Abstract

We report on a diffraction-dependent spin splitting of the paraxial Gaussian light beams on reflection theoretically and experimentally. In the case of horizontal incident polarization, the spin splitting is proportional to the diffraction length of light beams near the Brewster angle. However, the spin splitting is nearly independent with the diffraction length for the vertical incident polarization. By means of the angular spectrum theory, we find that the diffraction-dependent spin splitting is attributed to the first order expansion term of the reflection coefficients with respect to the transverse wave-vector which is closely related to the diffraction length.

© 2015 Optical Society of America

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References

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    [Crossref] [PubMed]
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2015 (1)

2013 (2)

K. Y. Bliokh and A. Aiello, “Goos-Hänchen and Imbert-Fedorov beam shifts: an overview,” J. Opt. 15, 014001 (2013).
[Crossref]

X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin Hall effect at metasurfaces,” Science 339(6126), 1405–1407 (2013).
[Crossref] [PubMed]

2012 (5)

J. Ren, Y. Li, Y. Lin, Y. Qin, R. Wu, J. Yang, Y. Xiao, H. Yang, and Q. Gong, “Spin Hall effect of light reflected from a magnetic thin film,” Appl. Phys. Lett. 101(17), 171103 (2012).
[Crossref]

L. Kong, X. Wang, S. Li, Y. Li, J. Chen, B. Gu, and H. Wang, “Spin Hall effect of reflected light from an air-glass interface around the Brewster angle,” Appl. Phys. Lett. 100(7), 071109 (2012).
[Crossref]

Y. Gorodetski, K. Y. Bliokh, B. Stein, C. Genet, N. Shitrit, V. Kleiner, E. Hasman, and T. W. Ebbesen, “Weak measurements of light chirality with a plasmonic slit,” Phys. Rev. Lett. 109(1), 013901 (2012).
[Crossref] [PubMed]

X. Zhou, X. Ling, H. Luo, and S. Wen, “Identifying graphene layers via spin Hall effect of light,” Appl. Phys. Lett 101(25), 251602 (2012).
[Crossref]

X. Zhou, Z. Xiao, H. Luo, and S. Wen, “Experimental observation of the spin Hall effect of light on a nanometal film via weak measurements,” Phys. Rev. A 85(4), 043809 (2012).
[Crossref]

2011 (2)

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(4), 043806 (2011).
[Crossref]

N. Shitrit, I. Bretner, Y. Gorodetski, V. Kleiner, and E. Hasman, “Optical spin Hall effects in plasmonic chains,”, Nano Lett. 11(5), 2038–2042 (2011).
[Crossref] [PubMed]

2010 (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]

J. M. Ménard, A. E. Mattacchione, H. M. vanDriel, 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 (4)

2008 (4)

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

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

Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, “Observation of the spin-based plasmonic effect in nanoscale structures,” Phys. Rev. Lett. 101(4), 043903 (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(3), 030404 (2008).
[Crossref] [PubMed]

2006 (1)

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]

2004 (1)

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

1990 (1)

1988 (1)

Y. Aharonov, D. Z. Albert, and L. Vaidman, “How the result of a measurement of a component of the spin of a spin -1/2 particle can turn out to be 100,” Phys. Rev. Lett. 60(14), 1351–1354 (1988).
[Crossref] [PubMed]

Aharonov, Y.

Y. Aharonov, D. Z. Albert, and L. Vaidman, “How the result of a measurement of a component of the spin of a spin -1/2 particle can turn out to be 100,” Phys. Rev. Lett. 60(14), 1351–1354 (1988).
[Crossref] [PubMed]

Aiello, A.

K. Y. Bliokh and A. Aiello, “Goos-Hänchen and Imbert-Fedorov beam shifts: an overview,” J. Opt. 15, 014001 (2013).
[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]

A. Aiello, M. Merano, and J. P. Woerdman, “Brewster cross polarization,” Opt. Lett. 34(8), 1207–1209 (2009).
[Crossref] [PubMed]

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

Albert, D. Z.

Y. Aharonov, D. Z. Albert, and L. Vaidman, “How the result of a measurement of a component of the spin of a spin -1/2 particle can turn out to be 100,” Phys. Rev. Lett. 60(14), 1351–1354 (1988).
[Crossref] [PubMed]

Betz, M.

