Abstract

The angular Goos-Hänchen shift of vortex beam is investigated theoretically when a Laguerre-Gaussian (LG) beam is reflected by an air-metamaterial interface. The upper limit of the angular GH shift is found to be half of the divergence angle of the incident beam, i.e., |Θup| = (|| + 1)1/2/k0w0, with , k0, and w0 being the vortex charge, wavenumber in vacuum, and beam waist, respectively. Interestingly, the upper limited angular GH shift is accompanied by the upper-limited spatial IF shift. A parameter F is introduced to compare the total beam shift with the beam size. F varies with the vortex charge and the propagation distance zr. The values of F at zr = ∞ plane can approach 0.5, which are always larger than those at zr = 0 plane. These findings provide a deeper insight into optical beam shifts, and they may have potential application in precision metrology.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  6. X. Qiu, L. Xie, X. Liu, L. Luo, Z. Zhang, and J. Du, “Estimation of optical rotation of chiral molecules with weak measurements,” Opt. Lett. 41(17), 4032–4035 (2016).
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    [Crossref]
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2017 (8)

W. Zhu, J. Yu, H. Guan, H. Lu, J. Tang, J. Zhang, Y. Luo, and Z. Chen, “The upper limit of the in-plane spin splitting of Gaussian beam reflected from a glass-air interface,” Sci. Rep. 7(1), 1150 (2017).
[Crossref] [PubMed]

L. Cai, M. Liu, S. Chen, Y. Liu, W. Shu, H. Luo, and S. Wen, “Quantized photonic spin Hall effect in graphene,” Phys. Rev. A 95(1), 013809 (2017).
[Crossref]

W. Zhu, J. Yu, H. Guan, H. Lu, J. Tang, Y. Luo, and Z. Chen, “Large spatial and angular spin splitting in a thin anisotropic ε-near-zero metamaterial,” Opt. Express 25(5), 5196–5205 (2017).
[Crossref] [PubMed]

C. Prajapati, “Numerical calculation of beam shifts for higher-order Laguerre-Gaussian beams upon transmission,” Opt. Commun. 389, 290–296 (2017).
[Crossref]

M. Jiang, W. Zhu, H. Guan, J. Yu, H. Lu, J. Tan, J. Zhang, and Z. Chen, “Giant spin splitting induced by orbital angular momentum in an epsilon-near-zero metamaterial slab,” Opt. Lett. 42(17), 3259–3262 (2017).
[Crossref] [PubMed]

I. Liberal, A. M. Mahmoud, Y. Li, B. Edwards, and N. Engheta, “Photonic doping of epsilon-near-zero media,” Science 355(6329), 1058–1062 (2017).
[Crossref] [PubMed]

S. Chen, C. Mi, L. Cai, M. Liu, H. Luo, and S. Wen, “Observation of the Goos-Hänchen shift in graphene via weak measurements,” Appl. Phys. Lett. 110, 4974212 (2017).

L. Luo and T. Tang, “Enhanced Imbert-Fedorov effect of reflected light from an epsilon-near-zero slab,” Superlattices Microstruct. 109, 259–263 (2017).
[Crossref]

2016 (5)

Y. Fan, N. H. Shen, F. Zhang, Z. Wei, H. Li, Q. Zhao, Q. Fu, P. Zhang, T. Koschny, and C. M. Soukoulis, “Electrically Tunable Goos-Hanchen Effect with Graphene in the Terahertz Regime,” Adv. Opt. Mater. 4(11), 1824–1828 (2016).
[Crossref]

T. Tang, J. Li, Y. Zhang, C. Li, and L. Luo, “Spin Hall effect of transmitted light in a three-layer waveguide with lossy epsilon-near-zero metamaterial,” Opt. Express 24(24), 28113–28121 (2016).
[Crossref] [PubMed]

M. Z. Alam, I. De Leon, and R. W. Boyd, “Large optical nonlinearity of indium tin oxide in its epsilon-near-zero region,” Science 352(6287), 795–797 (2016).
[Crossref] [PubMed]

T. Tang, C. Li, and L. Luo, “Enhanced spin Hall effect of tunneling light in hyperbolic metamaterial waveguide,” Sci. Rep. 6(1), 30762 (2016).
[Crossref] [PubMed]

