Dogariu, “Spin hall effect of light in spherical geometry,” Phys. Rev. Lett. 102(12), 123903 (2009).
[CrossRef] [PubMed]

Tang, Z. X.

H. L. Luo, S. C. Wen, W. X. Shu, Z. X. Tang, Y. H. Zou, and D. Y. Fan, “Spin Hall effect of a light beam in left-handed materials,” Phys. Rev. A 80(4), 043810 (2009).
[CrossRef]

van Driel, H. M.

J. M. Ménard, A. E. Mattacchione, H. M. van Driel, C. Hautmann, and M. Betz, “Ultrafast optical imaging of the spin Hall effect of light in semiconductors,” Phys. Rev. B 82(4), 045303 (2010).
[CrossRef]

J. M. Menard, A. E. Mattacchione, M. Betz, and H. M. van Driel, “Imaging the spin Hall effect of light inside semiconductors via absorption,” Opt. Lett. 34(15), 2312–2314 (2009).
[CrossRef] [PubMed]

van Exter, M. P.

M. Merano, A. Aiello, M. P. van Exter, and J. P. Woerdman, “Observing angular deviations in the specular reflection of a light beam,” Nat. Photonics 3(6), 337–340 (2009).
[CrossRef]

Wen, S. C.

H. L. Luo, S. C. Wen, W. X. Shu, Z. X. Tang, Y. H. Zou, and D. Y. Fan, “Spin Hall effect of a light beam in left-handed materials,” Phys. Rev. A 80(4), 043810 (2009).
[CrossRef]

Woerdman, J. P.

M. Merano, N. Hermosa, J. P. Woerdman, and A. Aiello, “How orbital angular momentum affects beam shifts in optical reflection,” Phys. Rev. A 82(2), 023817 (2010).
[CrossRef]

M. Merano, A. Aiello, M. P. van Exter, and J. P. Woerdman, “Observing angular deviations in the specular reflection of a light beam,” Nat. Photonics 3(6), 337–340 (2009).
[CrossRef]

A. Aiello and J. P. Woerdman, “Role of beam propagation in Goos-Hanchen and Imbert-Fedorov shifts,” Opt. Lett. 33(13), 1437–1439 (2008).
[CrossRef] [PubMed]

Xiao, Y. F.

Zel’dovich, B. Y.

A. V. Dooghin, N. D. Kundikova, V. S. Liberman, and B. Y. Zel’dovich, “Optical Magnus effect,” Phys. Rev. A 45(11), 8204–8208 (1992).
[CrossRef] [PubMed]

Zou, Y. H.

H. L. Luo, S. C. Wen, W. X. Shu, Z. X. Tang, Y. H. Zou, and D. Y. Fan, “Spin Hall effect of a light beam in left-handed materials,” Phys. Rev. A 80(4), 043810 (2009).
[CrossRef]

Ann. Phys. (1)

K. Artmann, “Berechnung der seitenversetzung des totalreflektierten strahles,” Ann. Phys. 437(1-2), 87–102 (1948).
[CrossRef]

Nat. Photonics (2)

M. Merano, A. Aiello, M. P. van Exter, and J. P. Woerdman, “Observing angular deviations in the specular reflection of a light beam,” Nat. Photonics 3(6), 337–340 (2009).
[CrossRef]

K. Y. Bliokh, A. Niv, V. Kleiner, and E. Hasman, “Geometrodynamics of spinning light,” Nat. Photonics 2(12), 748–753 (2008).
[CrossRef]

Opt. Express (1)

Opt. Lett. (4)

Phys. Lett. A (1)

A. Bérard and H. Mohrbach, “Spin Hall effect and Berry phase of spinning particles,” Phys. Lett. A 352(3), 190–195 (2006).
[CrossRef]

Phys. Rev. A (4)

H. L. Luo, S. C. Wen, W. X. Shu, Z. X. Tang, Y. H. Zou, and D. Y. Fan, “Spin Hall effect of a light beam in left-handed materials,” Phys. Rev. A 80(4), 043810 (2009).
[CrossRef]

