Abstract

The photonic spin Hall effect (SHE) manifests itself as the spin-dependent splitting of light beam. Usually, it shows a symmetric spin-dependent splitting, i.e., the left- and right-handed circularly polarized components are equally separated in position and intensity for linear polarization incidence. In this paper, we theoretically propose an asymmetric spin-dependent splitting at an air-glass interface under the illumination of elliptical polarization beam and experimentally demonstrate it with the weak measurement method. The left- and right-handed circularly polarized components show expectedly unequal intensity distributions and unexpectedly different spin-dependent shifts. Remarkably, the asymmetric spin-dependent splitting can be modulated by adjusting the handedness of incident polarization. The inherent physics behind this interesting phenomenon is attributed to the additional spatial Imbert-Fedorov shift. These findings offer us potential methods for developing new spin-based nanophotonic applications.

© 2016 Optical Society of America

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References

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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  4. 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]
  5. O. Hosten and P. Kwiat, “Observation of the spin Hall effect of light via weak measurements,” Science 319(5864), 787–790 (2008).
    [Crossref] [PubMed]
  6. 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]
  7. 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(4), 043810 (2009).
    [Crossref]
  8. 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]
  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. 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]
  11. P. Gosselin, A. Bérard, and H. Mohrbach, “Spin Hall effect of photons in a static gravitational field,” Phys. Rev. D 75(8), 084035 (2007).
    [Crossref]
  12. C. A. Dartora, G. G. Cabrera, K. Z. Nobrega, V. F. Montagner, M. H. K. Matielli, F. K. R. de Campos, and H. T. S. Filho, “Lagrangian-Hamiltonian formulation of paraxial optics and applications: Study of gauge symmetries and the optical spin Hall effect,” Phys. Rev. A 83(1), 012110 (2011)
    [Crossref]
  13. 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,” Phys. Rev. Lett. 109(1), 013901 (2012).
    [Crossref] [PubMed]
  14. N. Shitrit, I. Yulevich, E. Maguid, D. Ozeri, D. Veksler, V. Kleiner, and E. Hasman, “Spin-Optical metamaterial route to Spin-Controlled photonics,” Science 340(6133), 724–726 (2013).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
  18. 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. A 85(4), 043809 (2012).
    [Crossref]
  19. X. Zhou, X. Ling, H. Luo, and S. Wen, “Identifying graphene layers via spin Hall effect of light,” Appl. Phys. Lett. 101(25), 251602 (2012).
    [Crossref]
  20. X. Zhou, J. Zhang, X. Ling, S. Chen, H. Luo, and S. Wen, “Photonic spin Hall effect in topological insulators,” Phys. Rev. A 88(5), 053840 (2013).
    [Crossref]
  21. X. Qiu, X. Zhou, D. Hu, J. Du, F. Gao, Z. Zhang, and H. Luo, “Determination of magneto-optical constant of Fe films with weak measurements,” Appl. Phys. Lett. 105(13), 131111 (2014).
    [Crossref]
  22. X. Ling, X. Zhou, X. Yi, W. Shu, Y. Liu, S. Chen, H. Luo, S. Wen, and D. Fan, “Giant photonic spin Hall effect in momentum space in a structured metamaterial with spatially varying birefringence,” Light Sci. Appl. 4, e290 (2015).
    [Crossref]
  23. F. I. Fedorov, “Theory of total reflection,” Dokl. Akad. Nauk SSSR 105, 465–468 (1955).
  24. C. Imbert, “Calculation and experimental proof of the transverse shift induced by total internal reflection of a circularly polarized beam,” Phys. Rev. D 5(4), 787–796 (1972).
    [Crossref]
  25. 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]
  26. N. W. M. Ritchie, J. G. Story, and R. G. Hulet, “Realization of measurement of a weak value,” Phys. Rev. Lett. 66, 1107 (1991).
    [Crossref] [PubMed]
  27. Y. Susa, Y. Shikano, and A. Hosoya, “Optimal probe wave function of weak-value amplification,” Phys. Rev. A 85(5), 052110 (2012)
    [Crossref]
  28. J. Dressel, M. Malik, F. M. Miatto, A. N. Jordan, and R. W. Boyd, “Colloquium: Understanding quantum weak values: Basics and applications,” Rev. Mod. Phys. 86(1), 307–316 (2014).
    [Crossref]
  29. X. Zhou, X. Li, H. Luo, and S. Wen, “Optimal preselection and postselection in weak measurements for observing photonic spin Hall effect,” Appl. Phys. Lett. 104(5), 051130 (2014).
    [Crossref]
  30. A. Di Lorenzo, “Weak values and weak coupling maximizing the output of weak measurements,” Ann. Phys. 345, 178 (2014).
    [Crossref]
  31. P. B. Dixon, D. J. Starling, A. N. Jordan, and J. C. Howell, “Ultrasensitive beam deflection measurement via interferometric weak value amplification,” Phys. Rev. Lett. 102(17), 173601 (2009).
    [Crossref] [PubMed]
  32. N. Brunner and C. Simon, “Measuring small longitudinal phase shifts: Weak measurements or standard interferometry,” Phys. Rev. Lett. 105(1), 010405 (2010).
    [Crossref] [PubMed]
  33. X.-Y. Xu, Y. Kedem, K. Sun, L. Vaidman, C.-F. Li, and G.-C. Guo, “Phase estimation with weak measurement using a white light source,” Phys. Rev. Lett. 111(3), 033604 (2013).
    [Crossref] [PubMed]
  34. J. S. Lundeen, B. Sutherland, A. Patel, C. Stewart, and C. Bamber, “Direct measurement of the quantum wave-function,” Nature 474, 188–191 (2011).
    [Crossref] [PubMed]
  35. S. Kocsis, B. Braverman, S. Ravets, M. J. Stevens, R. P. Mirin, L. K. Shalm, and A. M. Steinberg, “Observing the average trajectories of single photons in a Two-Slit interferometer,” Science 332(6034), 1170–1173 (2011).
    [Crossref] [PubMed]
  36. J. Z. Salvail, M. Agnew, A. S. Johnson, E. Bolduc, J. Leach, and R. W. Boyd, “Full characterization of polarization states of light via direct measurement,” Nature Photon. 7, 316–321 (2013).
    [Crossref]
  37. A. N. Jordan, J. Martínez-Rincón, and J. C. Howell, “Technical advantages for weak-value amplification: When less is more,” Phys. Rev. X 4(1), 011031 (2014).
  38. J. B. Götte and M. R. Dennis, “Limits to superweak amplification of beam shifts,” Opt. Lett. 38(13), 2295 (2013).
    [Crossref] [PubMed]