J. M. Ménard, A. E. Mattacchione, H. M. vanDriel, 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. Ménard, A. E. Mattacchione, M. Betz, and H. M. vanDriel, “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. Aiello, “Goos-Hänchen and Imbert-Fedorov beam shifts: an overview,” J. Opt. 15, 014001 (2013).
[Crossref]

Y. Gorodetski, K. Y. Bliokh, B. Stein, C. Genet, N. Shitrit, V. Kleiner, E. Hasman, and T. W. Ebbesen, “Weak measurements of light chirality with a plasmonic slit,” Phys. Rev. Lett. 109(1), 013901 (2012).
[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]

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, “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]

Bretner, I.

N. Shitrit, I. Bretner, Y. Gorodetski, V. Kleiner, and E. Hasman, “Optical spin Hall effects in plasmonic chains,”, Nano Lett. 11(5), 2038–2042 (2011).
[Crossref] [PubMed]

Chen, J.

L. Kong, X. Wang, S. Li, Y. Li, J. Chen, B. Gu, and H. Wang, “Spin Hall effect of reflected light from an air-glass interface around the Brewster angle,” Appl. Phys. Lett. 100(7), 071109 (2012).
[Crossref]

Du, J.

Ebbesen, T. W.

Y. Gorodetski, K. Y. Bliokh, B. Stein, C. Genet, N. Shitrit, V. Kleiner, E. Hasman, and T. W. Ebbesen, “Weak measurements of light chirality with a plasmonic slit,” Phys. Rev. Lett. 109(1), 013901 (2012).
[Crossref] [PubMed]

Fan, D.

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(4), 043806 (2011).
[Crossref]

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

Gao, F.

Genet, C.

Y. Gorodetski, K. Y. Bliokh, B. Stein, C. Genet, N. Shitrit, V. Kleiner, E. Hasman, and T. W. Ebbesen, “Weak measurements of light chirality with a plasmonic slit,” Phys. Rev. Lett. 109(1), 013901 (2012).
[Crossref] [PubMed]

Gong, Q.

J. Ren, Y. Li, Y. Lin, Y. Qin, R. Wu, J. Yang, Y. Xiao, H. Yang, and Q. Gong, “Spin Hall effect of light reflected from a magnetic thin film,” Appl. Phys. Lett. 101(17), 171103 (2012).
[Crossref]

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

Gorodetski, Y.

Y. Gorodetski, K. Y. Bliokh, B. Stein, C. Genet, N. Shitrit, V. Kleiner, E. Hasman, and T. W. Ebbesen, “Weak measurements of light chirality with a plasmonic slit,” Phys. Rev. Lett. 109(1), 013901 (2012).
[Crossref] [PubMed]

N. Shitrit, I. Bretner, Y. Gorodetski, V. Kleiner, and E. Hasman, “Optical spin Hall effects in plasmonic chains,”, Nano Lett. 11(5), 2038–2042 (2011).
[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]

Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, “Observation of the spin-based plasmonic effect in nanoscale structures,” Phys. Rev. Lett. 101(4), 043903 (2008).
[Crossref] [PubMed]

Gu, B.

L. Kong, X. Wang, S. Li, Y. Li, J. Chen, B. Gu, and H. Wang, “Spin Hall effect of reflected light from an air-glass interface around the Brewster angle,” Appl. Phys. Lett. 100(7), 071109 (2012).
[Crossref]

Hasman, E.

Y. Gorodetski, K. Y. Bliokh, B. Stein, C. Genet, N. Shitrit, V. Kleiner, E. Hasman, and T. W. Ebbesen, “Weak measurements of light chirality with a plasmonic slit,” Phys. Rev. Lett. 109(1), 013901 (2012).
[Crossref] [PubMed]

N. Shitrit, I. Bretner, Y. Gorodetski, V. Kleiner, and E. Hasman, “Optical spin Hall effects in plasmonic chains,”, Nano Lett. 11(5), 2038–2042 (2011).
[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]

Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, “Observation of the spin-based plasmonic effect in nanoscale structures,” Phys. Rev. Lett. 101(4), 043903 (2008).
[Crossref] [PubMed]

Hautmann, C.