A. V. Dooghin, N. D. Kundikova, V. S. Liberman, and B. Y. Zel’dovich, “Optical Magnus effect,” Phys. Rev. A 45(11), 8204–8208 (1992).
[CrossRef] [PubMed]

K. Y. Bliokh and A. S. Desyatnikov, “Spin and orbital Hall effects for diffracting optical beams in gradient-index media,” Phys. Rev. A 79(1), 011807 (2009).
[CrossRef]

M. Merano, N. Hermosa, J. P. Woerdman, and A. Aiello, “How orbital angular momentum affects beam shifts in optical reflection,” Phys. Rev. A 82(2), 023817 (2010).
[CrossRef]

Phys. Rev. B (1)

J. M. Ménard, A. E. Mattacchione, H. M. van Driel, C. Hautmann, and M. Betz, “Ultrafast optical imaging of the spin Hall effect of light in semiconductors,” Phys. Rev. B 82(4), 045303 (2010).
[CrossRef]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

K. Y. Bliokh and Y. P. Bliokh, “Polarization, transverse shifts, and angular momentum conservation laws in partial reflection and refraction of an electromagnetic wave packet,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(6), 066609 (2007).
[CrossRef] [PubMed]

Phys. Rev. Lett. (5)

M. Onoda, S. Murakami, and N. Nagaosa, “Hall effect of light,” Phys. Rev. Lett. 93(8), 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(7), 073903 (2006).
[CrossRef] [PubMed]

D. Haefner, S. Sukhov, and A. Dogariu, “Spin hall effect of light in spherical geometry,” Phys. Rev. Lett. 102(12), 123903 (2009).
[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(3), 030404 (2008).
[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(10), 100401 (2009).
[CrossRef] [PubMed]

Science (1)

O. Hosten and P. Kwiat, “Observation of the spin hall effect of light via weak measurements,” Science 319(5864), 787–790 (2008).
[CrossRef] [PubMed]

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Figures (5)

Fig. 1
Fig. 1

Experimental setup for observing the in-plane spin separation of light. The He–Ne laser generates a Gaussian beam at 632.8 nm; HWP, half-wave plate for attenuating the intensity after P1 to prevent the position-sensitive detector (PSD) from saturating; L1 and L2, lenses with 25 and 125 mm focal lengths, respectively; P1 and P2, Glan polarizers; by replacing the PSD with a CCD, the intensity profiles of the beam after P2 can be captured. The insect shows the results when the incident angle θI = 30° and the polarization angle γI =30°.

Fig. 2
Fig. 2

The dependence of δ y | + > (a) and δ x | + > (b) of the | + > spin component induced by SHEL and IPSSL on the polarization angle γ I . The dots, circles and triangles are experimental data at three typical incident angles: 30°, 45° and 70°. The curves are the theoretical results. The insets show the theoretical prediction for a period from 0° to 180°.

Fig. 3
Fig. 3

Cross sections and polarization distributions of a reflected Gaussian beam. (a), (b), and (c) are schematics representing a linearly polarized beam, the reflected beam for |H> incidence and the reflected beam for an arbitrary linearly polarized incident beam, respectively. The yellow arrows and ellipses indicate the polarization distributions. (d), (e) and (f) are the corresponding intensity profiles after the beams going through a crossed polarizer. The spin separation, the ellipticity and the rotation angle of the elliptical polarizations in (b) and (c) are exaggerated for a better view.

Fig. 4
Fig. 4

Intensity profiles of the reflected beam passing through a crossed polarizer as a function of the polarization angle γ I . The incident angle θ I is 30° (a) and 70° (b), respectively. The experimental images of the intensity profiles are in excellent agreement with the numerical simulations in the upper row. The arrows indicate the total displacement of the | + > spin component.

Fig. 5
Fig. 5

Displacements of the | + > spin component of the refracted beam as the function of the polarization angle γ I at the incident angle of 49.3°, induced by SHEL ( δ y | + > , triangles) and IPSSL ( δ x | + > , dots), respectively. The error ranges are less than 2 nm. The curves indicate the theoretical results. The inset shows the theoretical prediction for a period from 0° to 180°.

