Abstract

We theoretically and experimentally study the spin Hall effect of reflected light at an air-uniaxial crystal interface. The spin-dependent nanometer-sized displacements depend not only on the incident polarization and the incident angle of the light beam, but also on the orientation of the crystal optic axis. The experimental results are in perfect agreement with theoretical predictions for the vertical and horizontal polarization incidence.

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References

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  1. C. Imbert, “Calculation and experimental proof of transverse shift induced by total internal reflection of a circularly polarized-lightbeam,” Phys. Rev. D Part. Fields 5(4), 787–796 (1972).
  2. V. G. Fedoseyev, “Conservation-Laws and transverse motion of energy on reflection and transmission of electromagnetic-waves,” J. Phys. A 21(9), 2045–2059 (1988).
    [CrossRef]
  3. M. A. Player, “Angular-Momentum balance and transverse shifts on reflection of light,” J. Phys. A 20(12), 3667–3678 (1987).
    [CrossRef]
  4. K. Y. Bliokh, I. V. Shadrivov, and Y. S. Kivshar, “Goos-Hänchen and Imbert-Fedorov shifts of polarized vortex beams,” Opt. Lett. 34(3), 389–391 (2009).
    [CrossRef] [PubMed]
  5. N. N. Punko and V. V. Filippov, “Beam splitting due to the finite size of the medium during total reflection,” JETP Lett. 39, 20–23 (1984).
  6. A. Ciattoni, B. Crosignani, and P. Di Porto, “Vectorial theory of propagation in uniaxially anisotropic media,” J. Opt. Soc. Am. A 18(7), 1656–1661 (2001).
    [CrossRef]
  7. A. Ciattoni and C. Palma, “Optical propagation in uniaxial crystals orthogonal to the optical axis: paraxial theory and beyond,” J. Opt. Soc. Am. A 20(11), 2163–2171 (2003).
    [CrossRef]
  8. F. Flossmann, U. T. Schwarz, M. Maier, and M. R. Dennis, “Polarization singularities from unfolding an optical vortex through a birefringent crystal,” Phys. Rev. Lett. 95(25), 253901 (2005).
    [CrossRef] [PubMed]
  9. E. Brasselet, Y. Izdebskaya, V. Shvedov, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, “Dynamics of optical spin-orbit coupling in uniaxial crystals,” Opt. Lett. 34(7), 1021–1023 (2009).
    [CrossRef] [PubMed]
  10. L. I. Perez, “Nonspecular transverse effects of polarized and unpolarized symmetric beams in isotropic-uniaxial interfaces,” J. Opt. Soc. Am. A 20(4), 741–752 (2003).
    [CrossRef]
  11. T. A. Fadeyeva, A. F. Rubass, and A. V. Volyar, “Transverse shift of a high-order paraxial vortex-beam induced by a homogeneous anisotropic medium,” Phys. Rev. A 79(5), 053815 (2009).
    [CrossRef]
  12. M. Onoda, S. Murakami, and N. Nagaosa, “Hall effect of light,” Phys. Rev. Lett. 93(8), 083901 (2004).
    [CrossRef] [PubMed]
  13. 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]
  14. 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]
  15. 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]
  16. K. Y. Bliokh, A. Niv, V. Kleiner, and E. Hasman, “Geometrodynamics of spinning light,” Nat. Photonics 2(12), 748–753 (2008).
    [CrossRef]
  17. 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]
  18. C. M. Krowne, “Spin moments of particles detected using the spin Hall effect of light through weak quantum measurements,” Phys. Lett. A 373(4), 466–472 (2009).
    [CrossRef]
  19. 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]
  20. 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]
  21. O. Hosten and P. Kwiat, “Observation of the spin hall effect of light via weak measurements,” Science 319(5864), 787–790 (2008).
    [CrossRef] [PubMed]
  22. 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]
  23. V. G. Fedoseyev, “Conservation laws and angular transverse shifts of the reflected and transmitted light beams,” Opt. Commun. 282(7), 1247–1251 (2009).
    [CrossRef]

2009 (8)

