Abstract

The photonic spin Hall effect (SHE) has been intensively studied and widely applied, especially in spin photonics. However, the SHE is weak and is difficult to detect directly. In this paper, we propose a method to enhance SHE with the guided-wave surface-plasmon resonance (SPR). By covering a dielectric with high refractive index on the surface of silver film, the photonic SHE can be greatly enhanced, and a giant transverse shift of horizontal polarization state is observed due to the evanescent field enhancement near the interface at the top dielectric layer and air. The maximum transverse shift of the horizontal polarization state with 11.5 μm is obtained when the thickness of Si film is optimum. There is at least an order of magnitude enhancement in contrast with the transverse shift in the conventional SPR configuration. Our research is important for providing an effective way to improve the photonic SHE and may offer the opportunity to characterize the parameters of the dielectric layer with the help of weak measurements and development of sensors based on the photonic SHE.

© 2017 Chinese Laser Press

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    [Crossref]
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    [Crossref]
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  5. K. Y. Bliokh, F. J. Rodríguez-Fortuño, F. Nori, and A. V. Zayats, “Spin-orbit interactions of light,” Nat. Photonics 9, 796–808 (2015).
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  6. X. Ling, X. Zhou, K. Huang, Y. Liu, C.-W. Qiu, H. Luo, and S. Wen, “Recent advances in the spin Hall effect of light,” Rep. Prog. Phys. 80, 066401 (2017).
    [Crossref]
  7. X. Ling, X. Zhou, H. Luo, and S. Wen, “Steering far-field spin-dependent splitting of light by inhomogeneous anisotropic media,” Phys. Rev. A 86, 053821 (2012).
    [Crossref]
  8. X. Zhou, X. Ling, H. Luo, and S. Wen, “Identifying graphene layers via spin Hall effect of light,” Appl. Phys. Lett. 101, 251602 (2012).
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  9. X. Checoury, D. Neel, P. Boucaud, C. Gesset, H. Girard, and S. Saada, “Nanocrystalline diamond photonics platform with high quality factor photonic crystal cavities,” Appl. Phys. Lett. 101, 171115 (2012).
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  10. H. Wang and X. Zhang, “Unusual spin Hall effect of a light beam in chiral metamaterials,” Phys. Rev. A 83, 053820 (2011).
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  11. J. Duan, H. Guo, S. Dong, T. Cai, W. Luo, Z. Liang, Q. He, L. Zhou, and S. Sun, “High-efficiency chirality-modulated spoof surface plasmon meta-coupler,” Sci. Rep. 7, 1354 (2017).
    [Crossref]
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    [Crossref]
  13. X. Zhou, J. Zhang, X. Ling, S. Chen, H. Luo, and S. Wen, “Photonic spin Hall effect in topological insulators,” Phys. Rev. A 88, 053840 (2013).
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  14. P. Wang, W. Li, Q. Liu, and X. Jiang, “Giant topological magnetoelectric and optical Hall effects for a topological insulator as a defect in photonic crystals,” Phys. Rev. A 90, 015801 (2014).
    [Crossref]
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  18. X. Zhou, Z. Xiao, H. Luo, and S. Wen, “Experimental observation of the spin Hall effect of light on a nano-metal film via weak measurements,” Phys. Rev. A 85, 043809 (2012).
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    [Crossref]
  21. 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, 033801 (2011).
    [Crossref]
  22. 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]
  23. W. Luo, S. Xiao, Q. He, S. Sun, and L. Zhou, “Photonic spin Hall effect with nearly 100% efficiency,” Adv. Opt. Mater. 3, 1102–1108 (2015).
    [Crossref]
  24. X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin Hall effect at metasurfaces,” Science 339, 1405–1407 (2013).
    [Crossref]
  25. W. Luo, S. Sun, H.-X. Xu, Q. He, and L. Zhou, “Transmissive ultrathin Pancharatnam-Berry metasurfaces with nearly 100% efficiency,” Phys. Rev. Appl. 7, 044033 (2017).
    [Crossref]
  26. 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, 043806 (2011).
    [Crossref]
  27. 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’s angle,” Appl. Phys. Lett. 100, 071109 (2012).
    [Crossref]
  28. W. Zhu and W. She, “Enhanced spin Hall effect of transmitted light through a thin epsilon-near-zero slab,” Opt. Lett. 40, 2961–2964 (2015).
    [Crossref]
  29. X. Zhou and X. Ling, “Enhanced photonic spin Hall effect due to surface plasmon resonance,” IEEE Photon. J. 8, 1–8 (2016).
    [Crossref]
  30. X.-J. Tan and X.-S. Zhu, “Enhancing photonic spin Hall effect via long-range surface plasmon resonance,” Opt. Lett. 41, 2478–2481 (2016).
    [Crossref]
  31. A. Lahav, M. Auslender, and I. Abdulhalim, “Sensitivity enhancement of guided-wave surface-plasmon resonance sensors,” Opt. Lett. 33, 2539–2541 (2008).
    [Crossref]
  32. A. Abbas, M. J. Linman, and Q. Cheng, “Sensitivity comparison of surface plasmon resonance and plasmon-waveguide resonance biosensors,” Sens. Actuators B Chem. 156, 169–175 (2011).
    [Crossref]

