Abstract

We reveal a large spin angular splitting of light beam on reflection at the Brewster angle both theoretically and experimentally. A simple weak measurements system manifesting itself for the built-in post-selection technique is proposed to explore this angular splitting. Remarkably, the directions of the spin accumulations can be switched by adjusting the initial handedness of polarization.

© 2012 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. Onoda, S. Murakami, and N. Nagaosa, “Hall effect of light,” Phys. Rev. Lett.93(8), 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(7), 073903 (2006).
    [CrossRef] [PubMed]
  3. O. Hosten and P. Kwiat, “Observation of the spin Hall effect of light via weak measurements,” Science319(5864), 787–790 (2008).
    [CrossRef] [PubMed]
  4. 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]
  5. 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]
  6. J.-M. Ménard, 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]
  7. 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. A85(4), 043809 (2012).
    [CrossRef]
  8. N. Hermosa, A. M. Nugrowati, A. Aiello, and J. P. Woerdman, “Spin Hall effect of light in metallic reflection,” Opt. Lett.36(16), 3200–3202 (2011).
    [CrossRef] [PubMed]
  9. Y. Qin, Y. Li, X. Feng, Y. F. Xiao, H. Yang, and Q. Gong, “Observation of the in-plane spin separation of light,” Opt. Express19(10), 9636–9645 (2011).
    [CrossRef] [PubMed]
  10. C. C. Chan and T. Tamir, “Angular shift of a Gaussian beam reflected near the Brewster angle,” Opt. Lett.10(8), 378–380 (1985).
    [CrossRef] [PubMed]
  11. M. Merano, A. Aiello, M. P. van Exter, and J. P. Woerdman, “Observing angular deviations in the specular reflection of a light beam,” Nat. Photonics3(6), 337–340 (2009).
    [CrossRef]
  12. M. Merano, N. Hermosa, A. Aiello, and J. P. Woerdman, “Demonstration of a quasi-scalar angular Goos-Hänchen effect,” Opt. Lett.35(21), 3562–3564 (2010).
    [CrossRef] [PubMed]
  13. C. Leyder, M. Romanelli, J. Ph. Karr, E. Giacobino, T. C. H. Liew, M. M. Glazov, A. V. Kavokin, G. Malpuech, and A. Bramati, “Observation of the optical spin Hall effect,” Nat. Phys.3, 628–631 (2007).
    [CrossRef]
  14. 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,” arXiv: 1204. 0378v2.
  15. 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]
  16. 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. A84(4), 043806 (2011).
    [CrossRef]
  17. N. Hermosa, M. Merano, A. Aiello, and J. P. Woerdman, “Orbital angular momentum induced beam shifts,” Proc. SPIE7950, 79500F (2011).
    [CrossRef]
  18. N. Hermosa, A. Aiello, and J. P. Woerdman, “Radial mode dependence of optical beam shifts,” Opt. Lett.37(6), 1044–1046 (2012).
    [CrossRef] [PubMed]
  19. H. Luo, X. Ling, X. Zhou, W. Shu, S. Wen, and D. Fan, “Enhancing or suppressing the spin Hall effect of light in layered nanostructures,” Phys. Rev. A84(3), 033801 (2011).
    [CrossRef]

2012

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. A85(4), 043809 (2012).
[CrossRef]

N. Hermosa, A. Aiello, and J. P. Woerdman, “Radial mode dependence of optical beam shifts,” Opt. Lett.37(6), 1044–1046 (2012).
[CrossRef] [PubMed]

2011

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. A84(4), 043806 (2011).
[CrossRef]

N. Hermosa, M. Merano, A. Aiello, and J. P. Woerdman, “Orbital angular momentum induced beam shifts,” Proc. SPIE7950, 79500F (2011).
[CrossRef]

H. Luo, X. Ling, X. Zhou, W. Shu, S. Wen, and D. Fan, “Enhancing or suppressing the spin Hall effect of light in layered nanostructures,” Phys. Rev. A84(3), 033801 (2011).
[CrossRef]

Y. Qin, Y. Li, X. Feng, Y. F. Xiao, H. Yang, and Q. Gong, “Observation of the in-plane spin separation of light,” Opt. Express19(10), 9636–9645 (2011).
[CrossRef] [PubMed]

N. Hermosa, A. M. Nugrowati, A. Aiello, and J. P. Woerdman, “Spin Hall effect of light in metallic reflection,” Opt. Lett.36(16), 3200–3202 (2011).
[CrossRef] [PubMed]

2010

2009

2008

O. Hosten and P. Kwiat, “Observation of the spin Hall effect of light via weak measurements,” Science319(5864), 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(13), 1437–1439 (2008).
[CrossRef] [PubMed]

2007

C. Leyder, M. Romanelli, J. Ph. Karr, E. Giacobino, T. C. H. Liew, M. M. Glazov, A. V. Kavokin, G. Malpuech, and A. Bramati, “Observation of the optical spin Hall effect,” Nat. Phys.3, 628–631 (2007).
[CrossRef]

2006

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

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

1988

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]

1985

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.

