Abstract

We show theoretically that after transmitted through a thin anisotropic ε-near-zero metamaterial, a linearly polarized Gaussian beam can undergo both transverse spatial and angular spin splitting. The upper limits of spatial and angular spin splitting are found to be the beam waist and divergence angle of incident Gaussian beam, respectively. The spin splitting of transmitted beam after propagating a distance z depends on both the spatial and angular spin splitting. By combining the spatial and angular spin splitting properly, we can maximize the spin splitting of propagated beam, which is nearly equal to the spot size of Gaussian beam w(z).

© 2017 Optical Society of America

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References

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    [Crossref]
  2. X. J. Tan and X. S. Zhu, “Enhancing photonic spin Hall effect via long-range surface plasmon resonance,” Opt. Lett. 41(11), 2478–2481 (2016).
    [Crossref] [PubMed]
  3. X. Qiu, L. Xie, J. Qiu, Z. Zhang, J. Du, and F. Gao, “Diffraction-dependent spin splitting in spin Hall effect of light on reflection,” Opt. Express 23(15), 18823–18831 (2015).
    [Crossref] [PubMed]
  4. X. Qiu, Z. Zhang, L. Xie, J. Qiu, F. Gao, and J. Du, “Incident-polarization-sensitive and large in-plane-photonic-spin-splitting at the Brewster angle,” Opt. Lett. 40(6), 1018–1021 (2015).
    [Crossref] [PubMed]
  5. X. Zhou and X. Ling, “Unveiling the photonic spin Hall effect with asymmetric spin-dependent splitting,” Opt. Express 24(3), 3025–3036 (2016).
    [Crossref] [PubMed]
  6. S. Grosche, M. Ornigotti, and A. Szameit, “Goos-Hänchen and Imbert-Fedorov shifts for Gaussian beams impinging on graphene-coated surfaces,” Opt. Express 23(23), 30195–30203 (2015).
    [Crossref] [PubMed]
  7. 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]
  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. 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]
  10. 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]
  11. X. Qiu, Z. Zhang, L. Xie, J. Qiu, F. Gao, and J. Du, “Incident-polarization-sensitive and large in-plane-photonic-spin-splitting at the Brewster angle,” Opt. Lett. 40(6), 1018–1021 (2015).
    [Crossref] [PubMed]
  12. J. B. Götte, W. Löffler, and M. R. Dennis, “Eigenpolarizations for giant transverse optical beam shifts,” Phys. Rev. Lett. 112(23), 233901 (2014).
    [Crossref] [PubMed]
  13. J. L. Ren, B. Wang, Y. F. Xiao, Q. Gong, and Y. Li, “Direct observation of a resolvable spin separation in the spin Hall effect of light at an air-glass interface,” Appl. Phys. Lett. 107(11), 54–59 (2015).
    [Crossref]
  14. H. Luo, S. Wen, W. Shu, and D. Fan, “Spin Hall effect of light in photon tunneling,” Phys. Rev. A 82(4), 043825 (2010).
    [Crossref]
  15. X. Zhou, X. Ling, Z. Zhang, H. Luo, and S. Wen, “Observation of spin Hall effect in photon tunneling via weak measurements,” Sci. Rep. 4, 7388 (2014).
    [Crossref] [PubMed]
  16. T. Tang, C. Li, and L. Luo, “Enhanced spin Hall effect of tunneling light in hyperbolic metamaterial waveguide,” Sci. Rep. 6, 30762 (2016).
    [Crossref] [PubMed]
  17. W. Zhu and W. She, “Enhanced spin Hall effect of transmitted light through a thin epsilon-near-zero slab,” Opt. Lett. 40(13), 2961–2964 (2015).
    [Crossref] [PubMed]
  18. S. Goswami, M. Pal, A. Nandi, P. K. Panigrahi, and N. Ghosh, “Simultaneous weak value amplification of angular Goos-Hänchen and Imbert-Fedorov shifts in partial reflection,” Opt. Lett. 39(21), 6229–6232 (2014).
    [Crossref] [PubMed]
  19. G. Jayaswal, G. Mistura, and M. Merano, “Observing angular deviations in light-beam reflection via weak measurements,” Opt. Lett. 39(21), 6257–6260 (2014).
    [Crossref] [PubMed]
  20. A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Corrigendum: Hyperbolic metamaterials,” Nat. Photonics 8(1), 78 (2013).
    [Crossref]
  21. P. Ginzburg, F. J. R. Fortuño, G. A. Wurtz, W. Dickson, A. Murphy, F. Morgan, R. J. Pollard, I. Iorsh, A. Atrashchenko, P. A. Belov, Y. S. Kivshar, A. Nevet, G. Ankonina, M. Orenstein, and A. V. Zayats, “Manipulating polarization of light with ultrathin epsilon-near-zero metamaterials,” Opt. Express 21(12), 14907–14917 (2013).
    [Crossref] [PubMed]
  22. O. J. S. Santana, S. A. Carvalho, S. De Leo, and L. E. de Araujo, “Weak measurement of the composite Goos-Hänchen shift in the critical region,” Opt. Lett. 41(16), 3884–3887 (2016).
    [Crossref] [PubMed]
  23. Y. Xu, C. T. Chan, and H. Chen, “Goos-Hänchen effect in epsilon-near-zero metamaterials,” Sci. Rep. 5, 8681 (2015).
    [Crossref] [PubMed]
  24. 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. A 84(3), 033801 (2011).
    [Crossref]
  25. A. Shaltout, J. Liu, A. Kildishev, and V. Shalaev, “Photonic spin Hall effect in gap–plasmon metasurfaces for on-chip chiroptical spectroscopy,” Optica 2(10), 860 (2015).
    [Crossref]
  26. K. Y. Bliokh, F. J. Rodríguez-Fortuño, F. Nori, and A. V. Zayats, “Spin-orbit interactions of light,” Nat. Photonics 9(12), 796–808 (2015).
    [Crossref]