2017 (3)

X. Ling, X. Zhou, K. Huang, Y. Liu, C.-W. Qiu, H. Luo, and S. Wen, “Recent advances in the spin Hall effect of light,” Rep. Prog. Phys. 80, 066401 (2017).
[Crossref]

J. Duan, H. Guo, S. Dong, T. Cai, W. Luo, Z. Liang, Q. He, L. Zhou, and S. Sun, “High-efficiency chirality-modulated spoof surface plasmon meta-coupler,” Sci. Rep. 7, 1354 (2017).
[Crossref]

W. Luo, S. Sun, H.-X. Xu, Q. He, and L. Zhou, “Transmissive ultrathin Pancharatnam-Berry metasurfaces with nearly 100% efficiency,” Phys. Rev. Appl. 7, 044033 (2017).
[Crossref]

2016 (2)

X. Zhou and X. Ling, “Enhanced photonic spin Hall effect due to surface plasmon resonance,” IEEE Photon. J. 8, 1–8 (2016).
[Crossref]

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

2015 (3)

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

W. Luo, S. Xiao, Q. He, S. Sun, and L. Zhou, “Photonic spin Hall effect with nearly 100% efficiency,” Adv. Opt. Mater. 3, 1102–1108 (2015).
[Crossref]

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

2014 (2)

P. Wang, W. Li, Q. Liu, and X. Jiang, “Giant topological magnetoelectric and optical Hall effects for a topological insulator as a defect in photonic crystals,” Phys. Rev. A 90, 015801 (2014).
[Crossref]

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]

2013 (2)

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

X. Zhou, J. Zhang, X. Ling, S. Chen, H. Luo, and S. Wen, “Photonic spin Hall effect in topological insulators,” Phys. Rev. A 88, 053840 (2013).
[Crossref]

2012 (6)

X. Ling, X. Zhou, and S. Wen, “Steering far-field spin-dependent splitting of light by inhomogeneous anisotropic media,” Phys. Rev. A 86, 053824 (2012).
[Crossref]

X. Ling, X. Zhou, H. Luo, and S. Wen, “Steering far-field spin-dependent splitting of light by inhomogeneous anisotropic media,” Phys. Rev. A 86, 053821 (2012).
[Crossref]

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

X. Checoury, D. Neel, P. Boucaud, C. Gesset, H. Girard, and S. Saada, “Nanocrystalline diamond photonics platform with high quality factor photonic crystal cavities,” Appl. Phys. Lett. 101, 171115 (2012).
[Crossref]

X. Zhou, Z. Xiao, H. Luo, and S. Wen, “Experimental observation of the spin Hall effect of light on a nano-metal film via weak measurements,” Phys. Rev. A 85, 043809 (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’s angle,” Appl. Phys. Lett. 100, 071109 (2012).
[Crossref]

2011 (5)

A. Abbas, M. J. Linman, and Q. Cheng, “Sensitivity comparison of surface plasmon resonance and plasmon-waveguide resonance biosensors,” Sens. Actuators B Chem. 156, 169–175 (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, 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, 043806 (2011).
[Crossref]

H. Wang and X. Zhang, “Unusual spin Hall effect of a light beam in chiral metamaterials,” Phys. Rev. A 83, 053820 (2011).
[Crossref]

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

2010 (1)

2009 (2)

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, 043810 (2009).
[Crossref]

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

2008 (2)

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

A. Lahav, M. Auslender, and I. Abdulhalim, “Sensitivity enhancement of guided-wave surface-plasmon resonance sensors,” Opt. Lett. 33, 2539–2541 (2008).
[Crossref]

2005 (1)

J. Wunderlich, B. Kaestner, J. Sinova, and T. Jungwirth, “Experimental discovery of the spin-Hall effect in Rashba spin-orbit coupled semiconductor systems,” Phys. Rev. Lett. 94, 047204 (2005).
[Crossref]

2004 (2)

J. Sinova, D. Culcer, Q. Niu, N. A. Sinitsyn, T. Jungwirth, and A. H. Macdonald, “Universal intrinsic spin Hall effect,” Phys. Rev. Lett. 92, 126603 (2004).
[Crossref]

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

2003 (1)

S. Murakami, N. Nagaosa, and S. Zhang, “Dissipationless quantum spin current at room temperature,” Science 301, 1348–1351 (2003).
[Crossref]

Abbas, A.