2015 (1)

X. Ling, X. Zhou, X. Yi, W. Shu, Y. Liu, S. Chen, H. Luo, S. Wen, and D. Fan, “Giant photonic spin Hall effect in momentum space in a structured metamaterial with spatially varying birefringence,” Light Sci. Appl. 4, e290 (2015).
[Crossref]

2014 (5)

X. Qiu, X. Zhou, D. Hu, J. Du, F. Gao, Z. Zhang, and H. Luo, “Determination of magneto-optical constant of Fe films with weak measurements,” Appl. Phys. Lett. 105(13), 131111 (2014).
[Crossref]

J. Dressel, M. Malik, F. M. Miatto, A. N. Jordan, and R. W. Boyd, “Colloquium: Understanding quantum weak values: Basics and applications,” Rev. Mod. Phys. 86(1), 307–316 (2014).
[Crossref]

X. Zhou, X. Li, H. Luo, and S. Wen, “Optimal preselection and postselection in weak measurements for observing photonic spin Hall effect,” Appl. Phys. Lett. 104(5), 051130 (2014).
[Crossref]

A. Di Lorenzo, “Weak values and weak coupling maximizing the output of weak measurements,” Ann. Phys. 345, 178 (2014).
[Crossref]

A. N. Jordan, J. Martínez-Rincón, and J. C. Howell, “Technical advantages for weak-value amplification: When less is more,” Phys. Rev. X 4(1), 011031 (2014).

2013 (6)

J. B. Götte and M. R. Dennis, “Limits to superweak amplification of beam shifts,” Opt. Lett. 38(13), 2295 (2013).
[Crossref] [PubMed]

J. Z. Salvail, M. Agnew, A. S. Johnson, E. Bolduc, J. Leach, and R. W. Boyd, “Full characterization of polarization states of light via direct measurement,” Nature Photon. 7, 316–321 (2013).
[Crossref]

X.-Y. Xu, Y. Kedem, K. Sun, L. Vaidman, C.-F. Li, and G.-C. Guo, “Phase estimation with weak measurement using a white light source,” Phys. Rev. Lett. 111(3), 033604 (2013).
[Crossref] [PubMed]

X. Zhou, J. Zhang, X. Ling, S. Chen, H. Luo, and S. Wen, “Photonic spin Hall effect in topological insulators,” Phys. Rev. A 88(5), 053840 (2013).
[Crossref]

N. Shitrit, I. Yulevich, E. Maguid, D. Ozeri, D. Veksler, V. Kleiner, and E. Hasman, “Spin-Optical metamaterial route to Spin-Controlled photonics,” Science 340(6133), 724–726 (2013).
[Crossref] [PubMed]

X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin Hall effect at metasurfaces,” Science 339(6126), 1405–1407 (2013).
[Crossref] [PubMed]

2012 (4)

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,” Phys. Rev. Lett. 109(1), 013901 (2012).
[Crossref] [PubMed]

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. A 85(4), 043809 (2012).
[Crossref]

X. Zhou, X. Ling, H. Luo, and S. Wen, “Identifying graphene layers via spin Hall effect of light,” Appl. Phys. Lett. 101(25), 251602 (2012).
[Crossref]

Y. Susa, Y. Shikano, and A. Hosoya, “Optimal probe wave function of weak-value amplification,” Phys. Rev. A 85(5), 052110 (2012)
[Crossref]

2011 (4)

J. S. Lundeen, B. Sutherland, A. Patel, C. Stewart, and C. Bamber, “Direct measurement of the quantum wave-function,” Nature 474, 188–191 (2011).
[Crossref] [PubMed]

S. Kocsis, B. Braverman, S. Ravets, M. J. Stevens, R. P. Mirin, L. K. Shalm, and A. M. Steinberg, “Observing the average trajectories of single photons in a Two-Slit interferometer,” Science 332(6034), 1170–1173 (2011).
[Crossref] [PubMed]

C. A. Dartora, G. G. Cabrera, K. Z. Nobrega, V. F. Montagner, M. H. K. Matielli, F. K. R. de Campos, and H. T. S. Filho, “Lagrangian-Hamiltonian formulation of paraxial optics and applications: Study of gauge symmetries and the optical spin Hall effect,” Phys. Rev. A 83(1), 012110 (2011)
[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]