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.

Bliokh, K. Y.

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. 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,” arXiv: 1204. 0378v2.

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]

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, “Observation of the optical spin Hall effect,” Nat. Phys.3, 628–631 (2007).
[CrossRef]

Chan, C. C.

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,” arXiv: 1204. 0378v2.

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. A84(4), 043806 (2011).
[CrossRef]

H. Luo, X. Ling, X. Zhou, W. Shu, S. Wen, and D. Fan, “Enhancing or suppressing the spin Hall effect of light in layered nanostructures,” Phys. Rev. A84(3), 033801 (2011).
[CrossRef]

Feng, X.

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,” arXiv: 1204. 0378v2.

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, “Observation of the optical spin Hall effect,” Nat. Phys.3, 628–631 (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, “Observation of the optical spin Hall effect,” Nat. Phys.3, 628–631 (2007).
[CrossRef]

Gong, Q.

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,” arXiv: 1204. 0378v2.

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,” arXiv: 1204. 0378v2.

He, H.

Hermosa, N.

Hosten, O.

O. Hosten and P. Kwiat, “Observation of the spin Hall effect of light via weak measurements,” Science319(5864), 787–790 (2008).
[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, “Observation of the optical spin Hall effect,” Nat. Phys.3, 628–631 (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, “Observation of the optical spin Hall effect,” Nat. Phys.3, 628–631 (2007).
[CrossRef]

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,” arXiv: 1204. 0378v2.

Kwiat, P.

O. Hosten and P. Kwiat, “Observation of the spin Hall effect of light via weak measurements,” Science319(5864), 787–790 (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, “Observation of the optical spin Hall effect,” Nat. Phys.3, 628–631 (2007).
[CrossRef]

Li, Y.

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, “Observation of the optical spin Hall effect,” Nat. Phys.3, 628–631 (2007).
[CrossRef]

Ling, X.

H. Luo, X. Ling, X. Zhou, W. Shu, S. Wen, and D. Fan, “Enhancing or suppressing the spin Hall effect of light in layered nanostructures,” Phys. Rev. A84(3), 033801 (2011).
[CrossRef]

Luo, H.

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. A85(4), 043809 (2012).
[CrossRef]

H. Luo, X. Ling, X. Zhou, W. Shu, S. Wen, and D. Fan, “Enhancing or suppressing the spin Hall effect of light in layered nanostructures,” Phys. Rev. A84(3), 033801 (2011).
[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. A84(4), 043806 (2011).
[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, “Observation of the optical spin Hall effect,” Nat. Phys.3, 628–631 (2007).
[CrossRef]

Mattacchione, A. E.

Ménard, J.-M.

Merano, M.

N. Hermosa, M. Merano, A. Aiello, and J. P. Woerdman, “Orbital angular momentum induced beam shifts,” Proc. SPIE7950, 79500F (2011).
[CrossRef]

M. Merano, N. Hermosa, A. Aiello, and J. P. Woerdman, “Demonstration of a quasi-scalar angular Goos-Hänchen effect,” Opt. Lett.35(21), 3562–3564 (2010).
[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. Photonics3(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]

Nugrowati, A. M.

Onoda, M.

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

Qin, Y.

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, “Observation of the optical spin Hall effect,” Nat. Phys.3, 628–631 (2007).
[CrossRef]

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,” arXiv: 1204. 0378v2.

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. A84(4), 043806 (2011).
[CrossRef]

H. Luo, X. Ling, X. Zhou, W. Shu, S. Wen, and D. Fan, “Enhancing or suppressing the spin Hall effect of light in layered nanostructures,” Phys. Rev. A84(3), 033801 (2011).
[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,” arXiv: 1204. 0378v2.

Tamir, T.

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]

van Driel, H. M.

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. Photonics3(6), 337–340 (2009).
[CrossRef]

Wen, S.

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. A85(4), 043809 (2012).
[CrossRef]

H. Luo, X. Ling, X. Zhou, W. Shu, S. Wen, and D. Fan, “Enhancing or suppressing the spin Hall effect of light in layered nanostructures,” Phys. Rev. A84(3), 033801 (2011).
[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. A84(4), 043806 (2011).
[CrossRef]

Woerdman, J. P.

Xiao, Y. F.

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. A85(4), 043809 (2012).
[CrossRef]

Yang, H.

Zhou, X.

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. A85(4), 043809 (2012).
[CrossRef]

H. Luo, X. Ling, X. Zhou, W. Shu, S. Wen, and D. Fan, “Enhancing or suppressing the spin Hall effect of light in layered nanostructures,” Phys. Rev. A84(3), 033801 (2011).
[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. A84(4), 043806 (2011).
[CrossRef]

Nat. Photonics

M. Merano, A. Aiello, M. P. van Exter, and J. P. Woerdman, “Observing angular deviations in the specular reflection of a light beam,” Nat. Photonics3(6), 337–340 (2009).
[CrossRef]

Nat. Phys.