A. Abbas, M. J. Linman, and Q. Cheng, “Sensitivity comparison of surface plasmon resonance and plasmon-waveguide resonance biosensors,” Sens. Actuators B Chem. 156, 169–175 (2011).
[Crossref]

Abdulhalim, I.

Aiello, A.

Auslender, M.

Bliokh, K. Y.

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

Boucaud, P.

X. Checoury, D. Neel, P. Boucaud, C. Gesset, H. Girard, and S. Saada, “Nanocrystalline diamond photonics platform with high quality factor photonic crystal cavities,” Appl. Phys. Lett. 101, 171115 (2012).
[Crossref]

Cai, T.

J. Duan, H. Guo, S. Dong, T. Cai, W. Luo, Z. Liang, Q. He, L. Zhou, and S. Sun, “High-efficiency chirality-modulated spoof surface plasmon meta-coupler,” Sci. Rep. 7, 1354 (2017).
[Crossref]

Checoury, X.

X. Checoury, D. Neel, P. Boucaud, C. Gesset, H. Girard, and S. Saada, “Nanocrystalline diamond photonics platform with high quality factor photonic crystal cavities,” Appl. Phys. Lett. 101, 171115 (2012).
[Crossref]

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’s angle,” Appl. Phys. Lett. 100, 071109 (2012).
[Crossref]

Chen, S.

X. Zhou, J. Zhang, X. Ling, S. Chen, H. Luo, and S. Wen, “Photonic spin Hall effect in topological insulators,” Phys. Rev. A 88, 053840 (2013).
[Crossref]

Cheng, Q.

A. Abbas, M. J. Linman, and Q. Cheng, “Sensitivity comparison of surface plasmon resonance and plasmon-waveguide resonance biosensors,” Sens. Actuators B Chem. 156, 169–175 (2011).
[Crossref]

Culcer, D.

J. Sinova, D. Culcer, Q. Niu, N. A. Sinitsyn, T. Jungwirth, and A. H. Macdonald, “Universal intrinsic spin Hall effect,” Phys. Rev. Lett. 92, 126603 (2004).
[Crossref]

Dong, S.

J. Duan, H. Guo, S. Dong, T. Cai, W. Luo, Z. Liang, Q. He, L. Zhou, and S. Sun, “High-efficiency chirality-modulated spoof surface plasmon meta-coupler,” Sci. Rep. 7, 1354 (2017).
[Crossref]

Duan, J.

J. Duan, H. Guo, S. Dong, T. Cai, W. Luo, Z. Liang, Q. He, L. Zhou, and S. Sun, “High-efficiency chirality-modulated spoof surface plasmon meta-coupler,” Sci. Rep. 7, 1354 (2017).
[Crossref]

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, 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, 033801 (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, 043810 (2009).
[Crossref]

Feng, X.

Gesset, C.

X. Checoury, D. Neel, P. Boucaud, C. Gesset, H. Girard, and S. Saada, “Nanocrystalline diamond photonics platform with high quality factor photonic crystal cavities,” Appl. Phys. Lett. 101, 171115 (2012).
[Crossref]

Girard, H.

X. Checoury, D. Neel, P. Boucaud, C. Gesset, H. Girard, and S. Saada, “Nanocrystalline diamond photonics platform with high quality factor photonic crystal cavities,” Appl. Phys. Lett. 101, 171115 (2012).
[Crossref]

Gong, Q.

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’s angle,” Appl. Phys. Lett. 100, 071109 (2012).
[Crossref]

Guo, H.

J. Duan, H. Guo, S. Dong, T. Cai, W. Luo, Z. Liang, Q. He, L. Zhou, and S. Sun, “High-efficiency chirality-modulated spoof surface plasmon meta-coupler,” Sci. Rep. 7, 1354 (2017).
[Crossref]

He, H.

He, Q.

W. Luo, S. Sun, H.-X. Xu, Q. He, and L. Zhou, “Transmissive ultrathin Pancharatnam-Berry metasurfaces with nearly 100% efficiency,” Phys. Rev. Appl. 7, 044033 (2017).
[Crossref]

J. Duan, H. Guo, S. Dong, T. Cai, W. Luo, Z. Liang, Q. He, L. Zhou, and S. Sun, “High-efficiency chirality-modulated spoof surface plasmon meta-coupler,” Sci. Rep. 7, 1354 (2017).
[Crossref]

W. Luo, S. Xiao, Q. He, S. Sun, and L. Zhou, “Photonic spin Hall effect with nearly 100% efficiency,” Adv. Opt. Mater. 3, 1102–1108 (2015).
[Crossref]

Hermosa, N.