2010 (1)

N. Brunner and C. Simon, “Measuring small longitudinal phase shifts: Weak measurements or standard interferometry,” Phys. Rev. Lett. 105(1), 010405 (2010).
[Crossref] [PubMed]

2009 (4)

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]

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(4), 043810 (2009).
[Crossref]

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]

P. B. Dixon, D. J. Starling, A. N. Jordan, and J. C. Howell, “Ultrasensitive beam deflection measurement via interferometric weak value amplification,” Phys. Rev. Lett. 102(17), 173601 (2009).
[Crossref] [PubMed]

2008 (4)

O. Hosten and P. Kwiat, “Observation of the spin Hall effect of light via weak measurements,” Science 319(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]

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

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]

2007 (1)

P. Gosselin, A. Bérard, and H. Mohrbach, “Spin Hall effect of photons in a static gravitational field,” Phys. Rev. D 75(8), 084035 (2007).
[Crossref]

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]

2004 (2)

Y. K. Kato, R. C. Myers, A. C. Gossard, and D. D. Awschalom, “Observation of the Spin Hall effect in semiconductors,” Science 306(5703), 1910–1913 (2004).
[Crossref] [PubMed]

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

1999 (1)

J. E. Hirsch, “Spin Hall effect,” Phys. Rev. Lett. 83(9), 1834 (1999).
[Crossref]

1991 (1)

N. W. M. Ritchie, J. G. Story, and R. G. Hulet, “Realization of measurement of a weak value,” Phys. Rev. Lett. 66, 1107 (1991).
[Crossref] [PubMed]

1988 (1)

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]

1972 (1)

C. Imbert, “Calculation and experimental proof of the transverse shift induced by total internal reflection of a circularly polarized beam,” Phys. Rev. D 5(4), 787–796 (1972).
[Crossref]

1955 (1)

F. I. Fedorov, “Theory of total reflection,” Dokl. Akad. Nauk SSSR 105, 465–468 (1955).

Agnew, M.

J. Z. Salvail, M. Agnew, A. S. Johnson, E. Bolduc, J. Leach, and R. W. Boyd, “Full characterization of polarization states of light via direct measurement,” Nature Photon. 7, 316–321 (2013).
[Crossref]

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]

Awschalom, D. D.

Y. K. Kato, R. C. Myers, A. C. Gossard, and D. D. Awschalom, “Observation of the Spin Hall effect in semiconductors,” Science 306(5703), 1910–1913 (2004).
[Crossref] [PubMed]

Bamber, C.

J. S. Lundeen, B. Sutherland, A. Patel, C. Stewart, and C. Bamber, “Direct measurement of the quantum wave-function,” Nature 474, 188–191 (2011).
[Crossref] [PubMed]

Bérard, A.

P. Gosselin, A. Bérard, and H. Mohrbach, “Spin Hall effect of photons in a static gravitational field,” Phys. Rev. D 75(8), 084035 (2007).
[Crossref]

Betz, M.

Bliokh, K. 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,” Phys. Rev. Lett. 109(1), 013901 (2012).
[Crossref] [PubMed]

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

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 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]

Bolduc, E.

J. Z. Salvail, M. Agnew, A. S. Johnson, E. Bolduc, J. Leach, and R. W. Boyd, “Full characterization of polarization states of light via direct measurement,” Nature Photon. 7, 316–321 (2013).
[Crossref]

Boyd, R. W.

J. Dressel, M. Malik, F. M. Miatto, A. N. Jordan, and R. W. Boyd, “Colloquium: Understanding quantum weak values: Basics and applications,” Rev. Mod. Phys. 86(1), 307–316 (2014).
[Crossref]

J. Z. Salvail, M. Agnew, A. S. Johnson, E. Bolduc, J. Leach, and R. W. Boyd, “Full characterization of polarization states of light via direct measurement,” Nature Photon. 7, 316–321 (2013).
[Crossref]

Braverman, B.

S. Kocsis, B. Braverman, S. Ravets, M. J. Stevens, R. P. Mirin, L. K. Shalm, and A. M. Steinberg, “Observing the average trajectories of single photons in a Two-Slit interferometer,” Science 332(6034), 1170–1173 (2011).
[Crossref] [PubMed]

Brunner, N.

N. Brunner and C. Simon, “Measuring small longitudinal phase shifts: Weak measurements or standard interferometry,” Phys. Rev. Lett. 105(1), 010405 (2010).
[Crossref] [PubMed]

Cabrera, G. G.

C. A. Dartora, G. G. Cabrera, K. Z. Nobrega, V. F. Montagner, M. H. K. Matielli, F. K. R. de Campos, and H. T. S. Filho, “Lagrangian-Hamiltonian formulation of paraxial optics and applications: Study of gauge symmetries and the optical spin Hall effect,” Phys. Rev. A 83(1), 012110 (2011)
[Crossref]

Chen, S.

X. Ling, X. Zhou, X. Yi, W. Shu, Y. Liu, S. Chen, H. Luo, S. Wen, and D. Fan, “Giant photonic spin Hall effect in momentum space in a structured metamaterial with spatially varying birefringence,” Light Sci. Appl. 4, e290 (2015).
[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(5), 053840 (2013).
[Crossref]

Dartora, C. A.