J. M. Ménard, A. E. Mattacchione, H. M. vanDriel, 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.

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]

Kleiner, V.

Y. Gorodetski, K. Y. Bliokh, B. Stein, C. Genet, N. Shitrit, V. Kleiner, E. Hasman, and T. W. Ebbesen, “Weak measurements of light chirality with a plasmonic slit,” Phys. Rev. Lett. 109(1), 013901 (2012).
[Crossref] [PubMed]

N. Shitrit, I. Bretner, Y. Gorodetski, V. Kleiner, and E. Hasman, “Optical spin Hall effects in plasmonic chains,”, Nano Lett. 11(5), 2038–2042 (2011).
[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]

Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, “Observation of the spin-based plasmonic effect in nanoscale structures,” Phys. Rev. Lett. 101(4), 043903 (2008).
[Crossref] [PubMed]

Kong, L.

L. Kong, X. Wang, S. Li, Y. Li, J. Chen, B. Gu, and H. Wang, “Spin Hall effect of reflected light from an air-glass interface around the Brewster angle,” Appl. Phys. Lett. 100(7), 071109 (2012).
[Crossref]

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]

Li, S.

L. Kong, X. Wang, S. Li, Y. Li, J. Chen, B. Gu, and H. Wang, “Spin Hall effect of reflected light from an air-glass interface around the Brewster angle,” Appl. Phys. Lett. 100(7), 071109 (2012).
[Crossref]

Li, Y.

L. Kong, X. Wang, S. Li, Y. Li, J. Chen, B. Gu, and H. Wang, “Spin Hall effect of reflected light from an air-glass interface around the Brewster angle,” Appl. Phys. Lett. 100(7), 071109 (2012).
[Crossref]

J. Ren, Y. Li, Y. Lin, Y. Qin, R. Wu, J. Yang, Y. Xiao, H. Yang, and Q. Gong, “Spin Hall effect of light reflected from a magnetic thin film,” Appl. Phys. Lett. 101(17), 171103 (2012).
[Crossref]

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

Lin, Y.

J. Ren, Y. Li, Y. Lin, Y. Qin, R. Wu, J. Yang, Y. Xiao, H. Yang, and Q. Gong, “Spin Hall effect of light reflected from a magnetic thin film,” Appl. Phys. Lett. 101(17), 171103 (2012).
[Crossref]

Ling, X.

X. Zhou, X. Ling, H. Luo, and S. Wen, “Identifying graphene layers via spin Hall effect of light,” Appl. Phys. Lett 101(25), 251602 (2012).
[Crossref]

Luo, H.

X. Zhou, X. Ling, H. Luo, and S. Wen, “Identifying graphene layers via spin Hall effect of light,” Appl. Phys. Lett 101(25), 251602 (2012).
[Crossref]

X. Zhou, Z. Xiao, H. Luo, and S. Wen, “Experimental observation of the spin Hall effect of light on a nanometal film via weak measurements,” Phys. Rev. A 85(4), 043809 (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(4), 043806 (2011).
[Crossref]

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

Mattacchione, A. E.

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

Ménard, J. M.

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

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]

A. Aiello, M. Merano, and J. P. Woerdman, “Brewster cross polarization,” Opt. Lett. 34(8), 1207–1209 (2009).
[Crossref] [PubMed]

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]

Napolitano, J.

J. J. Sakurai and J. Napolitano, Modern Quantum Mechanics (Addison-Wesley, 2011).

Nemoto, S.

Niv, A.

Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, “Observation of the spin-based plasmonic effect in nanoscale structures,” Phys. Rev. Lett. 101(4), 043903 (2008).
[Crossref] [PubMed]

Onoda, M.

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

Qin, Y.

J. Ren, Y. Li, Y. Lin, Y. Qin, R. Wu, J. Yang, Y. Xiao, H. Yang, and Q. Gong, “Spin Hall effect of light reflected from a magnetic thin film,” Appl. Phys. Lett. 101(17), 171103 (2012).
[Crossref]

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

Qiu, J.

Qiu, X.

Ren, J.

J. Ren, Y. Li, Y. Lin, Y. Qin, R. Wu, J. Yang, Y. Xiao, H. Yang, and Q. Gong, “Spin Hall effect of light reflected from a magnetic thin film,” Appl. Phys. Lett. 101(17), 171103 (2012).
[Crossref]

Rho, J.