Hosten, O.

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

Huang, K.

X. Ling, X. Zhou, K. Huang, Y. Liu, C.-W. Qiu, H. Luo, and S. Wen, “Recent advances in the spin Hall effect of light,” Rep. Prog. Phys. 80, 066401 (2017).
[Crossref]

Jiang, X.

P. Wang, W. Li, Q. Liu, and X. Jiang, “Giant topological magnetoelectric and optical Hall effects for a topological insulator as a defect in photonic crystals,” Phys. Rev. A 90, 015801 (2014).
[Crossref]

Jungwirth, T.

J. Wunderlich, B. Kaestner, J. Sinova, and T. Jungwirth, “Experimental discovery of the spin-Hall effect in Rashba spin-orbit coupled semiconductor systems,” Phys. Rev. Lett. 94, 047204 (2005).
[Crossref]

J. Sinova, D. Culcer, Q. Niu, N. A. Sinitsyn, T. Jungwirth, and A. H. Macdonald, “Universal intrinsic spin Hall effect,” Phys. Rev. Lett. 92, 126603 (2004).
[Crossref]

Kaestner, B.

J. Wunderlich, B. Kaestner, J. Sinova, and T. Jungwirth, “Experimental discovery of the spin-Hall effect in Rashba spin-orbit coupled semiconductor systems,” Phys. Rev. Lett. 94, 047204 (2005).
[Crossref]

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’s angle,” Appl. Phys. Lett. 100, 071109 (2012).
[Crossref]

Kwiat, P.

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

Lahav, A.

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’s angle,” Appl. Phys. Lett. 100, 071109 (2012).
[Crossref]

Li, W.

P. Wang, W. Li, Q. Liu, and X. Jiang, “Giant topological magnetoelectric and optical Hall effects for a topological insulator as a defect in photonic crystals,” Phys. Rev. A 90, 015801 (2014).
[Crossref]

Li, Y.

Liang, Z.

J. Duan, H. Guo, S. Dong, T. Cai, W. Luo, Z. Liang, Q. He, L. Zhou, and S. Sun, “High-efficiency chirality-modulated spoof surface plasmon meta-coupler,” Sci. Rep. 7, 1354 (2017).
[Crossref]

Ling, X.

X. Ling, X. Zhou, K. Huang, Y. Liu, C.-W. Qiu, H. Luo, and S. Wen, “Recent advances in the spin Hall effect of light,” Rep. Prog. Phys. 80, 066401 (2017).
[Crossref]

X. Zhou and X. Ling, “Enhanced photonic spin Hall effect due to surface plasmon resonance,” IEEE Photon. J. 8, 1–8 (2016).
[Crossref]

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]

X. Zhou, J. Zhang, X. Ling, S. Chen, H. Luo, and S. Wen, “Photonic spin Hall effect in topological insulators,” Phys. Rev. A 88, 053840 (2013).
[Crossref]

X. Ling, X. Zhou, and S. Wen, “Steering far-field spin-dependent splitting of light by inhomogeneous anisotropic media,” Phys. Rev. A 86, 053824 (2012).
[Crossref]

X. Ling, X. Zhou, H. Luo, and S. Wen, “Steering far-field spin-dependent splitting of light by inhomogeneous anisotropic media,” Phys. Rev. A 86, 053821 (2012).
[Crossref]

X. Zhou, X. Ling, H. Luo, and S. Wen, “Identifying graphene layers via spin Hall effect of light,” Appl. Phys. Lett. 101, 251602 (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. A 84, 033801 (2011).
[Crossref]

Linman, M. J.

A. Abbas, M. J. Linman, and Q. Cheng, “Sensitivity comparison of surface plasmon resonance and plasmon-waveguide resonance biosensors,” Sens. Actuators B Chem. 156, 169–175 (2011).
[Crossref]

Liu, Q.

P. Wang, W. Li, Q. Liu, and X. Jiang, “Giant topological magnetoelectric and optical Hall effects for a topological insulator as a defect in photonic crystals,” Phys. Rev. A 90, 015801 (2014).
[Crossref]

Liu, Y.

X. Ling, X. Zhou, K. Huang, Y. Liu, C.-W. Qiu, H. Luo, and S. Wen, “Recent advances in the spin Hall effect of light,” Rep. Prog. Phys. 80, 066401 (2017).
[Crossref]

Liu, Z.

Luo, H.

