Abstract

We have measured the spin-dependent nanometer-sized displacements of the spin Hall effect of the reflected light from a planar air–glass interface. In the case of the vertical polarization, the displacement is found to increase with the incident angle and subsequently decrease after 48deg, while in the case of the horizontal polarization, it changes rapidly near the Brewster angle. For a fixed incident angle of 30deg, the displacement decreases to zero as the polarization angle approaches 39deg from 0deg (the horizontal polarization) and then increases in the opposite direction until 90deg (the vertical polarization).

© 2009 Optical Society of America

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  1. M. Onoda, S. Murakami, and N. Nagaosa, Phys. Rev. Lett. 93, 083901 (2004).
    [CrossRef] [PubMed]
  2. K. Yu. Bliokh and Y. P. Bliokh, Phys. Rev. Lett. 96, 073903 (2006).
    [CrossRef] [PubMed]
  3. K. Yu. Bliokh and Y. P. Bliokh, Phys. Rev. E 75, 066609 (2007).
    [CrossRef]
  4. K. Y. Bliokh, A. Niv, V. Kleiner, and E. Hasman, Nat. Photonics 2, 748 (2008).
    [CrossRef]
  5. C. M. Krowne, Phys. Lett. A 373, 466 (2009).
    [CrossRef]
  6. O. Hosten and P. Kwiat, Science 319, 787 (2008).
    [CrossRef] [PubMed]
  7. B. Simon, Phys. Rev. Lett. 51, 2167 (1983).
    [CrossRef]
  8. Ch.-F. Li, Phys. Rev. A 76, 013811 (2007).
    [CrossRef]
  9. C. Leyder, M. Romanelli, J. Ph. Karr, E. Giacobino, T. C. H. Liew, M. M. Glazov, A. V. Kavokin, G. Malpuech, and A. Bramati, Nat. Phys. 3, 628 (2007).
    [CrossRef]
  10. A. Aiello and J. P. Woerdman, Opt. Lett. 33, 1437 (2008).
    [CrossRef] [PubMed]
  11. Y. Aharonov and L. Vaidman, Phys. Rev. A 41, 11 (1990).
    [CrossRef] [PubMed]
  12. N. W. M. Ritchie, J. G. Story, and R. G. Hulet, Phys. Rev. Lett. 66, 1107 (1991).
    [CrossRef] [PubMed]

2009 (1)

C. M. Krowne, Phys. Lett. A 373, 466 (2009).
[CrossRef]

2008 (3)

O. Hosten and P. Kwiat, Science 319, 787 (2008).
[CrossRef] [PubMed]

K. Y. Bliokh, A. Niv, V. Kleiner, and E. Hasman, Nat. Photonics 2, 748 (2008).
[CrossRef]

A. Aiello and J. P. Woerdman, Opt. Lett. 33, 1437 (2008).
[CrossRef] [PubMed]

2007 (3)

K. Yu. Bliokh and Y. P. Bliokh, Phys. Rev. E 75, 066609 (2007).
[CrossRef]

Ch.-F. Li, Phys. Rev. A 76, 013811 (2007).
[CrossRef]

C. Leyder, M. Romanelli, J. Ph. Karr, E. Giacobino, T. C. H. Liew, M. M. Glazov, A. V. Kavokin, G. Malpuech, and A. Bramati, Nat. Phys. 3, 628 (2007).
[CrossRef]

2006 (1)

K. Yu. Bliokh and Y. P. Bliokh, Phys. Rev. Lett. 96, 073903 (2006).
[CrossRef] [PubMed]

2004 (1)

M. Onoda, S. Murakami, and N. Nagaosa, Phys. Rev. Lett. 93, 083901 (2004).
[CrossRef] [PubMed]

1991 (1)

N. W. M. Ritchie, J. G. Story, and R. G. Hulet, Phys. Rev. Lett. 66, 1107 (1991).
[CrossRef] [PubMed]

1990 (1)

Y. Aharonov and L. Vaidman, Phys. Rev. A 41, 11 (1990).
[CrossRef] [PubMed]

1983 (1)

B. Simon, Phys. Rev. Lett. 51, 2167 (1983).
[CrossRef]

Aharonov, Y.

Y. Aharonov and L. Vaidman, Phys. Rev. A 41, 11 (1990).
[CrossRef] [PubMed]

Aiello, A.

Bliokh, K. Y.

K. Y. Bliokh, A. Niv, V. Kleiner, and E. Hasman, Nat. Photonics 2, 748 (2008).
[CrossRef]

Bliokh, K. Yu.