C. Leyder, M. Romanelli, J. Ph. Karr, E. Giacobino, T. C. H. Liew, M. M. Glazov, A. V. Kavokin, G. Malpuech, and A. Bramati, “Observation of the optical spin Hall effect,” Nat. Phys.3, 628–631 (2007).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

H. Luo, X. Ling, X. Zhou, W. Shu, S. Wen, and D. Fan, “Enhancing or suppressing the spin Hall effect of light in layered nanostructures,” Phys. Rev. A84(3), 033801 (2011).
[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. A84(4), 043806 (2011).
[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. A85(4), 043809 (2012).
[CrossRef]

Phys. Rev. Lett.

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]

Proc. SPIE

N. Hermosa, M. Merano, A. Aiello, and J. P. Woerdman, “Orbital angular momentum induced beam shifts,” Proc. SPIE7950, 79500F (2011).
[CrossRef]

Science

O. Hosten and P. Kwiat, “Observation of the spin Hall effect of light via weak measurements,” Science319(5864), 787–790 (2008).
[CrossRef] [PubMed]

Other

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,” arXiv: 1204. 0378v2.

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 (4)

Fig. 1
Fig. 1

(a) Schematic illustrating the spin angular splitting compared to the geometrical-optics prediction. (b) The incident beam has an uniform polarization direction in the cross section. (c) The polarization handedness experience different rotations in reflection to satisfy transversality.

Fig. 2
Fig. 2

(a) Experimental setup for characterizing the large spin angular splitting on reflection at the Brewster angle. The light source is a 17mW linearly polarized He-Ne laser at 632.8nm (Thorlabs HRP170); Prism with refractive index n = 1.515 (BK7 at 632.8nm); Lens, lens with effective focal length: 50mm; HWP, half-wave plate (for adjusting the intensity); QWP1 and QWP2, quarter-wave plates; GLP1 and GLP2, Glan Laser polarizers; Here, QWP2 together with GLP2 allow for measuring the Stokes parameter S3; K, knife edge (The purpose of the knife is to produce a single spin accumulation so that only one spin component can be detected in the CCD); CCD, charge-coupled device (Coherent LaserCam HR). The inset: The incident beam is preselected in the left- or right-elliptical polarization state by GLP1 whose optical axis make angles Δ or (−Δ) with xi-axis. Here, we choose Δ=0.5°.

Fig. 3
Fig. 3

(a) Presection and postselection of polarizations give rise to an amplified spin angular splitting. (b) Theoretical and experimental results of two spin components induced by the spin angular splitting for beam waist w0 = 18.66μm. We measured the zr from the beam waist. The incident light beam is left-elliptical polarization for Δ=0.5° from the xi-axis and incidents at the Brewster angle θi = 56.57°.

Fig. 4
Fig. 4

Theoretical and experimental results of Stokes parameter S3: (a), (b) Theoretical calculation of Stokes parameter S3 for the left- and right-elliptical polarization; (c), (d) Experimental results concluded from the intensity distributions on CCD. The directions of the spin accumulation can be switched by adjusting the initial handedness of polarizations. Here, the parameters are the same as that of Fig. 3. The distributions in the plane zr = 300mm are plotted with normalized units.

Equations (6)

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

[ E ˜ r H E ˜ r V ] = [ r p k r y ( r p + r s ) cot θ i k 0 k r y ( r p + r s ) cot θ i k 0 r s ] [ E ˜ i H E ˜ i V ] .
E ˜ i = w 0 2 π exp [ w 0 2 ( k i x 2 + k i y 2 ) 4 ] ,
E ˜ r = r p cos Δ 2 [ ( 1 + i tan Δ k r y δ r y + η ) E ˜ r + + ( 1 + i tan Δ k r y δ r y η ) E ˜ r ] .
δ ± = ξ ˜ r ± * i k r x ξ ˜ r ± d k r x d k r y ξ ˜ r ± * ξ ˜ r ± d k r x d k r y ,
r p , s ( k i x ) = r p , s ( k i x = 0 ) + k i x [ r p , s ( k i x ) k i x ] k i x = 0 + j = 2 N k i x N j ! [ j r p , s ( k i x ) k i x j ] k i x = 0 .
δ ± = ± 2 z r r s r p θ i [ ( k 0 R + csc 2 θ i 1 ) sin 2 Δ + csc 2 θ i 1 ] k 0 R [ 2 k 0 R r s 2 ( r p θ i ) 2 ] cos 2 Δ [ 2 k 0 R r s 2 + ( r p θ i ) 2 ] ( k 0 R + csc 2 θ i + cot 2 θ i sin 2 Δ 1 ) .

Metrics