X. Ling, X. Zhou, K. Huang, Y. Liu, C.-W. Qiu, H. Luo, and S. Wen, “Recent advances in the spin Hall effect of light,” Rep. Prog. Phys. 80, 066401 (2017).
[Crossref]

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]

X. Zhou, J. Zhang, X. Ling, S. Chen, H. Luo, and S. Wen, “Photonic spin Hall effect in topological insulators,” Phys. Rev. A 88, 053840 (2013).
[Crossref]

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

X. Ling, X. Zhou, H. Luo, and S. Wen, “Steering far-field spin-dependent splitting of light by inhomogeneous anisotropic media,” Phys. Rev. A 86, 053821 (2012).
[Crossref]

X. Zhou, Z. Xiao, H. Luo, and S. Wen, “Experimental observation of the spin Hall effect of light on a nano-metal film via weak measurements,” Phys. Rev. A 85, 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, 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, 033801 (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, 043810 (2009).
[Crossref]

Luo, W.

J. Duan, H. Guo, S. Dong, T. Cai, W. Luo, Z. Liang, Q. He, L. Zhou, and S. Sun, “High-efficiency chirality-modulated spoof surface plasmon meta-coupler,” Sci. Rep. 7, 1354 (2017).
[Crossref]

W. Luo, S. Sun, H.-X. Xu, Q. He, and L. Zhou, “Transmissive ultrathin Pancharatnam-Berry metasurfaces with nearly 100% efficiency,” Phys. Rev. Appl. 7, 044033 (2017).
[Crossref]

W. Luo, S. Xiao, Q. He, S. Sun, and L. Zhou, “Photonic spin Hall effect with nearly 100% efficiency,” Adv. Opt. Mater. 3, 1102–1108 (2015).
[Crossref]

Macdonald, A. H.

J. Sinova, D. Culcer, Q. Niu, N. A. Sinitsyn, T. Jungwirth, and A. H. Macdonald, “Universal intrinsic spin Hall effect,” Phys. Rev. Lett. 92, 126603 (2004).
[Crossref]

Murakami, S.

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

S. Murakami, N. Nagaosa, and S. Zhang, “Dissipationless quantum spin current at room temperature,” Science 301, 1348–1351 (2003).
[Crossref]

Nagaosa, N.

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

S. Murakami, N. Nagaosa, and S. Zhang, “Dissipationless quantum spin current at room temperature,” Science 301, 1348–1351 (2003).
[Crossref]

Neel, D.

X. Checoury, D. Neel, P. Boucaud, C. Gesset, H. Girard, and S. Saada, “Nanocrystalline diamond photonics platform with high quality factor photonic crystal cavities,” Appl. Phys. Lett. 101, 171115 (2012).
[Crossref]

Niu, Q.

J. Sinova, D. Culcer, Q. Niu, N. A. Sinitsyn, T. Jungwirth, and A. H. Macdonald, “Universal intrinsic spin Hall effect,” Phys. Rev. Lett. 92, 126603 (2004).
[Crossref]

Nori, F.

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

Nugrowati, A. M.

Onoda, M.

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

Qin, Y.

Qiu, C.-W.

X. Ling, X. Zhou, K. Huang, Y. Liu, C.-W. Qiu, H. Luo, and S. Wen, “Recent advances in the spin Hall effect of light,” Rep. Prog. Phys. 80, 066401 (2017).
[Crossref]

Rho, J.

X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin Hall effect at metasurfaces,” Science 339, 1405–1407 (2013).
[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, 796–808 (2015).
[Crossref]

Saada, S.

X. Checoury, D. Neel, P. Boucaud, C. Gesset, H. Girard, and S. Saada, “Nanocrystalline diamond photonics platform with high quality factor photonic crystal cavities,” Appl. Phys. Lett. 101, 171115 (2012).
[Crossref]

She, W.

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, 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, 033801 (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, 043810 (2009).
[Crossref]

Sinitsyn, N. A.

J. Sinova, D. Culcer, Q. Niu, N. A. Sinitsyn, T. Jungwirth, and A. H. Macdonald, “Universal intrinsic spin Hall effect,” Phys. Rev. Lett. 92, 126603 (2004).
[Crossref]

Sinova, J.

J. Wunderlich, B. Kaestner, J. Sinova, and T. Jungwirth, “Experimental discovery of the spin-Hall effect in Rashba spin-orbit coupled semiconductor systems,” Phys. Rev. Lett. 94, 047204 (2005).
[Crossref]

J. Sinova, D. Culcer, Q. Niu, N. A. Sinitsyn, T. Jungwirth, and A. H. Macdonald, “Universal intrinsic spin Hall effect,” Phys. Rev. Lett. 92, 126603 (2004).
[Crossref]

Sun, S.