T. A. Fadeyeva, A. F. Rubass, and A. V. Volyar, “Transverse shift of a high-order paraxial vortex-beam induced by a homogeneous anisotropic medium,” Phys. Rev. A 79(5), 053815 (2009).
[CrossRef]

C. M. Krowne, “Spin moments of particles detected using the spin Hall effect of light through weak quantum measurements,” Phys. Lett. A 373(4), 466–472 (2009).
[CrossRef]

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]

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]

V. G. Fedoseyev, “Conservation laws and angular transverse shifts of the reflected and transmitted light beams,” Opt. Commun. 282(7), 1247–1251 (2009).
[CrossRef]

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

E. Brasselet, Y. Izdebskaya, V. Shvedov, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, “Dynamics of optical spin-orbit coupling in uniaxial crystals,” Opt. Lett. 34(7), 1021–1023 (2009).
[CrossRef] [PubMed]

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]

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]

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]

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

2005 (1)

F. Flossmann, U. T. Schwarz, M. Maier, and M. R. Dennis, “Polarization singularities from unfolding an optical vortex through a birefringent crystal,” Phys. Rev. Lett. 95(25), 253901 (2005).
[CrossRef] [PubMed]

2004 (1)

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

2003 (2)

2001 (1)

1988 (1)

V. G. Fedoseyev, “Conservation-Laws and transverse motion of energy on reflection and transmission of electromagnetic-waves,” J. Phys. A 21(9), 2045–2059 (1988).
[CrossRef]

1987 (1)

M. A. Player, “Angular-Momentum balance and transverse shifts on reflection of light,” J. Phys. A 20(12), 3667–3678 (1987).
[CrossRef]

1984 (1)

N. N. Punko and V. V. Filippov, “Beam splitting due to the finite size of the medium during total reflection,” JETP Lett. 39, 20–23 (1984).

1972 (1)

C. Imbert, “Calculation and experimental proof of transverse shift induced by total internal reflection of a circularly polarized-lightbeam,” Phys. Rev. D Part. Fields 5(4), 787–796 (1972).

Aiello, A.

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-Hänchen and Imbert-Fedorov shifts,” Opt. Lett. 33(13), 1437–1439 (2008).
[CrossRef] [PubMed]

Bliokh, K. Y.

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

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 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]

Brasselet, E.

Ciattoni, A.

Crosignani, B.

Dennis, M. R.

F. Flossmann, U. T. Schwarz, M. Maier, and M. R. Dennis, “Polarization singularities from unfolding an optical vortex through a birefringent crystal,” Phys. Rev. Lett. 95(25), 253901 (2005).
[CrossRef] [PubMed]

Desyatnikov, A. S.

Di Porto, P.

Fadeyeva, T. A.

T. A. Fadeyeva, A. F. Rubass, and A. V. Volyar, “Transverse shift of a high-order paraxial vortex-beam induced by a homogeneous anisotropic medium,” Phys. Rev. A 79(5), 053815 (2009).
[CrossRef]

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]

Fedoseyev, V. G.

V. G. Fedoseyev, “Conservation laws and angular transverse shifts of the reflected and transmitted light beams,” Opt. Commun. 282(7), 1247–1251 (2009).
[CrossRef]

V. G. Fedoseyev, “Conservation-Laws and transverse motion of energy on reflection and transmission of electromagnetic-waves,” J. Phys. A 21(9), 2045–2059 (1988).
[CrossRef]

Filippov, V. V.

N. N. Punko and V. V. Filippov, “Beam splitting due to the finite size of the medium during total reflection,” JETP Lett. 39, 20–23 (1984).

Flossmann, F.

F. Flossmann, U. T. Schwarz, M. Maier, and M. R. Dennis, “Polarization singularities from unfolding an optical vortex through a birefringent crystal,” Phys. Rev. Lett. 95(25), 253901 (2005).
[CrossRef] [PubMed]

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]

Hasman, E.

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]

He, H. Y.

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]

Imbert, C.

C. Imbert, “Calculation and experimental proof of transverse shift induced by total internal reflection of a circularly polarized-lightbeam,” Phys. Rev. D Part. Fields 5(4), 787–796 (1972).

Izdebskaya, Y.