C. A. Dartora, G. G. Cabrera, K. Z. Nobrega, V. F. Montagner, M. H. K. Matielli, F. K. R. de Campos, and H. T. S. Filho, “Lagrangian-Hamiltonian formulation of paraxial optics and applications: Study of gauge symmetries and the optical spin Hall effect,” Phys. Rev. A 83(1), 012110 (2011)
[Crossref]

de Campos, F. K. R.

C. A. Dartora, G. G. Cabrera, K. Z. Nobrega, V. F. Montagner, M. H. K. Matielli, F. K. R. de Campos, and H. T. S. Filho, “Lagrangian-Hamiltonian formulation of paraxial optics and applications: Study of gauge symmetries and the optical spin Hall effect,” Phys. Rev. A 83(1), 012110 (2011)
[Crossref]

Dennis, M. R.

Di Lorenzo, A.

A. Di Lorenzo, “Weak values and weak coupling maximizing the output of weak measurements,” Ann. Phys. 345, 178 (2014).
[Crossref]

Dixon, P. B.

P. B. Dixon, D. J. Starling, A. N. Jordan, and J. C. Howell, “Ultrasensitive beam deflection measurement via interferometric weak value amplification,” Phys. Rev. Lett. 102(17), 173601 (2009).
[Crossref] [PubMed]

Dressel, J.

J. Dressel, M. Malik, F. M. Miatto, A. N. Jordan, and R. W. Boyd, “Colloquium: Understanding quantum weak values: Basics and applications,” Rev. Mod. Phys. 86(1), 307–316 (2014).
[Crossref]

Du, J.

X. Qiu, X. Zhou, D. Hu, J. Du, F. Gao, Z. Zhang, and H. Luo, “Determination of magneto-optical constant of Fe films with weak measurements,” Appl. Phys. Lett. 105(13), 131111 (2014).
[Crossref]

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,” Phys. Rev. Lett. 109(1), 013901 (2012).
[Crossref] [PubMed]

Fan, D.

X. Ling, X. Zhou, X. Yi, W. Shu, Y. Liu, S. Chen, H. Luo, S. Wen, and D. Fan, “Giant photonic spin Hall effect in momentum space in a structured metamaterial with spatially varying birefringence,” Light Sci. Appl. 4, e290 (2015).
[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(4), 043810 (2009).
[Crossref]

Fedorov, F. I.

F. I. Fedorov, “Theory of total reflection,” Dokl. Akad. Nauk SSSR 105, 465–468 (1955).

Filho, H. T. S.

C. A. Dartora, G. G. Cabrera, K. Z. Nobrega, V. F. Montagner, M. H. K. Matielli, F. K. R. de Campos, and H. T. S. Filho, “Lagrangian-Hamiltonian formulation of paraxial optics and applications: Study of gauge symmetries and the optical spin Hall effect,” Phys. Rev. A 83(1), 012110 (2011)
[Crossref]

Gao, F.

X. Qiu, X. Zhou, D. Hu, J. Du, F. Gao, Z. Zhang, and H. Luo, “Determination of magneto-optical constant of Fe films with weak measurements,” Appl. Phys. Lett. 105(13), 131111 (2014).
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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,” Phys. Rev. Lett. 109(1), 013901 (2012).
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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,” Phys. Rev. Lett. 109(1), 013901 (2012).
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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).
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Y. K. Kato, R. C. Myers, A. C. Gossard, and D. D. Awschalom, “Observation of the Spin Hall effect in semiconductors,” Science 306(5703), 1910–1913 (2004).
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Guo, G.-C.

X.-Y. Xu, Y. Kedem, K. Sun, L. Vaidman, C.-F. Li, and G.-C. Guo, “Phase estimation with weak measurement using a white light source,” Phys. Rev. Lett. 111(3), 033604 (2013).
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Hasman, E.

N. Shitrit, I. Yulevich, E. Maguid, D. Ozeri, D. Veksler, V. Kleiner, and E. Hasman, “Spin-Optical metamaterial route to Spin-Controlled photonics,” Science 340(6133), 724–726 (2013).
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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,” Phys. Rev. Lett. 109(1), 013901 (2012).
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K. Y. Bliokh, A. Niv, V. Kleiner, and E. Hasman, “Geometrodynamics of spinning light,” Nature Photon. 2, 748–753 (2008).
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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).
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Y. Susa, Y. Shikano, and A. Hosoya, “Optimal probe wave function of weak-value amplification,” Phys. Rev. A 85(5), 052110 (2012)
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O. Hosten and P. Kwiat, “Observation of the spin Hall effect of light via weak measurements,” Science 319(5864), 787–790 (2008).
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A. N. Jordan, J. Martínez-Rincón, and J. C. Howell, “Technical advantages for weak-value amplification: When less is more,” Phys. Rev. X 4(1), 011031 (2014).

P. B. Dixon, D. J. Starling, A. N. Jordan, and J. C. Howell, “Ultrasensitive beam deflection measurement via interferometric weak value amplification,” Phys. Rev. Lett. 102(17), 173601 (2009).
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X. Qiu, X. Zhou, D. Hu, J. Du, F. Gao, Z. Zhang, and H. Luo, “Determination of magneto-optical constant of Fe films with weak measurements,” Appl. Phys. Lett. 105(13), 131111 (2014).
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N. W. M. Ritchie, J. G. Story, and R. G. Hulet, “Realization of measurement of a weak value,” Phys. Rev. Lett. 66, 1107 (1991).
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J. Z. Salvail, M. Agnew, A. S. Johnson, E. Bolduc, J. Leach, and R. W. Boyd, “Full characterization of polarization states of light via direct measurement,” Nature Photon. 7, 316–321 (2013).
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Jordan, A. N.