J. Duan, H. Guo, S. Dong, T. Cai, W. Luo, Z. Liang, Q. He, L. Zhou, and S. Sun, “High-efficiency chirality-modulated spoof surface plasmon meta-coupler,” Sci. Rep. 7, 1354 (2017).
[Crossref]

W. Luo, S. Sun, H.-X. Xu, Q. He, and L. Zhou, “Transmissive ultrathin Pancharatnam-Berry metasurfaces with nearly 100% efficiency,” Phys. Rev. Appl. 7, 044033 (2017).
[Crossref]

W. Luo, S. Xiao, Q. He, S. Sun, and L. Zhou, “Photonic spin Hall effect with nearly 100% efficiency,” Adv. Opt. Mater. 3, 1102–1108 (2015).
[Crossref]

Tan, X.-J.

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, 043810 (2009).
[Crossref]

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’s angle,” Appl. Phys. Lett. 100, 071109 (2012).
[Crossref]

H. Wang and X. Zhang, “Unusual spin Hall effect of a light beam in chiral metamaterials,” Phys. Rev. A 83, 053820 (2011).
[Crossref]

Wang, P.

P. Wang, W. Li, Q. Liu, and X. Jiang, “Giant topological magnetoelectric and optical Hall effects for a topological insulator as a defect in photonic crystals,” Phys. Rev. A 90, 015801 (2014).
[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’s angle,” Appl. Phys. Lett. 100, 071109 (2012).
[Crossref]

Wang, Y.

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

Wen, S.

X. Ling, X. Zhou, K. Huang, Y. Liu, C.-W. Qiu, H. Luo, and S. Wen, “Recent advances in the spin Hall effect of light,” Rep. Prog. Phys. 80, 066401 (2017).
[Crossref]

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]

X. Zhou, J. Zhang, X. Ling, S. Chen, H. Luo, and S. Wen, “Photonic spin Hall effect in topological insulators,” Phys. Rev. A 88, 053840 (2013).
[Crossref]

X. Ling, X. Zhou, and S. Wen, “Steering far-field spin-dependent splitting of light by inhomogeneous anisotropic media,” Phys. Rev. A 86, 053824 (2012).
[Crossref]

X. Ling, X. Zhou, H. Luo, and S. Wen, “Steering far-field spin-dependent splitting of light by inhomogeneous anisotropic media,” Phys. Rev. A 86, 053821 (2012).
[Crossref]

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

X. Zhou, Z. Xiao, H. Luo, and S. Wen, “Experimental observation of the spin Hall effect of light on a nano-metal film via weak measurements,” Phys. Rev. A 85, 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. A 84, 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, 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, 043810 (2009).
[Crossref]

Woerdman, J. P.

Wunderlich, J.

J. Wunderlich, B. Kaestner, J. Sinova, and T. Jungwirth, “Experimental discovery of the spin-Hall effect in Rashba spin-orbit coupled semiconductor systems,” Phys. Rev. Lett. 94, 047204 (2005).
[Crossref]

Xiao, S.

W. Luo, S. Xiao, Q. He, S. Sun, and L. Zhou, “Photonic spin Hall effect with nearly 100% efficiency,” Adv. Opt. Mater. 3, 1102–1108 (2015).
[Crossref]

Xiao, Y.

Xiao, Z.

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

Xu, H.-X.

W. Luo, S. Sun, H.-X. Xu, Q. He, and L. Zhou, “Transmissive ultrathin Pancharatnam-Berry metasurfaces with nearly 100% efficiency,” Phys. Rev. Appl. 7, 044033 (2017).
[Crossref]

Ye, Z.

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

Yin, X.

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

Zayats, A. V.

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

Zhang, J.

X. Zhou, J. Zhang, X. Ling, S. Chen, H. Luo, and S. Wen, “Photonic spin Hall effect in topological insulators,” Phys. Rev. A 88, 053840 (2013).
[Crossref]

Zhang, S.

S. Murakami, N. Nagaosa, and S. Zhang, “Dissipationless quantum spin current at room temperature,” Science 301, 1348–1351 (2003).
[Crossref]

Zhang, X.

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

H. Wang and X. Zhang, “Unusual spin Hall effect of a light beam in chiral metamaterials,” Phys. Rev. A 83, 053820 (2011).
[Crossref]

Zhang, Z.

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]

Zhou, L.