K. Yu. Bliokh and Y. P. Bliokh, Phys. Rev. E 75, 066609 (2007).
[CrossRef]

K. Yu. Bliokh and Y. P. Bliokh, Phys. Rev. Lett. 96, 073903 (2006).
[CrossRef] [PubMed]

Bliokh, Y. P.

K. Yu. Bliokh and Y. P. Bliokh, Phys. Rev. E 75, 066609 (2007).
[CrossRef]

K. Yu. Bliokh and Y. P. Bliokh, Phys. Rev. Lett. 96, 073903 (2006).
[CrossRef] [PubMed]

Bramati, A.

C. Leyder, M. Romanelli, J. Ph. Karr, E. Giacobino, T. C. H. Liew, M. M. Glazov, A. V. Kavokin, G. Malpuech, and A. Bramati, Nat. Phys. 3, 628 (2007).
[CrossRef]

Giacobino, E.

C. Leyder, M. Romanelli, J. Ph. Karr, E. Giacobino, T. C. H. Liew, M. M. Glazov, A. V. Kavokin, G. Malpuech, and A. Bramati, Nat. Phys. 3, 628 (2007).
[CrossRef]

Glazov, M. M.

C. Leyder, M. Romanelli, J. Ph. Karr, E. Giacobino, T. C. H. Liew, M. M. Glazov, A. V. Kavokin, G. Malpuech, and A. Bramati, Nat. Phys. 3, 628 (2007).
[CrossRef]

Hasman, E.

K. Y. Bliokh, A. Niv, V. Kleiner, and E. Hasman, Nat. Photonics 2, 748 (2008).
[CrossRef]

Hosten, O.

O. Hosten and P. Kwiat, Science 319, 787 (2008).
[CrossRef] [PubMed]

Hulet, R. G.

N. W. M. Ritchie, J. G. Story, and R. G. Hulet, Phys. Rev. Lett. 66, 1107 (1991).
[CrossRef] [PubMed]

Karr, J. Ph.

C. Leyder, M. Romanelli, J. Ph. Karr, E. Giacobino, T. C. H. Liew, M. M. Glazov, A. V. Kavokin, G. Malpuech, and A. Bramati, Nat. Phys. 3, 628 (2007).
[CrossRef]

Kavokin, A. V.

C. Leyder, M. Romanelli, J. Ph. Karr, E. Giacobino, T. C. H. Liew, M. M. Glazov, A. V. Kavokin, G. Malpuech, and A. Bramati, Nat. Phys. 3, 628 (2007).
[CrossRef]

Kleiner, V.

K. Y. Bliokh, A. Niv, V. Kleiner, and E. Hasman, Nat. Photonics 2, 748 (2008).
[CrossRef]

Krowne, C. M.

C. M. Krowne, Phys. Lett. A 373, 466 (2009).
[CrossRef]

Kwiat, P.

O. Hosten and P. Kwiat, Science 319, 787 (2008).
[CrossRef] [PubMed]

Leyder, C.

C. Leyder, M. Romanelli, J. Ph. Karr, E. Giacobino, T. C. H. Liew, M. M. Glazov, A. V. Kavokin, G. Malpuech, and A. Bramati, Nat. Phys. 3, 628 (2007).
[CrossRef]

Li, Ch.-F.

Ch.-F. Li, Phys. Rev. A 76, 013811 (2007).
[CrossRef]

Liew, T. C. H.

C. Leyder, M. Romanelli, J. Ph. Karr, E. Giacobino, T. C. H. Liew, M. M. Glazov, A. V. Kavokin, G. Malpuech, and A. Bramati, Nat. Phys. 3, 628 (2007).
[CrossRef]

Malpuech, G.

C. Leyder, M. Romanelli, J. Ph. Karr, E. Giacobino, T. C. H. Liew, M. M. Glazov, A. V. Kavokin, G. Malpuech, and A. Bramati, Nat. Phys. 3, 628 (2007).
[CrossRef]

Murakami, S.

M. Onoda, S. Murakami, and N. Nagaosa, Phys. Rev. Lett. 93, 083901 (2004).
[CrossRef] [PubMed]

Nagaosa, N.

M. Onoda, S. Murakami, and N. Nagaosa, Phys. Rev. Lett. 93, 083901 (2004).
[CrossRef] [PubMed]

Niv, A.

K. Y. Bliokh, A. Niv, V. Kleiner, and E. Hasman, Nat. Photonics 2, 748 (2008).
[CrossRef]

Onoda, M.

M. Onoda, S. Murakami, and N. Nagaosa, Phys. Rev. Lett. 93, 083901 (2004).
[CrossRef] [PubMed]

Ritchie, N. W. M.

N. W. M. Ritchie, J. G. Story, and R. G. Hulet, Phys. Rev. Lett. 66, 1107 (1991).
[CrossRef] [PubMed]

Romanelli, M.