J. Dressel, M. Malik, F. M. Miatto, A. N. Jordan, and R. W. Boyd, “Colloquium: Understanding quantum weak values: Basics and applications,” Rev. Mod. Phys. 86(1), 307–316 (2014).
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A. N. Jordan, J. Martínez-Rincón, and J. C. Howell, “Technical advantages for weak-value amplification: When less is more,” Phys. Rev. X 4(1), 011031 (2014).

P. B. Dixon, D. J. Starling, A. N. Jordan, and J. C. Howell, “Ultrasensitive beam deflection measurement via interferometric weak value amplification,” Phys. Rev. Lett. 102(17), 173601 (2009).
[Crossref] [PubMed]

Kato, Y. K.

Y. K. Kato, R. C. Myers, A. C. Gossard, and D. D. Awschalom, “Observation of the Spin Hall effect in semiconductors,” Science 306(5703), 1910–1913 (2004).
[Crossref] [PubMed]

Kedem, Y.

X.-Y. Xu, Y. Kedem, K. Sun, L. Vaidman, C.-F. Li, and G.-C. Guo, “Phase estimation with weak measurement using a white light source,” Phys. Rev. Lett. 111(3), 033604 (2013).
[Crossref] [PubMed]

Kleiner, V.

N. Shitrit, I. Yulevich, E. Maguid, D. Ozeri, D. Veksler, V. Kleiner, and E. Hasman, “Spin-Optical metamaterial route to Spin-Controlled photonics,” Science 340(6133), 724–726 (2013).
[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,” Phys. Rev. Lett. 109(1), 013901 (2012).
[Crossref] [PubMed]

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

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]

Kocsis, S.

S. Kocsis, B. Braverman, S. Ravets, M. J. Stevens, R. P. Mirin, L. K. Shalm, and A. M. Steinberg, “Observing the average trajectories of single photons in a Two-Slit interferometer,” Science 332(6034), 1170–1173 (2011).
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Kwiat, P.

O. Hosten and P. Kwiat, “Observation of the spin Hall effect of light via weak measurements,” Science 319(5864), 787–790 (2008).
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J. Z. Salvail, M. Agnew, A. S. Johnson, E. Bolduc, J. Leach, and R. W. Boyd, “Full characterization of polarization states of light via direct measurement,” Nature Photon. 7, 316–321 (2013).
[Crossref]

Li, C.-F.

X.-Y. Xu, Y. Kedem, K. Sun, L. Vaidman, C.-F. Li, and G.-C. Guo, “Phase estimation with weak measurement using a white light source,” Phys. Rev. Lett. 111(3), 033604 (2013).
[Crossref] [PubMed]

Li, X.

X. Zhou, X. Li, H. Luo, and S. Wen, “Optimal preselection and postselection in weak measurements for observing photonic spin Hall effect,” Appl. Phys. Lett. 104(5), 051130 (2014).
[Crossref]

Li, Y.

Ling, X.

X. Ling, X. Zhou, X. Yi, W. Shu, Y. Liu, S. Chen, H. Luo, S. Wen, and D. Fan, “Giant photonic spin Hall effect in momentum space in a structured metamaterial with spatially varying birefringence,” Light Sci. Appl. 4, e290 (2015).
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X. Zhou, J. Zhang, X. Ling, S. Chen, H. Luo, and S. Wen, “Photonic spin Hall effect in topological insulators,” Phys. Rev. A 88(5), 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(25), 251602 (2012).
[Crossref]

Liu, Y.

X. Ling, X. Zhou, X. Yi, W. Shu, Y. Liu, S. Chen, H. Luo, S. Wen, and D. Fan, “Giant photonic spin Hall effect in momentum space in a structured metamaterial with spatially varying birefringence,” Light Sci. Appl. 4, e290 (2015).
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J. S. Lundeen, B. Sutherland, A. Patel, C. Stewart, and C. Bamber, “Direct measurement of the quantum wave-function,” Nature 474, 188–191 (2011).
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X. Ling, X. Zhou, X. Yi, W. Shu, Y. Liu, S. Chen, H. Luo, S. Wen, and D. Fan, “Giant photonic spin Hall effect in momentum space in a structured metamaterial with spatially varying birefringence,” Light Sci. Appl. 4, e290 (2015).
[Crossref]

X. Qiu, X. Zhou, D. Hu, J. Du, F. Gao, Z. Zhang, and H. Luo, “Determination of magneto-optical constant of Fe films with weak measurements,” Appl. Phys. Lett. 105(13), 131111 (2014).
[Crossref]

X. Zhou, X. Li, H. Luo, and S. Wen, “Optimal preselection and postselection in weak measurements for observing photonic spin Hall effect,” Appl. Phys. Lett. 104(5), 051130 (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(5), 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(25), 251602 (2012).
[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. A 85(4), 043809 (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(4), 043810 (2009).
[Crossref]

Maguid, E.

N. Shitrit, I. Yulevich, E. Maguid, D. Ozeri, D. Veksler, V. Kleiner, and E. Hasman, “Spin-Optical metamaterial route to Spin-Controlled photonics,” Science 340(6133), 724–726 (2013).
[Crossref] [PubMed]

Malik, M.