2016 (4)

2015 (9)

Y. Xu, C. T. Chan, and H. Chen, “Goos-Hänchen effect in epsilon-near-zero metamaterials,” Sci. Rep. 5, 8681 (2015).
[Crossref] [PubMed]

A. Shaltout, J. Liu, A. Kildishev, and V. Shalaev, “Photonic spin Hall effect in gap–plasmon metasurfaces for on-chip chiroptical spectroscopy,” Optica 2(10), 860 (2015).
[Crossref]

K. Y. Bliokh, F. J. Rodríguez-Fortuño, F. Nori, and A. V. Zayats, “Spin-orbit interactions of light,” Nat. Photonics 9(12), 796–808 (2015).
[Crossref]

W. Zhu and W. She, “Enhanced spin Hall effect of transmitted light through a thin epsilon-near-zero slab,” Opt. Lett. 40(13), 2961–2964 (2015).
[Crossref] [PubMed]

X. Qiu, Z. Zhang, L. Xie, J. Qiu, F. Gao, and J. Du, “Incident-polarization-sensitive and large in-plane-photonic-spin-splitting at the Brewster angle,” Opt. Lett. 40(6), 1018–1021 (2015).
[Crossref] [PubMed]

J. L. Ren, B. Wang, Y. F. Xiao, Q. Gong, and Y. Li, “Direct observation of a resolvable spin separation in the spin Hall effect of light at an air-glass interface,” Appl. Phys. Lett. 107(11), 54–59 (2015).
[Crossref]

S. Grosche, M. Ornigotti, and A. Szameit, “Goos-Hänchen and Imbert-Fedorov shifts for Gaussian beams impinging on graphene-coated surfaces,” Opt. Express 23(23), 30195–30203 (2015).
[Crossref] [PubMed]

X. Qiu, L. Xie, J. Qiu, Z. Zhang, J. Du, and F. Gao, “Diffraction-dependent spin splitting in spin Hall effect of light on reflection,” Opt. Express 23(15), 18823–18831 (2015).
[Crossref] [PubMed]

X. Qiu, Z. Zhang, L. Xie, J. Qiu, F. Gao, and J. Du, “Incident-polarization-sensitive and large in-plane-photonic-spin-splitting at the Brewster angle,” Opt. Lett. 40(6), 1018–1021 (2015).
[Crossref] [PubMed]

2014 (4)

J. B. Götte, W. Löffler, and M. R. Dennis, “Eigenpolarizations for giant transverse optical beam shifts,” Phys. Rev. Lett. 112(23), 233901 (2014).
[Crossref] [PubMed]