C. Leyder, M. Romanelli, J. Ph. Karr, E. Giacobino, T. C. H. Liew, M. M. Glazov, A. V. Kavokin, G. Malpuech, and A. Bramati, Nat. Phys. 3, 628 (2007).
[CrossRef]

Simon, B.

B. Simon, Phys. Rev. Lett. 51, 2167 (1983).
[CrossRef]

Story, J. G.

N. W. M. Ritchie, J. G. Story, and R. G. Hulet, Phys. Rev. Lett. 66, 1107 (1991).
[CrossRef] [PubMed]

Vaidman, L.

Y. Aharonov and L. Vaidman, Phys. Rev. A 41, 11 (1990).
[CrossRef] [PubMed]

Woerdman, J. P.

Nat. Photonics (1)

K. Y. Bliokh, A. Niv, V. Kleiner, and E. Hasman, Nat. Photonics 2, 748 (2008).
[CrossRef]

Nat. Phys. (1)

C. Leyder, M. Romanelli, J. Ph. Karr, E. Giacobino, T. C. H. Liew, M. M. Glazov, A. V. Kavokin, G. Malpuech, and A. Bramati, Nat. Phys. 3, 628 (2007).
[CrossRef]

Opt. Lett. (1)

Phys. Lett. A (1)

C. M. Krowne, Phys. Lett. A 373, 466 (2009).
[CrossRef]

Phys. Rev. A (2)

Y. Aharonov and L. Vaidman, Phys. Rev. A 41, 11 (1990).
[CrossRef] [PubMed]

Ch.-F. Li, Phys. Rev. A 76, 013811 (2007).
[CrossRef]

Phys. Rev. E (1)

K. Yu. Bliokh and Y. P. Bliokh, Phys. Rev. E 75, 066609 (2007).
[CrossRef]

Phys. Rev. Lett. (4)

B. Simon, Phys. Rev. Lett. 51, 2167 (1983).
[CrossRef]

N. W. M. Ritchie, J. G. Story, and R. G. Hulet, Phys. Rev. Lett. 66, 1107 (1991).
[CrossRef] [PubMed]

M. Onoda, S. Murakami, and N. Nagaosa, Phys. Rev. Lett. 93, 083901 (2004).
[CrossRef] [PubMed]

K. Yu. Bliokh and Y. P. Bliokh, Phys. Rev. Lett. 96, 073903 (2006).
[CrossRef] [PubMed]

Science (1)

O. Hosten and P. Kwiat, Science 319, 787 (2008).
[CrossRef] [PubMed]

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Figures (5)

Fig. 1
Fig. 1

Schematic of SHEL at an air–glass interface. θ I , incident angle; δ | + , the displacement of |+⟩ spin component; γ I , polarization angle, the angle between x I and the central electric-field-vector E. The superscripts I and R correspond to incident and reflected light, respectively.

Fig. 2
Fig. 2

Experimental setup: HWP, half-wave plate for attenuating the intensity after P1 to prevent the position-sensitive detector (PSD) from saturating; P1 and P2, Glan polarizers; L1 and L2, lenses with 25 and 125 mm focal lengths, respectively; Prism, a right-angle prism with an angle of 30 deg . The laser is a linearly polarized He–Ne laser at 632.8 nm , 18 mW .

Fig. 3
Fig. 3

Displacement of the |+⟩ spin component, δ | + V , as a function of incidence angle θ I , in the case of vertical polarization. Solid curve indicates the theory; dots are experimental data. The error ranges are less than 2 nm .

Fig. 4
Fig. 4

Displacement of the |+⟩ spin component, δ | + H , as a function of incidence angle θ I , in the case of horizontal polarization. Solid curves indicate the theory; dots are experimental data. The inset shows the results near the Brewster angle.

Fig. 5
Fig. 5

y-displacement, δ | + γ I , dependence on the polarization angle γ I when the incident angle is 30 deg . The error ranges are less than 2 nm .

Equations (6)

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

δ | ± H = cot ( θ I ) ( 1 + r s r p ) k I ,
δ | ± V = cot ( θ I ) ( 1 + r p r s ) k I ,
δ | ± γ I = cos 2 ( γ R ) δ | ± H + sin 2 ( γ R ) δ | ± V ,
cos ( γ R ) = cos ( γ I ) r p ( ( cos ( γ I ) r p ) 2 + ( sin ( γ I ) r s ) 2 ) 1 2 ,
sin ( γ R ) = sin ( γ I ) r s ( ( cos ( γ I ) r p ) 2 + ( sin ( γ I ) r s ) 2 ) 1 2 .
L = ± ( F Δ ) δ ,

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