J. Dressel, M. Malik, F. M. Miatto, A. N. Jordan, and R. W. Boyd, “Colloquium: Understanding quantum weak values: Basics and applications,” Rev. Mod. Phys. 86(1), 307–316 (2014).
[Crossref]

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A. N. Jordan, J. Martínez-Rincón, and J. C. Howell, “Technical advantages for weak-value amplification: When less is more,” Phys. Rev. X 4(1), 011031 (2014).

Matielli, M. H. K.

C. A. Dartora, G. G. Cabrera, K. Z. Nobrega, V. F. Montagner, M. H. K. Matielli, F. K. R. de Campos, and H. T. S. Filho, “Lagrangian-Hamiltonian formulation of paraxial optics and applications: Study of gauge symmetries and the optical spin Hall effect,” Phys. Rev. A 83(1), 012110 (2011)
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Ménard, J.-M.

Miatto, F. M.

J. Dressel, M. Malik, F. M. Miatto, A. N. Jordan, and R. W. Boyd, “Colloquium: Understanding quantum weak values: Basics and applications,” Rev. Mod. Phys. 86(1), 307–316 (2014).
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S. Kocsis, B. Braverman, S. Ravets, M. J. Stevens, R. P. Mirin, L. K. Shalm, and A. M. Steinberg, “Observing the average trajectories of single photons in a Two-Slit interferometer,” Science 332(6034), 1170–1173 (2011).
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P. Gosselin, A. Bérard, and H. Mohrbach, “Spin Hall effect of photons in a static gravitational field,” Phys. Rev. D 75(8), 084035 (2007).
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C. A. Dartora, G. G. Cabrera, K. Z. Nobrega, V. F. Montagner, M. H. K. Matielli, F. K. R. de Campos, and H. T. S. Filho, “Lagrangian-Hamiltonian formulation of paraxial optics and applications: Study of gauge symmetries and the optical spin Hall effect,” Phys. Rev. A 83(1), 012110 (2011)
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M. Onoda, S. Murakami, and N. Nagaosa, “Hall effect of light,” Phys. Rev. Lett. 93(8), 083901 (2004).
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Y. K. Kato, R. C. Myers, A. C. Gossard, and D. D. Awschalom, “Observation of the Spin Hall effect in semiconductors,” Science 306(5703), 1910–1913 (2004).
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M. Onoda, S. Murakami, and N. Nagaosa, “Hall effect of light,” Phys. Rev. Lett. 93(8), 083901 (2004).
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K. Y. Bliokh, A. Niv, V. Kleiner, and E. Hasman, “Geometrodynamics of spinning light,” Nature Photon. 2, 748–753 (2008).
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C. A. Dartora, G. G. Cabrera, K. Z. Nobrega, V. F. Montagner, M. H. K. Matielli, F. K. R. de Campos, and H. T. S. Filho, “Lagrangian-Hamiltonian formulation of paraxial optics and applications: Study of gauge symmetries and the optical spin Hall effect,” Phys. Rev. A 83(1), 012110 (2011)
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Onoda, M.

M. Onoda, S. Murakami, and N. Nagaosa, “Hall effect of light,” Phys. Rev. Lett. 93(8), 083901 (2004).
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N. Shitrit, I. Yulevich, E. Maguid, D. Ozeri, D. Veksler, V. Kleiner, and E. Hasman, “Spin-Optical metamaterial route to Spin-Controlled photonics,” Science 340(6133), 724–726 (2013).
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Patel, A.

J. S. Lundeen, B. Sutherland, A. Patel, C. Stewart, and C. Bamber, “Direct measurement of the quantum wave-function,” Nature 474, 188–191 (2011).
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Qin, Y.

Qiu, X.

X. Qiu, X. Zhou, D. Hu, J. Du, F. Gao, Z. Zhang, and H. Luo, “Determination of magneto-optical constant of Fe films with weak measurements,” Appl. Phys. Lett. 105(13), 131111 (2014).
[Crossref]

Ravets, S.

S. Kocsis, B. Braverman, S. Ravets, M. J. Stevens, R. P. Mirin, L. K. Shalm, and A. M. Steinberg, “Observing the average trajectories of single photons in a Two-Slit interferometer,” Science 332(6034), 1170–1173 (2011).
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Rho, J.

X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin Hall effect at metasurfaces,” Science 339(6126), 1405–1407 (2013).
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Ritchie, N. W. M.

N. W. M. Ritchie, J. G. Story, and R. G. Hulet, “Realization of measurement of a weak value,” Phys. Rev. Lett. 66, 1107 (1991).
[Crossref] [PubMed]

Salvail, J. Z.

J. Z. Salvail, M. Agnew, A. S. Johnson, E. Bolduc, J. Leach, and R. W. Boyd, “Full characterization of polarization states of light via direct measurement,” Nature Photon. 7, 316–321 (2013).
[Crossref]

Shalm, L. K.

S. Kocsis, B. Braverman, S. Ravets, M. J. Stevens, R. P. Mirin, L. K. Shalm, and A. M. Steinberg, “Observing the average trajectories of single photons in a Two-Slit interferometer,” Science 332(6034), 1170–1173 (2011).
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Y. Susa, Y. Shikano, and A. Hosoya, “Optimal probe wave function of weak-value amplification,” Phys. Rev. A 85(5), 052110 (2012)
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N. Shitrit, I. Yulevich, E. Maguid, D. Ozeri, D. Veksler, V. Kleiner, and E. Hasman, “Spin-Optical metamaterial route to Spin-Controlled photonics,” Science 340(6133), 724–726 (2013).
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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,” Phys. Rev. Lett. 109(1), 013901 (2012).
[Crossref] [PubMed]

Shu, W.