S. Goswami, M. Pal, A. Nandi, P. K. Panigrahi, and N. Ghosh, “Simultaneous weak value amplification of angular Goos-Hänchen and Imbert-Fedorov shifts in partial reflection,” Opt. Lett. 39(21), 6229–6232 (2014).
[Crossref] [PubMed]

G. Jayaswal, G. Mistura, and M. Merano, “Observing angular deviations in light-beam reflection via weak measurements,” Opt. Lett. 39(21), 6257–6260 (2014).
[Crossref] [PubMed]

X. Zhou, X. Ling, Z. Zhang, H. Luo, and S. Wen, “Observation of spin Hall effect in photon tunneling via weak measurements,” Sci. Rep. 4, 7388 (2014).
[Crossref] [PubMed]

2013 (3)

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Corrigendum: Hyperbolic metamaterials,” Nat. Photonics 8(1), 78 (2013).
[Crossref]

P. Ginzburg, F. J. R. Fortuño, G. A. Wurtz, W. Dickson, A. Murphy, F. Morgan, R. J. Pollard, I. Iorsh, A. Atrashchenko, P. A. Belov, Y. S. Kivshar, A. Nevet, G. Ankonina, M. Orenstein, and A. V. Zayats, “Manipulating polarization of light with ultrathin epsilon-near-zero metamaterials,” Opt. Express 21(12), 14907–14917 (2013).
[Crossref] [PubMed]

K. Y. Bliokh and A. Aiello, “Goos-hächen and imbert-fedorov beam shifts: an overview,” J. Opt. 15(1), 014001 (2013).
[Crossref]

2011 (3)

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]

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, 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. A 84(3), 033801 (2011).
[Crossref]

2010 (1)

H. Luo, S. Wen, W. Shu, and D. Fan, “Spin Hall effect of light in photon tunneling,” Phys. Rev. A 82(4), 043825 (2010).
[Crossref]

2008 (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]

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]

Aiello, A.

K. Y. Bliokh and A. Aiello, “Goos-hächen and imbert-fedorov beam shifts: an overview,” J. Opt. 15(1), 014001 (2013).
[Crossref]

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]

Ankonina, G.

Atrashchenko, A.

Belov, P.

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Corrigendum: Hyperbolic metamaterials,” Nat. Photonics 8(1), 78 (2013).
[Crossref]

Belov, P. A.

Bliokh, K. Y.

K. Y. Bliokh, F. J. Rodríguez-Fortuño, F. Nori, and A. V. Zayats, “Spin-orbit interactions of light,” Nat. Photonics 9(12), 796–808 (2015).
[Crossref]

K. Y. Bliokh and A. Aiello, “Goos-hächen and imbert-fedorov beam shifts: an overview,” J. Opt. 15(1), 014001 (2013).
[Crossref]

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]

Carvalho, S. A.

Chan, C. T.

Y. Xu, C. T. Chan, and H. Chen, “Goos-Hänchen effect in epsilon-near-zero metamaterials,” Sci. Rep. 5, 8681 (2015).
[Crossref] [PubMed]

Chen, H.

Y. Xu, C. T. Chan, and H. Chen, “Goos-Hänchen effect in epsilon-near-zero metamaterials,” Sci. Rep. 5, 8681 (2015).
[Crossref] [PubMed]

de Araujo, L. E.

De Leo, S.

Dennis, M. R.

J. B. Götte, W. Löffler, and M. R. Dennis, “Eigenpolarizations for giant transverse optical beam shifts,” Phys. Rev. Lett. 112(23), 233901 (2014).
[Crossref] [PubMed]

Dickson, W.

Du, J.

Fan, D.

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. A 84(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. A 84(4), 043806 (2011).
[Crossref]

H. Luo, S. Wen, W. Shu, and D. Fan, “Spin Hall effect of light in photon tunneling,” Phys. Rev. A 82(4), 043825 (2010).
[Crossref]

Fortuño, F. J. R.

Gao, F.

Ghosh, N.

Ginzburg, P.

Gong, Q.