Equations (21)

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| H ( k ( I , R ) ) > = | p ( k ( I , R ) ) > cot θ I , R κ y ( I , R ) | s ( k ( I , R ) ) >     , | V ( k ( I , R ) )     > = | s ( k ( I , R ) )     > + cot θ I , R κ y ( I , R ) | p ( k ( I , R ) ) > .
r p = r p θ I + r p θ I k x I k I , r s = r s θ I + r s θ I k x I k I .
| H ( k ( I ) ) > r p θ I ( | H ( k ( R ) ) > + k x R Δ H | H ( k ( R ) ) > + k y δ H | V ( k ( R ) ) > ) , | V ( k ( I ) ) > r s θ I ( | V ( k ( R ) ) > + k x R Δ V | V ( k ( R ) ) > k y δ V | H ( k ( R ) ) > ) ,
δ H = cot θ I ( e R r s θ I / r p θ I ) / k I ,
δ V = cot θ I ( e R r p θ I / r s θ I ) / k I ,
Δ H = e R ( ln r p / θ I ) / k I = e R ( r p / r p θ I 1 ) / k x I ,
Δ V = e R ( ln r s / θ I ) / k I = e R ( r s / r s θ I 1 ) / k x I .
| H ( k ( I ) ) > r p θ I 2 [ exp ( i k y δ H ) exp ( k x R Δ H ) | + > + exp ( i k y δ H ) exp ( k x R Δ H ) | > ] , | V ( k ( I ) ) > i r s θ I 2 [ exp ( i k y δ V ) exp ( k x R Δ V ) | + > exp ( i k y δ V ) exp ( k x R Δ V ) | > ] ,
| m ( I ) > = 1 1 + | m | 2 ( | H > + m | V > ) ,
| φ > = r p θ I 2 ( 1 + | m | 2 ) ( 1 i m β θ I ) exp [ i k y ( δ y | + > m + i Δ y | + > m ) ] exp [ i k x R ( δ x | + > m + i Δ x | + > m ) ] | + > + r p θ I 2 ( 1 + | m | 2 ) ( 1 + i m β θ I ) exp [ i k y ( δ y | > m + i Δ y | > m ) ] exp [ i k x R ( δ x | > m + i Δ x | > m ) ] | > .
δ y | σ > m = σ δ H + σ m i β θ I ( δ H + δ V ) + | m | 2 | β θ I | 2 δ V | 1 i m σ β θ I | 2 ,
Δ x | σ > m = Δ H + σ m i β θ I ( Δ H + Δ V ) + | m | 2 | β θ I | 2 Δ V | 1 i m σ β θ I | 2 ,
Δ y | σ > m = m r β θ I ( δ H δ V ) | 1 i m σ β θ I | 2 ,
δ x | σ > m = σ m r β θ I ( Δ H Δ V ) | 1 i m σ β θ I | 2 ,
δ x | σ > γ I = σ 2 sin ( 2 γ R ) ( Δ H Δ V ) , δ y | σ > γ I = σ ( cos 2 γ R δ H + sin 2 γ R δ V ) ,
Δ x | σ > γ I = cos 2 γ R Δ H + sin 2 γ R Δ V , Δ y | σ > γ I = 1 2 sin ( 2 γ R ) ( δ H δ V ) ,
< k x R m > = k I 2 Λ e R 2 ( 1 2 k I e R θ I + Δ H + | m | 2 | β θ I | 2 Δ V 1 + | m | 2 β θ I 2 ) , < k y R m > = k I 2 Λ m r β θ I ( δ H δ V ) 1 + | m | 2 β θ I 2 ,
< x R m > = z R k I < k x R m > , < y R m > = z R k I < k y R m > ,
< k x R γ I > = k I 2 Λ e R 2 ( 1 2 k I e R θ I + Δ x | σ > γ I ) , < k y R γ I > = k I 2 Λ Δ y | σ > γ I ,
< x R γ I > = z R k I < k x R γ I > , < y R γ I > = z R k I < k y R γ I > .
I p 2 γ I | 1 1 + tan 2 γ I r p θ I w z R 2 cos 2 γ R exp ( x R 2 + y 2 2 w z R 2 ) ( δ x | + > γ I x R + δ y | + > γ I y ) | 2 .

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