X. Ling, X. Zhou, X. Yi, W. Shu, Y. Liu, S. Chen, H. Luo, S. Wen, and D. Fan, “Giant photonic spin Hall effect in momentum space in a structured metamaterial with spatially varying birefringence,” Light Sci. Appl. 4, e290 (2015).
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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(4), 043810 (2009).
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N. Brunner and C. Simon, “Measuring small longitudinal phase shifts: Weak measurements or standard interferometry,” Phys. Rev. Lett. 105(1), 010405 (2010).
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P. B. Dixon, D. J. Starling, A. N. Jordan, and J. C. Howell, “Ultrasensitive beam deflection measurement via interferometric weak value amplification,” Phys. Rev. Lett. 102(17), 173601 (2009).
[Crossref] [PubMed]

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,” Phys. Rev. Lett. 109(1), 013901 (2012).
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S. Kocsis, B. Braverman, S. Ravets, M. J. Stevens, R. P. Mirin, L. K. Shalm, and A. M. Steinberg, “Observing the average trajectories of single photons in a Two-Slit interferometer,” Science 332(6034), 1170–1173 (2011).
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Stevens, M. J.

S. Kocsis, B. Braverman, S. Ravets, M. J. Stevens, R. P. Mirin, L. K. Shalm, and A. M. Steinberg, “Observing the average trajectories of single photons in a Two-Slit interferometer,” Science 332(6034), 1170–1173 (2011).
[Crossref] [PubMed]

Stewart, C.

J. S. Lundeen, B. Sutherland, A. Patel, C. Stewart, and C. Bamber, “Direct measurement of the quantum wave-function,” Nature 474, 188–191 (2011).
[Crossref] [PubMed]

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N. W. M. Ritchie, J. G. Story, and R. G. Hulet, “Realization of measurement of a weak value,” Phys. Rev. Lett. 66, 1107 (1991).
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X.-Y. Xu, Y. Kedem, K. Sun, L. Vaidman, C.-F. Li, and G.-C. Guo, “Phase estimation with weak measurement using a white light source,” Phys. Rev. Lett. 111(3), 033604 (2013).
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Y. Susa, Y. Shikano, and A. Hosoya, “Optimal probe wave function of weak-value amplification,” Phys. Rev. A 85(5), 052110 (2012)
[Crossref]

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J. S. Lundeen, B. Sutherland, A. Patel, C. Stewart, and C. Bamber, “Direct measurement of the quantum wave-function,” Nature 474, 188–191 (2011).
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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(4), 043810 (2009).
[Crossref]

Vaidman, L.

X.-Y. Xu, Y. Kedem, K. Sun, L. Vaidman, C.-F. Li, and G.-C. Guo, “Phase estimation with weak measurement using a white light source,” Phys. Rev. Lett. 111(3), 033604 (2013).
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van Driel, H. M.

Veksler, D.

N. Shitrit, I. Yulevich, E. Maguid, D. Ozeri, D. Veksler, V. Kleiner, and E. Hasman, “Spin-Optical metamaterial route to Spin-Controlled photonics,” Science 340(6133), 724–726 (2013).
[Crossref] [PubMed]

Wang, Y.

X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin Hall effect at metasurfaces,” Science 339(6126), 1405–1407 (2013).
[Crossref] [PubMed]

Wen, S.

X. Ling, X. Zhou, X. Yi, W. Shu, Y. Liu, S. Chen, H. Luo, S. Wen, and D. Fan, “Giant photonic spin Hall effect in momentum space in a structured metamaterial with spatially varying birefringence,” Light Sci. Appl. 4, e290 (2015).
[Crossref]

X. Zhou, X. Li, H. Luo, and S. Wen, “Optimal preselection and postselection in weak measurements for observing photonic spin Hall effect,” Appl. Phys. Lett. 104(5), 051130 (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(5), 053840 (2013).
[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. A 85(4), 043809 (2012).
[Crossref]

X. Zhou, X. Ling, H. Luo, and S. Wen, “Identifying graphene layers via spin Hall effect of light,” Appl. Phys. Lett. 101(25), 251602 (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(4), 043810 (2009).
[Crossref]

Woerdman, J. P.

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. A 85(4), 043809 (2012).
[Crossref]

Xu, X.-Y.

X.-Y. Xu, Y. Kedem, K. Sun, L. Vaidman, C.-F. Li, and G.-C. Guo, “Phase estimation with weak measurement using a white light source,” Phys. Rev. Lett. 111(3), 033604 (2013).
[Crossref] [PubMed]

Ye, Z.

X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin Hall effect at metasurfaces,” Science 339(6126), 1405–1407 (2013).
[Crossref] [PubMed]

Yi, X.

X. Ling, X. Zhou, X. Yi, W. Shu, Y. Liu, S. Chen, H. Luo, S. Wen, and D. Fan, “Giant photonic spin Hall effect in momentum space in a structured metamaterial with spatially varying birefringence,” Light Sci. Appl. 4, e290 (2015).
[Crossref]

Yin, X.

X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin Hall effect at metasurfaces,” Science 339(6126), 1405–1407 (2013).
[Crossref] [PubMed]

Yulevich, I.

N. Shitrit, I. Yulevich, E. Maguid, D. Ozeri, D. Veksler, V. Kleiner, and E. Hasman, “Spin-Optical metamaterial route to Spin-Controlled photonics,” Science 340(6133), 724–726 (2013).
[Crossref] [PubMed]

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(5), 053840 (2013).
[Crossref]

Zhang, X.