X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin Hall effect at metasurfaces,” Science 339(6126), 1405–1407 (2013).
[Crossref] [PubMed]

Sakurai, J. J.

J. J. Sakurai and J. Napolitano, Modern Quantum Mechanics (Addison-Wesley, 2011).

Shitrit, N.

Y. Gorodetski, K. Y. Bliokh, B. Stein, C. Genet, N. Shitrit, V. Kleiner, E. Hasman, and T. W. Ebbesen, “Weak measurements of light chirality with a plasmonic slit,” Phys. Rev. Lett. 109(1), 013901 (2012).
[Crossref] [PubMed]

N. Shitrit, I. Bretner, Y. Gorodetski, V. Kleiner, and E. Hasman, “Optical spin Hall effects in plasmonic chains,”, Nano Lett. 11(5), 2038–2042 (2011).
[Crossref] [PubMed]

Shu, W.

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(4), 043806 (2011).
[Crossref]

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

Stein, B.

Y. Gorodetski, K. Y. Bliokh, B. Stein, C. Genet, N. Shitrit, V. Kleiner, E. Hasman, and T. W. Ebbesen, “Weak measurements of light chirality with a plasmonic slit,” Phys. Rev. Lett. 109(1), 013901 (2012).
[Crossref] [PubMed]

Tang, Z.

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

Vaidman, L.

Y. Aharonov, D. Z. Albert, and L. Vaidman, “How the result of a measurement of a component of the spin of a spin -1/2 particle can turn out to be 100,” Phys. Rev. Lett. 60(14), 1351–1354 (1988).
[Crossref] [PubMed]

vanDriel, H. M.

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

Wang, H.

L. Kong, X. Wang, S. Li, Y. Li, J. Chen, B. Gu, and H. Wang, “Spin Hall effect of reflected light from an air-glass interface around the Brewster angle,” Appl. Phys. Lett. 100(7), 071109 (2012).
[Crossref]

Wang, X.

L. Kong, X. Wang, S. Li, Y. Li, J. Chen, B. Gu, and H. Wang, “Spin Hall effect of reflected light from an air-glass interface around the Brewster angle,” Appl. Phys. Lett. 100(7), 071109 (2012).
[Crossref]

Wang, Y.

X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin Hall effect at metasurfaces,” Science 339(6126), 1405–1407 (2013).
[Crossref] [PubMed]

Wen, S.

X. Zhou, X. Ling, H. Luo, and S. Wen, “Identifying graphene layers via spin Hall effect of light,” Appl. Phys. Lett 101(25), 251602 (2012).
[Crossref]

X. Zhou, Z. Xiao, H. Luo, and S. Wen, “Experimental observation of the spin Hall effect of light on a nanometal film via weak measurements,” Phys. Rev. A 85(4), 043809 (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(4), 043806 (2011).
[Crossref]

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

Woerdman, J. P.

Wu, R.

J. Ren, Y. Li, Y. Lin, Y. Qin, R. Wu, J. Yang, Y. Xiao, H. Yang, and Q. Gong, “Spin Hall effect of light reflected from a magnetic thin film,” Appl. Phys. Lett. 101(17), 171103 (2012).
[Crossref]

Xiao, Y.

J. Ren, Y. Li, Y. Lin, Y. Qin, R. Wu, J. Yang, Y. Xiao, H. Yang, and Q. Gong, “Spin Hall effect of light reflected from a magnetic thin film,” Appl. Phys. Lett. 101(17), 171103 (2012).
[Crossref]

Xiao, Z.

X. Zhou, Z. Xiao, H. Luo, and S. Wen, “Experimental observation of the spin Hall effect of light on a nanometal film via weak measurements,” Phys. Rev. A 85(4), 043809 (2012).
[Crossref]

Xie, L.

Yang, H.

J. Ren, Y. Li, Y. Lin, Y. Qin, R. Wu, J. Yang, Y. Xiao, H. Yang, and Q. Gong, “Spin Hall effect of light reflected from a magnetic thin film,” Appl. Phys. Lett. 101(17), 171103 (2012).
[Crossref]

Yang, J.