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]

Krolikowski, W.

Krowne, C. M.

C. M. Krowne, “Spin moments of particles detected using the spin Hall effect of light through weak quantum measurements,” Phys. Lett. A 373(4), 466–472 (2009).
[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, Y.

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]

Maier, M.

F. Flossmann, U. T. Schwarz, M. Maier, and M. R. Dennis, “Polarization singularities from unfolding an optical vortex through a birefringent crystal,” Phys. Rev. Lett. 95(25), 253901 (2005).
[CrossRef] [PubMed]

Merano, M.

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]

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]

Palma, C.

Perez, L. I.

Player, M. A.

M. A. Player, “Angular-Momentum balance and transverse shifts on reflection of light,” J. Phys. A 20(12), 3667–3678 (1987).
[CrossRef]

Punko, N. N.

N. N. Punko and V. V. Filippov, “Beam splitting due to the finite size of the medium during total reflection,” JETP Lett. 39, 20–23 (1984).

Qin, Y.

Rubass, A. F.

T. A. Fadeyeva, A. F. Rubass, and A. V. Volyar, “Transverse shift of a high-order paraxial vortex-beam induced by a homogeneous anisotropic medium,” Phys. Rev. A 79(5), 053815 (2009).
[CrossRef]

Schwarz, U. T.

F. Flossmann, U. T. Schwarz, M. Maier, and M. R. Dennis, “Polarization singularities from unfolding an optical vortex through a birefringent crystal,” Phys. Rev. Lett. 95(25), 253901 (2005).
[CrossRef] [PubMed]

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]

Shvedov, V.

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 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]

Volyar, A. V.

T. A. Fadeyeva, A. F. Rubass, and A. V. Volyar, “Transverse shift of a high-order paraxial vortex-beam induced by a homogeneous anisotropic medium,” Phys. Rev. A 79(5), 053815 (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, 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-Hänchen and Imbert-Fedorov shifts,” Opt. Lett. 33(13), 1437–1439 (2008).
[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]

J. Opt. Soc. Am. A (3)

J. Phys. A (2)

V. G. Fedoseyev, “Conservation-Laws and transverse motion of energy on reflection and transmission of electromagnetic-waves,” J. Phys. A 21(9), 2045–2059 (1988).
[CrossRef]

M. A. Player, “Angular-Momentum balance and transverse shifts on reflection of light,” J. Phys. A 20(12), 3667–3678 (1987).
[CrossRef]

JETP Lett. (1)

N. N. Punko and V. V. Filippov, “Beam splitting due to the finite size of the medium during total reflection,” JETP Lett. 39, 20–23 (1984).

Nat. Photonics (2)

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

Opt. Commun. (1)

V. G. Fedoseyev, “Conservation laws and angular transverse shifts of the reflected and transmitted light beams,” Opt. Commun. 282(7), 1247–1251 (2009).
[CrossRef]

Opt. Lett. (4)

Phys. Lett. A (1)

C. M. Krowne, “Spin moments of particles detected using the spin Hall effect of light through weak quantum measurements,” Phys. Lett. A 373(4), 466–472 (2009).
[CrossRef]

Phys. Rev. A (2)

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]

T. A. Fadeyeva, A. F. Rubass, and A. V. Volyar, “Transverse shift of a high-order paraxial vortex-beam induced by a homogeneous anisotropic medium,” Phys. Rev. A 79(5), 053815 (2009).
[CrossRef]

Phys. Rev. D Part. Fields (1)

C. Imbert, “Calculation and experimental proof of transverse shift induced by total internal reflection of a circularly polarized-lightbeam,” Phys. Rev. D Part. Fields 5(4), 787–796 (1972).

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. (4)

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]

F. Flossmann, U. T. Schwarz, M. Maier, and M. R. Dennis, “Polarization singularities from unfolding an optical vortex through a birefringent crystal,” Phys. Rev. Lett. 95(25), 253901 (2005).
[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 (4)

Fig. 1
Fig. 1

Schematic of SHEL at an air–uniaxial crystal interface. θ I , incident angle; δ y | + > , the displacement of | + > spin component. The subscripts I and R correspond to incident and reflected light, respectively.