X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin Hall effect at metasurfaces,” Science 339(6126), 1405–1407 (2013).
[Crossref] [PubMed]

Zhang, Z.

X. Qiu, X. Zhou, D. Hu, J. Du, F. Gao, Z. Zhang, and H. Luo, “Determination of magneto-optical constant of Fe films with weak measurements,” Appl. Phys. Lett. 105(13), 131111 (2014).
[Crossref]

Zhou, X.

X. Ling, X. Zhou, X. Yi, W. Shu, Y. Liu, S. Chen, H. Luo, S. Wen, and D. Fan, “Giant photonic spin Hall effect in momentum space in a structured metamaterial with spatially varying birefringence,” Light Sci. Appl. 4, e290 (2015).
[Crossref]

X. Qiu, X. Zhou, D. Hu, J. Du, F. Gao, Z. Zhang, and H. Luo, “Determination of magneto-optical constant of Fe films with weak measurements,” Appl. Phys. Lett. 105(13), 131111 (2014).
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Figures (5)

Fig. 1
Fig. 1 Schematic of the symmetric and asymmetric photonic SHE at the air-glass interface. The first and second column show the polarization and intensity distributions of incident Gaussian beam. The intensity distributions and spin-dependent shifts of left- and right-handed circularly polarized components of reflected beam are described in the third column. Here, we consider the elliptical polarization beam with its long and short axis along to the horizontal and vertical directions.
Fig. 2
Fig. 2 The intensity distributions (a–d) and initial spin-dependent shifts (e–h) of left- and right-handed circularly polarized components in the asymmetric photonic SHE. The ellipticity are chosen as β = 0.2° and β = 5°. The intensity is plotted in normalized units. (a) and (b) show the intensity distributions when the incident angle is selected as θi = 30°. The long axis of incident elliptical polarization beam is along to the horizontal direction and the handedness of incident polarization is left. (c) and (d) stand for the intensity distributions under the condition of incident angle is selected as θi = 45°. Here, the handedness of incident polarization and the direction of long axis are chosen as the same as above. (e) and (f) denote the displacements in the case of the handedness of incident polarizations are left and right, and the long axis of incident elliptical polarization beam is along to the horizontal direction. (g) and (h) describe the shifts under the condition of the long axis of incident elliptical polarization beam along to the vertical direction.
Fig. 3
Fig. 3 (a) Schematic of the preselection and postselection states on Bloch sphere. (b) and (c) show the results of |〈f|i〉Re(Aw)| and |〈f|i〉Im(Aw)| as a function of the the ellipticity β and amplification angle Δ. Both of the functions are plotted in normalized units.
Fig. 4
Fig. 4 Experimental setup for measuring the asymmetric photonic SHE and the corresponding weak measurements process. (a) shows the experimental setup. The sample is a BK7 glass. The light source is a 21mW linearly polarized He-Ne laser at 632.8nm (Thorlabs HNL210L-EC). L1 and L2, lenses with effective focal length 50mm and 250mm, respectively. HWP, half-wave plate (for adjusting the intensity). QWP, quarter-wave plate for generating elliptical polarization beam. P1 and P2, Glan Laser polarizers. CCD, charge-coupled device (Coherent LaserCam HR). The inset: The incident beam is preselected in the left- or right-elliptical polarization state by P1 and QWP. The optical axis of P1 make the angles β or −β with horizontal axis. (b) denotes the weak measurements process with linear polarization (the first row) and elliptical polarization (the second row) beam.
Fig. 5
Fig. 5 The amplified (a, b) and initial (c, d) spin-dependent shifts of asymmetric photonic SHE in the case of elliptical polarization beam with its long and short axis along to the horizontal (the left column) and vertical directions (the right column). Here, the ellipticity is chosen as β = 0.2° and the handedness of incident polarization is left. The lines indicate the theoretical value. The diamonds, squares, and triangles show the experimental results.

Equations (12)

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| E ˜ i = ( e i x + i σ e i y ) w 0 2 π exp [ w 0 2 ( k i x 2 + k i y 2 ) 4 ] ,
| E ˜ L H = r p cos β 2 { exp [ k r y ( + i δ H + i δ H tan β ) ] exp ( + η ) } | + + r p cos β 2 { exp [ k r y ( i δ H + i δ H tan β ) ] exp ( η ) } | ,
| E ˜ L V = r s sin β 2 { exp [ k r y ( + i δ V + i δ V cot β ) ] exp ( + ϑ ) } | + + r s sin β 2 { exp [ k r y ( i δ V + i δ V cot β ) ] exp ( ϑ ) } | .
y ± H , V = E ˜ | i k ry | E ˜ E ˜ | E ˜ + z k 0 E ˜ | k ry | E ˜ E ˜ | E ˜ .
y ± H , V = δ ± H , V + δ I F H , V ,
A w = f | A ^ | i f | i .
| i = cos ( Θ + β 2 ) | + + e i Φ sin ( Θ + β 2 ) | ,
| f = sin ( Θ 2 ) | + e i ( Φ + Δ ) cos ( Θ 2 ) | .
Re ( A w ) = sin β cos β cos Δ 1 ,
Im ( A w ) = 1 cot Δ csc Δ sec β .
y w = ( A Re + FA Im ) | δ ± H , V | ,
y w FA Im | δ ± H , V | .

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