W. Luo, S. Sun, H.-X. Xu, Q. He, and L. Zhou, “Transmissive ultrathin Pancharatnam-Berry metasurfaces with nearly 100% efficiency,” Phys. Rev. Appl. 7, 044033 (2017).
[Crossref]

J. Duan, H. Guo, S. Dong, T. Cai, W. Luo, Z. Liang, Q. He, L. Zhou, and S. Sun, “High-efficiency chirality-modulated spoof surface plasmon meta-coupler,” Sci. Rep. 7, 1354 (2017).
[Crossref]

W. Luo, S. Xiao, Q. He, S. Sun, and L. Zhou, “Photonic spin Hall effect with nearly 100% efficiency,” Adv. Opt. Mater. 3, 1102–1108 (2015).
[Crossref]

Zhou, X.

X. Ling, X. Zhou, K. Huang, Y. Liu, C.-W. Qiu, H. Luo, and S. Wen, “Recent advances in the spin Hall effect of light,” Rep. Prog. Phys. 80, 066401 (2017).
[Crossref]

X. Zhou and X. Ling, “Enhanced photonic spin Hall effect due to surface plasmon resonance,” IEEE Photon. J. 8, 1–8 (2016).
[Crossref]

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]

X. Zhou, J. Zhang, X. Ling, S. Chen, H. Luo, and S. Wen, “Photonic spin Hall effect in topological insulators,” Phys. Rev. A 88, 053840 (2013).
[Crossref]

X. Ling, X. Zhou, and S. Wen, “Steering far-field spin-dependent splitting of light by inhomogeneous anisotropic media,” Phys. Rev. A 86, 053824 (2012).
[Crossref]

X. Ling, X. Zhou, H. Luo, and S. Wen, “Steering far-field spin-dependent splitting of light by inhomogeneous anisotropic media,” Phys. Rev. A 86, 053821 (2012).
[Crossref]

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

X. Zhou, Z. Xiao, H. Luo, and S. Wen, “Experimental observation of the spin Hall effect of light on a nano-metal film via weak measurements,” Phys. Rev. A 85, 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, 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, 033801 (2011).
[Crossref]

Zhu, W.

Zhu, X.-S.

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, 043810 (2009).
[Crossref]

Adv. Opt. Mater. (1)

W. Luo, S. Xiao, Q. He, S. Sun, and L. Zhou, “Photonic spin Hall effect with nearly 100% efficiency,” Adv. Opt. Mater. 3, 1102–1108 (2015).
[Crossref]

Appl. Phys. Lett. (3)

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’s angle,” Appl. Phys. Lett. 100, 071109 (2012).
[Crossref]

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

X. Checoury, D. Neel, P. Boucaud, C. Gesset, H. Girard, and S. Saada, “Nanocrystalline diamond photonics platform with high quality factor photonic crystal cavities,” Appl. Phys. Lett. 101, 171115 (2012).
[Crossref]

IEEE Photon. J. (1)

X. Zhou and X. Ling, “Enhanced photonic spin Hall effect due to surface plasmon resonance,” IEEE Photon. J. 8, 1–8 (2016).
[Crossref]

Nat. Photonics (1)

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

Opt. Express (1)

Opt. Lett. (5)

Phys. Rev. A (9)

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, 043806 (2011).
[Crossref]

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

X. Ling, X. Zhou, H. Luo, and S. Wen, “Steering far-field spin-dependent splitting of light by inhomogeneous anisotropic media,” Phys. Rev. A 86, 053821 (2012).
[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, 043810 (2009).
[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, 033801 (2011).
[Crossref]

X. Ling, X. Zhou, and S. Wen, “Steering far-field spin-dependent splitting of light by inhomogeneous anisotropic media,” Phys. Rev. A 86, 053824 (2012).
[Crossref]

X. Zhou, J. Zhang, X. Ling, S. Chen, H. Luo, and S. Wen, “Photonic spin Hall effect in topological insulators,” Phys. Rev. A 88, 053840 (2013).
[Crossref]

P. Wang, W. Li, Q. Liu, and X. Jiang, “Giant topological magnetoelectric and optical Hall effects for a topological insulator as a defect in photonic crystals,” Phys. Rev. A 90, 015801 (2014).
[Crossref]

H. Wang and X. Zhang, “Unusual spin Hall effect of a light beam in chiral metamaterials,” Phys. Rev. A 83, 053820 (2011).
[Crossref]

Phys. Rev. Appl. (1)

W. Luo, S. Sun, H.-X. Xu, Q. He, and L. Zhou, “Transmissive ultrathin Pancharatnam-Berry metasurfaces with nearly 100% efficiency,” Phys. Rev. Appl. 7, 044033 (2017).
[Crossref]

Phys. Rev. Lett. (3)

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

J. Sinova, D. Culcer, Q. Niu, N. A. Sinitsyn, T. Jungwirth, and A. H. Macdonald, “Universal intrinsic spin Hall effect,” Phys. Rev. Lett. 92, 126603 (2004).
[Crossref]