J. Ren, Y. Li, Y. Lin, Y. Qin, R. Wu, J. Yang, Y. Xiao, H. Yang, and Q. Gong, “Spin Hall effect of light reflected from a magnetic thin film,” Appl. Phys. Lett. 101(17), 171103 (2012).
[Crossref]

Ye, Z.

X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin Hall effect at metasurfaces,” Science 339(6126), 1405–1407 (2013).
[Crossref] [PubMed]

Yin, X.

X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin Hall effect at metasurfaces,” Science 339(6126), 1405–1407 (2013).
[Crossref] [PubMed]

Zhang, X.

X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin Hall effect at metasurfaces,” Science 339(6126), 1405–1407 (2013).
[Crossref] [PubMed]

Zhang, Z.

Zhou, X.

X. Zhou, X. Ling, H. Luo, and S. Wen, “Identifying graphene layers via spin Hall effect of light,” Appl. Phys. Lett 101(25), 251602 (2012).
[Crossref]

X. Zhou, Z. Xiao, H. Luo, and S. Wen, “Experimental observation of the spin Hall effect of light on a nanometal film via weak measurements,” Phys. Rev. A 85(4), 043809 (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(4), 043806 (2011).
[Crossref]

Zou, Y.

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

Appl. Opt. (1)

Appl. Phys. Lett (1)

X. Zhou, X. Ling, H. Luo, and S. Wen, “Identifying graphene layers via spin Hall effect of light,” Appl. Phys. Lett 101(25), 251602 (2012).
[Crossref]

Appl. Phys. Lett. (2)

J. Ren, Y. Li, Y. Lin, Y. Qin, R. Wu, J. Yang, Y. Xiao, H. Yang, and Q. Gong, “Spin Hall effect of light reflected from a magnetic thin film,” Appl. Phys. Lett. 101(17), 171103 (2012).
[Crossref]

L. Kong, X. Wang, S. Li, Y. Li, J. Chen, B. Gu, and H. Wang, “Spin Hall effect of reflected light from an air-glass interface around the Brewster angle,” Appl. Phys. Lett. 100(7), 071109 (2012).
[Crossref]

J. Opt. (1)

K. Y. Bliokh and A. Aiello, “Goos-Hänchen and Imbert-Fedorov beam shifts: an overview,” J. Opt. 15, 014001 (2013).
[Crossref]

Nano Lett. (1)

N. Shitrit, I. Bretner, Y. Gorodetski, V. Kleiner, and E. Hasman, “Optical spin Hall effects in plasmonic chains,”, Nano Lett. 11(5), 2038–2042 (2011).
[Crossref] [PubMed]

Opt. Lett. (5)

Phys. Rev. A (4)

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]

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

X. Zhou, Z. Xiao, H. Luo, and S. Wen, “Experimental observation of the spin Hall effect of light on a nanometal film via weak measurements,” Phys. Rev. A 85(4), 043809 (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(4), 043806 (2011).
[Crossref]

Phys. Rev. B (1)

J. M. Ménard, A. E. Mattacchione, H. M. vanDriel, 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. Lett. (6)

Y. Gorodetski, K. Y. Bliokh, B. Stein, C. Genet, N. Shitrit, V. Kleiner, E. Hasman, and T. W. Ebbesen, “Weak measurements of light chirality with a plasmonic slit,” Phys. Rev. Lett. 109(1), 013901 (2012).
[Crossref] [PubMed]

Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, “Observation of the spin-based plasmonic effect in nanoscale structures,” Phys. Rev. Lett. 101(4), 043903 (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(3), 030404 (2008).
[Crossref] [PubMed]

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]

Y. Aharonov, D. Z. Albert, and L. Vaidman, “How the result of a measurement of a component of the spin of a spin -1/2 particle can turn out to be 100,” Phys. Rev. Lett. 60(14), 1351–1354 (1988).
[Crossref] [PubMed]

Science (2)

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

X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin Hall effect at metasurfaces,” Science 339(6126), 1405–1407 (2013).
[Crossref] [PubMed]

Other (1)

J. J. Sakurai and J. Napolitano, Modern Quantum Mechanics (Addison-Wesley, 2011).

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Figures (5)

Fig. 1
Fig. 1

(a) The coordinate systems: (X,Y,Z) is the laboratory coordinate system. (xi,yi,zi) and (xr,yr,zr) denote incident and reflected light beam coordinate systems, respectively. (b) The schematic of the SHEL originating from the spin-orbit coupling, δ|±〉 denotes the spin splitting induced by the SHEL.