J. L. Ren, B. Wang, Y. F. Xiao, Q. Gong, and Y. Li, “Direct observation of a resolvable spin separation in the spin Hall effect of light at an air-glass interface,” Appl. Phys. Lett. 107(11), 54–59 (2015).
[Crossref]

Goswami, S.

Götte, J. B.

J. B. Götte, W. Löffler, and M. R. Dennis, “Eigenpolarizations for giant transverse optical beam shifts,” Phys. Rev. Lett. 112(23), 233901 (2014).
[Crossref] [PubMed]

Grosche, S.

Hermosa, N.

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]

Iorsh, I.

Jayaswal, G.

Kildishev, A.

Kivshar, Y.

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Corrigendum: Hyperbolic metamaterials,” Nat. Photonics 8(1), 78 (2013).
[Crossref]

Kivshar, Y. S.

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, C.

T. Tang, C. Li, and L. Luo, “Enhanced spin Hall effect of tunneling light in hyperbolic metamaterial waveguide,” Sci. Rep. 6, 30762 (2016).
[Crossref] [PubMed]

Li, Y.

J. L. Ren, B. Wang, Y. F. Xiao, Q. Gong, and Y. Li, “Direct observation of a resolvable spin separation in the spin Hall effect of light at an air-glass interface,” Appl. Phys. Lett. 107(11), 54–59 (2015).
[Crossref]

Ling, X.

X. Zhou and X. Ling, “Unveiling the photonic spin Hall effect with asymmetric spin-dependent splitting,” Opt. Express 24(3), 3025–3036 (2016).
[Crossref] [PubMed]

X. Zhou, X. Ling, Z. Zhang, H. Luo, and S. Wen, “Observation of spin Hall effect in photon tunneling via weak measurements,” Sci. Rep. 4, 7388 (2014).
[Crossref] [PubMed]

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. A 84(3), 033801 (2011).
[Crossref]

Liu, J.

Löffler, W.

J. B. Götte, W. Löffler, and M. R. Dennis, “Eigenpolarizations for giant transverse optical beam shifts,” Phys. Rev. Lett. 112(23), 233901 (2014).
[Crossref] [PubMed]

Luo, H.

X. Zhou, X. Ling, Z. Zhang, H. Luo, and S. Wen, “Observation of spin Hall effect in photon tunneling via weak measurements,” Sci. Rep. 4, 7388 (2014).
[Crossref] [PubMed]

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. A 84(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. A 84(4), 043806 (2011).
[Crossref]

H. Luo, S. Wen, W. Shu, and D. Fan, “Spin Hall effect of light in photon tunneling,” Phys. Rev. A 82(4), 043825 (2010).
[Crossref]

Luo, L.

T. Tang, C. Li, and L. Luo, “Enhanced spin Hall effect of tunneling light in hyperbolic metamaterial waveguide,” Sci. Rep. 6, 30762 (2016).
[Crossref] [PubMed]

Merano, M.

Mistura, G.

Morgan, F.

Murphy, A.

Nandi, A.

Nevet, A.

Nori, F.

K. Y. Bliokh, F. J. Rodríguez-Fortuño, F. Nori, and A. V. Zayats, “Spin-orbit interactions of light,” Nat. Photonics 9(12), 796–808 (2015).
[Crossref]

Nugrowati, A. M.

Orenstein, M.

Ornigotti, M.

Pal, M.

Panigrahi, P. K.

Poddubny, A.

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Corrigendum: Hyperbolic metamaterials,” Nat. Photonics 8(1), 78 (2013).
[Crossref]

Pollard, R. J.

Qiu, J.

Qiu, X.

Ren, J. L.

J. L. Ren, B. Wang, Y. F. Xiao, Q. Gong, and Y. Li, “Direct observation of a resolvable spin separation in the spin Hall effect of light at an air-glass interface,” Appl. Phys. Lett. 107(11), 54–59 (2015).
[Crossref]

Rodríguez-Fortuño, F. J.

K. Y. Bliokh, F. J. Rodríguez-Fortuño, F. Nori, and A. V. Zayats, “Spin-orbit interactions of light,” Nat. Photonics 9(12), 796–808 (2015).
[Crossref]

Santana, O. J. S.

Shalaev, V.

Shaltout, A.

She, W.

Shu, W.