Fig. 2
Fig. 2

Experimental setup. 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.

Fig. 3
Fig. 3

Displacements of the | + > spin component, δ | + > V , as a function of incidence angle, θ I , in the case of vertical polarization. The dots, circles, triangles correspond to the cases that the crystal optic axis is along x, y, z axis respectively. The solid curves represent the theoretical predictions.

Fig. 4
Fig. 4

Displacements δ | + > H as a function of incidence angle θ I , in the case of horizontal polarization. The blue, red, green curves indicate the theoretical prediction when the crystal optic axis is along x, y, z axis, respectively, and the dots, circles, triangles are the corresponding experimental data. (a) θ I < Brewster angle θ B . The inset shows the results for 0< θ I <90°; (b) θ I > θB. The inset shows the enlarged image for 71° < θ I <75°.

Equations (15)

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

| 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 ) ) > .
| p ( k ( I ) ) > = | e ( k ( I ) ) > + ( tan θ I + cot θ I ) κ y ( I ) | o ( k ( I ) ) > , | s ( k ( I ) ) > = | o ( k ( I ) ) > ( tan θ I + cot θ I ) κ y ( I ) | e ( k ( I ) ) > ,
| H ( k ( I ) ) > = | p e ( k ( I ) ) > ( tan θ I + cot θ I ) κ y ( I ) | s e ( k ( I ) ) > + tan θ I κ y ( I ) | s o ( k ( I ) ) > , | V ( k ( I ) ) > = | s o ( k ( I ) ) > + ( tan θ I + cot θ I ) κ y ( I ) | p o ( k ( I ) ) > tan θ I κ y ( I ) | p e ( k ( I ) ) > .
| H ( k ( I ) ) > r p , e x ( | H ( k ( R ) ) > + k y δ y x H | V ( k ( R ) ) > ) , | V ( k ( I ) )     > r s , o     ( | V ( k ( R ) )       > k y δ y x V | H ( k ( R ) ) > ) .
| H ( k ( I ) ) >       r p , e x 2 [ exp ( i k y δ y x | + > H ) | + > + exp ( i k y δ y x | > H ) | > ] , | V ( k ( I ) )     > i r s , o 2 [ exp ( i k y δ y x | + > V ) | + > exp ( i k y δ y x | > V )     | > ] ,
δ y x | ± > H = cot θ I k I ( 1 + r s , e x r p , e x 1 cos 2 θ I r s , o r p , e x tan 2 θ I ) ,
δ y x | ± > V = cot θ I k I ( 1 + r p , o r s , o 1 cos 2 θ I r p , e x r s , o tan 2 θ I ) .
| p ( k ( I ) ) > = | o ( k ( I ) ) > + cot θ I κ y ( I ) | e ( k ( I ) ) > , | s ( k ( I ) ) > = | e ( k ( I ) ) > cot θ I κ y ( I ) | o ( k ( I ) ) > .
| H ( k ( I ) ) >         r p , o 2 [ exp ( i k y δ y y | + > H ) | + > + exp ( i k y δ y y | > H ) | > ] , | V ( k ( I ) )     > i r s , e y 2 [ exp ( i k y δ y y | + > V ) | + >     exp ( i k y δ y y | > V ) | > ] ,
δ y y | ± > H = cot θ I k I ( 1 + r s , o r p , o ) ,
δ y y | ± > V = cot θ I k I ( 1 + r p , e y r s , e y ) .
| p ( k ( I ) ) ) = | e ( k ( I ) ) > , | s ( k ( I ) ) > = | o ( k ( I ) ) > ,
| H ( k ( I ) ) >     r p , e z 2     [ exp ( i k y δ y z | + > H ) | + > + exp ( i k y δ y z | > H ) | > ] , | V ( k ( I ) )     > i r s , o 2 [ exp ( i k y δ y z | + > V ) | + > exp ( i k y δ y z | > V )     | > ] ,
δ y z | ± > H = cot θ I k I ( 1 + r s , o r p , e z ) ,
δ y z | ± > V = cot θ I k I ( 1 + r p , e z r s , o ) .

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