J. Wunderlich, B. Kaestner, J. Sinova, and T. Jungwirth, “Experimental discovery of the spin-Hall effect in Rashba spin-orbit coupled semiconductor systems,” Phys. Rev. Lett. 94, 047204 (2005).
[Crossref]

Rep. Prog. Phys. (1)

X. Ling, X. Zhou, K. Huang, Y. Liu, C.-W. Qiu, H. Luo, and S. Wen, “Recent advances in the spin Hall effect of light,” Rep. Prog. Phys. 80, 066401 (2017).
[Crossref]

Sci. Rep. (2)

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]

J. Duan, H. Guo, S. Dong, T. Cai, W. Luo, Z. Liang, Q. He, L. Zhou, and S. Sun, “High-efficiency chirality-modulated spoof surface plasmon meta-coupler,” Sci. Rep. 7, 1354 (2017).
[Crossref]

Science (3)

S. Murakami, N. Nagaosa, and S. Zhang, “Dissipationless quantum spin current at room temperature,” Science 301, 1348–1351 (2003).
[Crossref]

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

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

Sens. Actuators B Chem. (1)

A. Abbas, M. J. Linman, and Q. Cheng, “Sensitivity comparison of surface plasmon resonance and plasmon-waveguide resonance biosensors,” Sens. Actuators B Chem. 156, 169–175 (2011).
[Crossref]

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Figures (6)

Fig. 1.
Fig. 1.

Schematic of the photonic SHE of a beam upon reflection of a GWSPR configuration. δ+ and δ indicate the transverse displacements for left- and right-circular polarization components, respectively.

Fig. 2.
Fig. 2.

Dependences of transverse beam shifts on the metal film thickness and the incident angle with d3=0: (a) H-polarization state; (b) V-polarization state.

Fig. 3.
Fig. 3.

Dependences of the Fresnel reflectance Rs and Rp on the incident angle with the different thickness of silicon, where the silicon film thickness (dsi=d3) is fixed to the three values: 0, 8, and 12 nm, when d2=46  nm.

Fig. 4.
Fig. 4.

(a) Relation of minimum value of rp and incident angle at the minimum value of rp with the thickness of the Si film. (b) Value of |rs/rp| changing with the incident angles under the Si film thickness are fixed to four values: 8, 10, 12, and 14 nm, where d2=46  nm.

Fig. 5.
Fig. 5.

Photonic SHE in GWSPR model for H- and V-polarization state; we show the spin-dependent splitting varying with the incident angles under d2=46  nm. Here, we choose three different thicknesses: (a) 0 nm; (b) 8 nm; (c) and the optimal thickness 12 nm.

Fig. 6.
Fig. 6.

Dependence of the displacements (a) H-polarization state and (b) V-polarization state on the incident angle and the thickness of Si.

Equations (15)

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

E˜i=w02πexp[w02(kix2+kiy2)/4],
[E˜rHE˜rV]=[rpkry(rp+rs)cotθi/k0kry(rp+rs)cotθi/k0rs][E˜iHE˜iV],
rp,s=r12+r234exp(ik2zd2)1+r12r234exp(ik2zd2),
r234=r23+r34exp(ik3zd3)1+r23r34exp(ik3zd3),
rlm=klzkmzklz+kmz,
rlm=klz/ϵlkmz/ϵmklz/ϵl+kmz/ϵm,
rp,s(kix)=rp,s(kix=0)+kix[rp,s(kix)kix]kix=0+n=2NkixNn![jrp,s(kix)kixj]kix=0,
rp,s(kix)=rp,s(kix=0)+kix[rp,s(kix)kix]kix=0,
EHr±=(erx±iery)πw0zRzR+izrexp(ikrzr)exp[k02xr2+yr2zR+izr][rpixzR+izrrpθi±yzR+izr(rp+rs)±ixy(zR+izr)2(rpθi+rsθi)],
EVr±=i(erx±iery)πw0zRzR+izrexp(ikrzr)exp[k02xr2+yr2zR+izr][rsixzR+izrrsθi±yzR+izr(rp+rs)±ixy(zR+izr)2(rpθi+rsθi)],
δH,V±=yr|Er±H,V|2dxrdyr|Er±H,V|2dxrdyr.
δH±=k0w02(1+Re[rs]/Re[rp])cotθk02w02+|lnrpθi|+|(1+rsrp)cotθ|2
δV±=k0w02(1+Re[rp]/Re[rs])cotθk02w02+|lnrsθi|+|(1+rprs)cotθ|2.
δH±=(1+Re[rs]/Re[rp])cotθ/k0,
δV±=(1+Re[rp]/Re[rs])cotθ/k0,