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. A 84(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. A 84(4), 043806 (2011).
[Crossref]

H. Luo, S. Wen, W. Shu, and D. Fan, “Spin Hall effect of light in photon tunneling,” Phys. Rev. A 82(4), 043825 (2010).
[Crossref]

Szameit, A.

Tan, X. J.

Tang, T.

T. Tang, C. Li, and L. Luo, “Enhanced spin Hall effect of tunneling light in hyperbolic metamaterial waveguide,” Sci. Rep. 6, 30762 (2016).
[Crossref] [PubMed]

Wang, B.

J. L. Ren, B. Wang, Y. F. Xiao, Q. Gong, and Y. Li, “Direct observation of a resolvable spin separation in the spin Hall effect of light at an air-glass interface,” Appl. Phys. Lett. 107(11), 54–59 (2015).
[Crossref]

Wen, S.

X. Zhou, X. Ling, Z. Zhang, H. Luo, and S. Wen, “Observation of spin Hall effect in photon tunneling via weak measurements,” Sci. Rep. 4, 7388 (2014).
[Crossref] [PubMed]

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, 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. A 84(3), 033801 (2011).
[Crossref]

H. Luo, S. Wen, W. Shu, and D. Fan, “Spin Hall effect of light in photon tunneling,” Phys. Rev. A 82(4), 043825 (2010).
[Crossref]

Woerdman, J. P.

Wurtz, G. A.

Xiao, Y. F.

J. L. Ren, B. Wang, Y. F. Xiao, Q. Gong, and Y. Li, “Direct observation of a resolvable spin separation in the spin Hall effect of light at an air-glass interface,” Appl. Phys. Lett. 107(11), 54–59 (2015).
[Crossref]

Xie, L.

Xu, Y.

Y. Xu, C. T. Chan, and H. Chen, “Goos-Hänchen effect in epsilon-near-zero metamaterials,” Sci. Rep. 5, 8681 (2015).
[Crossref] [PubMed]

Zayats, A. V.

Zhang, Z.

Zhou, X.

X. Zhou and X. Ling, “Unveiling the photonic spin Hall effect with asymmetric spin-dependent splitting,” Opt. Express 24(3), 3025–3036 (2016).
[Crossref] [PubMed]

X. Zhou, X. Ling, Z. Zhang, H. Luo, and S. Wen, “Observation of spin Hall effect in photon tunneling via weak measurements,” Sci. Rep. 4, 7388 (2014).
[Crossref] [PubMed]

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, 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. A 84(3), 033801 (2011).
[Crossref]

Zhu, W.

Zhu, X. S.

Appl. Phys. Lett. (1)

J. L. Ren, B. Wang, Y. F. Xiao, Q. Gong, and Y. Li, “Direct observation of a resolvable spin separation in the spin Hall effect of light at an air-glass interface,” Appl. Phys. Lett. 107(11), 54–59 (2015).
[Crossref]

J. Opt. (1)

K. Y. Bliokh and A. Aiello, “Goos-hächen and imbert-fedorov beam shifts: an overview,” J. Opt. 15(1), 014001 (2013).
[Crossref]

Nat. Photonics (2)

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Corrigendum: Hyperbolic metamaterials,” Nat. Photonics 8(1), 78 (2013).
[Crossref]

K. Y. Bliokh, F. J. Rodríguez-Fortuño, F. Nori, and A. V. Zayats, “Spin-orbit interactions of light,” Nat. Photonics 9(12), 796–808 (2015).
[Crossref]

Opt. Express (4)

Opt. Lett. (8)

X. Qiu, Z. Zhang, L. Xie, J. Qiu, F. Gao, and J. Du, “Incident-polarization-sensitive and large in-plane-photonic-spin-splitting at the Brewster angle,” Opt. Lett. 40(6), 1018–1021 (2015).
[Crossref] [PubMed]

X. J. Tan and X. S. Zhu, “Enhancing photonic spin Hall effect via long-range surface plasmon resonance,” Opt. Lett. 41(11), 2478–2481 (2016).
[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]

X. Qiu, Z. Zhang, L. Xie, J. Qiu, F. Gao, and J. Du, “Incident-polarization-sensitive and large in-plane-photonic-spin-splitting at the Brewster angle,” Opt. Lett. 40(6), 1018–1021 (2015).
[Crossref] [PubMed]