Fig. 2
Fig. 2

Theoretical calculation of the spin splitting induced by the SHEL on reflection of the paraxial Gaussian light beams with different diffraction length R0. (a) The spin splitting for the |H〉 incident polarization. (b) Detailed drawing of the spin splitting for the |H〉 incident polarization near the Brewster angle θB. (c) The spin splitting for the |V〉 incident polarization.

Fig. 3
Fig. 3

Experimental setup: The half-wave plate (HWP) is used to adjust the intensity of the Gaussian light beam which is generated by the He-Ne laser. Two Glan polarizers act as the pre- and post-selections. The paraxial Gaussian light beams with different diffraction length R0 is obtained by adjusting the focal length of the first lens (L1). The CCD is used to record the intensity barycenter of the reflected light beam collected by the second lens (L2). The BK7 prism with a refractive index of 1.515 at 632.8nm plays the role of reflected interface and the incident angle is controlled by the rotation stage. Inset: The schematic of the paraxial light beam focused by L1.

Fig. 4
Fig. 4

The solid line shows the relation between the diffraction length Ro and the focal length of L1. The squares denote the experimental values obtained by L1.

Fig. 5
Fig. 5

The spin splitting induced by the SHEL changes with the diffraction length at different incident angles around the Brewster angle. The lines denote theoretical calculation results and the dots denote the experimental data. (a) and (b) are for the |H〉 and |V〉 incident polarizations, respectively.

Equations (16)

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| ψ = 1 1 + | m | 2 ( | H + m | V ) .
| H ( k i , r ) = | p ( k i , r ) cot θ i , r k ( i , r ) y k i , r | s ( k i , r ) ,
| V ( k i , r ) = | s ( k i , r ) + cot θ i , r k ( i , r ) y k i , r | p ( k i , r ) .
[ | p ( k i ) | s ( k i ) ] = [ r p 0 0 r s ] [ | p ( k r ) | s ( k r ) ] ,
r p , s = r ( p , s ) θ i + k i x k 0 r p , s θ i .
| ψ = 1 2 ( 1 + | m | 2 ) { [ r p θ i exp ( i σ k y δ H ) χ k r x k 0 exp ( i σ k y δ H ) ] i σ m [ r s θ i exp ( i σ k y δ V ) + γ k r x k 0 exp ( i σ k y δ V ) ] } | σ .
| Ψ = d k r x d k r y Φ ( k r x , k r y ) | k r x | k r y | Ψ ,
Φ ( k r x , k r y ) = w 0 2 π exp [ w 0 2 ( k r x 2 + k r y 2 ) 4 ] .
δ | σ = Ψ | i k | Ψ Ψ | Ψ .
δ | σ H = 2 σ R 0 [ 2 k 0 r p θ i R 0 ( r p θ i + r s θ i ) + χ ( χ + γ ) ] 2 k 0 R 0 [ 2 k 0 r p θ i 2 R 0 + χ 2 ] tan θ i + [ 2 k 0 R 0 ( r p θ i + r s θ i ) 2 + ( χ + γ ) 2 ] cot θ i ,
δ | σ V = 2 σ R 0 [ 2 k 0 r s θ i R 0 ( r p θ i + r s θ i ) + γ ( χ + γ ) ] 2 k 0 R 0 [ 2 k 0 r s θ i 2 R 0 + γ 2 ] tan θ i + [ 2 k 0 R 0 ( r p θ i + r s θ i ) 2 + ( χ + γ ) 2 ] cot θ i .
| ψ H = 1 2 [ r p θ i exp ( i σ k y δ H ) χ k r x k 0 exp ( i σ k y δ H ) ] | σ ,
| ψ V = i σ 2 [ r p θ i exp ( i σ k y δ V ) + γ k r x k 0 exp ( i σ k y δ V ) ] | σ ,
w 0 = f 1 w R 2 + ( d f 1 ) 2 ,
δ | + H = δ M H F ,
δ | + V = δ M H | A w | F ,

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