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Optica (1)

Phys. Rev. A (3)

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[Crossref]

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[Crossref]

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[Crossref]

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Figures (6)

Fig. 1
Fig. 1 The schematic of spin splitting of transmitted beam. A linearly polarized Gaussian beam is incident onto an anisotropic metamaterial with an incident angle of θi, two opposite spin components of the transmitted beam will be separated in z = 0 plane due to the spatial spin splitting ΔY ± . Owing to the angular spin splitting, the spin separation Δ ± will change with the propagation distance. The inset shows the structure of the metamaterial.
Fig. 2
Fig. 2 The changes of phase parameter φ (a), normalized spatial spin splitting ΔY/w0 (b), and normalized angular spin splitting Δθ/θd (c) as functions of incident angle θi and thickness of metamaterial d. In calculation, ε// = 1, ε = 0.01, w0 = 40λ.
Fig. 3
Fig. 3 The dependences of normalized spatial spin splitting ΔY/w0 (a), and normalized angular spin splitting Δθ/θd (b) on incident angle θi for w0 = 20λ (blue color), 40λ (orange color), 100λ (yellow color), 200λ (purple color), 500λ (light green color), respectively.
Fig. 4
Fig. 4 The dependences of normalized spatial spin splitting ΔY/w0 (a), and normalized angular spin splitting Δθ/θd (b) on incident angle θi for Im [ ε ] = 0 (blue color), 0.003 (orange color), 0.01 (yellow color), 0.03 (purple color), 0.1 (light green color), respectively. In calculation, Re [ ε ] = 0.01.
Fig. 5
Fig. 5 The same as Fig. 4 excepting for Re [ ε ] = 0 (blue color), 0.005 (orange color), 0.01 (yellow color), 0.05 (purple color), 0.1 (light green color), respectively. In calculation, Im [ ε ] = 0.
Fig. 6
Fig. 6 (a) The dependences of spin dependent displacements Δ+ (solid line) and Δ- (dashed line) on the propagation distance z for three different cases. In case 1 (red color), d = 0.42λ, θi = 11.4°. In case 2 (blue color), d = 0.78λ, θi = 7.5°. In case 3 (green color), d = 0.61λ, θi = 8.7°. The black lines correspond to the upper limit of spin splitting of propagated beam, and the distance between two black dashed lines is equal to the radius of spot size of Gaussian beam size w(z). (b) The intensity distributions of RCP and LCP components of transmitted beam in z = 0, z0, and 2.5z0 planes for three different cases.

Equations (9)

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E ˜ t = w 0 2 π exp [ ( k x 2 + k y 2 ) w 0 2 4 ] { [ t p θ i + k x k 0 t p θ i ] e ^ x + [ k y k 0 ( t p θ i t s θ i ) cot θ i ] e ^ y } ,
t p θ i = 1 cos δ p i sin δ p 2 ε ( 1 + cos 2 θ i ) sin 2 θ i cos θ i ε / / ε ( ε sin 2 θ i ) ,
t s θ i = 1 cos δ s i sin δ s 2 cos 2 θ i + ε / / cos θ i ε / / sin 2 θ i ,
E ± = 1 π w 0 z 0 z 0 + i z exp [ k 0 ( x 2 + y 2 ) 2 ( z 0 + i z ) ] [ t p θ i + i x z 0 + i z t p θ i ± y ( t p θ i t s θ i ) cot θ i z 0 + i z ] e ^ ± ,
Δ ± = y | E ± | 2 d x d y / | E ± | 2 d x d y .
Δ Y ± = ± w 0 | t p θ i | | M | cos φ | t p θ i | 2 + 1 k 0 2 w 0 2 | t p θ i | 2 + | M | 2 ,
Δ θ ± = ± 2 k 0 w 0 | t p θ i | | M | sin φ | t p θ i | 2 + 1 k 0 2 w 0 2 | t p θ i | 2 + | M | 2 ,
| Δ Y | m = w 0 1 + 1 2 | t p θ i | 2 k 0 2 w 0 2 | t p θ i | 2 .
| Δ θ | m = 2 k 0 w 0 1 1 + 1 2 | t p θ i | 2 k 0 2 w 0 2 | t p θ i | 2 .

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