X. Qiu, L. Xie, X. Liu, L. Luo, Z. Zhang, and J. Du, “Estimation of optical rotation of chiral molecules with weak measurements,” Opt. Lett. 41(17), 4032–4035 (2016).
[Crossref] [PubMed]

2015 (2)

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]

Y. Xu, C. T. Chan, and H. Chen, “Goos-Hänchen effect in epsilon-near-zero metamaterials,” Sci. Rep. 5(1), 8681 (2015).
[Crossref] [PubMed]

2014 (1)

2013 (3)

P. Moitra, Y. Yang, Z. Anderson, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Realization of an all-dielectric zero-index optical metamaterial,” Nat. Photonics 7(10), 791–795 (2013).
[Crossref]

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

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Hyperbolic metamaterials,” Nat. Photonics 7(12), 948–957 (2013).
[Crossref]

2012 (2)

A. Aiello, “Goos–Hänchen and Imbert–Fedorov shifts: a novel perspective,” New J. Phys. 14(1), 013058 (2012).
[Crossref]

Z. Xiao, H. Luo, and S. Wen, “Goos-Hanchen and Imbert-Fedorov shifts of vortex beams at air left-handed-material interfaces,” Phys. Rev. A 85(5), 33–35 (2012).
[Crossref]

2010 (1)

M. Merano, N. Hermosa, J. P. Woerdman, and A. Aiello, “How orbital angular momentum affects beam shifts in optical reflection,” Phys. Rev. A 82(2), 023817 (2010).
[Crossref]

2009 (1)

M. Merano, A. Aiello, M. P. van Exter, and J. P. Woerdman, “Observing angular deviations in the specular reflection of a light beam,” Nat. Photonics 3(6), 337–340 (2009).
[Crossref]

2006 (2)

K. Y. Bliokh and Y. P. Bliokh, “Conservation of angular momentum, transverse shift, and spin hall effect in reflection and refraction of an electromagnetic wave packet,” Phys. Rev. Lett. 96(7), 073903 (2006).
[Crossref] [PubMed]

R. Dasgupta and P. K. Gupta, “Experimental observation of spin-independent transverse shift of the centre of gravity of a reflected Laguerre-Gaussian light beam,” Opt. Commun. 257(1), 91–96 (2006).
[Crossref]

2005 (1)

C. Paterson, “Atmospheric turbulence and orbital angular momentum of single photons for optical communication,” Phys. Rev. Lett. 94(15), 153901 (2005).
[Crossref] [PubMed]

2001 (1)

V. G. Fedoseyev, “Spin-independent transverse shift of the centre of gravity of a reflected and of a refracted light beam,” Opt. Commun. 193(1), 9–18 (2001).
[Crossref]

Aiello, A.

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

A. Aiello, “Goos–Hänchen and Imbert–Fedorov shifts: a novel perspective,” New J. Phys. 14(1), 013058 (2012).
[Crossref]

M. Merano, N. Hermosa, J. P. Woerdman, and A. Aiello, “How orbital angular momentum affects beam shifts in optical reflection,” Phys. Rev. A 82(2), 023817 (2010).
[Crossref]

M. Merano, A. Aiello, M. P. van Exter, and J. P. Woerdman, “Observing angular deviations in the specular reflection of a light beam,” Nat. Photonics 3(6), 337–340 (2009).
[Crossref]

Alam, M. Z.

M. Z. Alam, I. De Leon, and R. W. Boyd, “Large optical nonlinearity of indium tin oxide in its epsilon-near-zero region,” Science 352(6287), 795–797 (2016).
[Crossref] [PubMed]

Anderson, Z.

P. Moitra, Y. Yang, Z. Anderson, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Realization of an all-dielectric zero-index optical metamaterial,” Nat. Photonics 7(10), 791–795 (2013).
[Crossref]

Belov, P.

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Hyperbolic metamaterials,” Nat. Photonics 7(12), 948–957 (2013).
[Crossref]

Bliokh, K. Y.

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]

Boyd, R. W.

M. Z. Alam, I. De Leon, and R. W. Boyd, “Large optical nonlinearity of indium tin oxide in its epsilon-near-zero region,” Science 352(6287), 795–797 (2016).
[Crossref] [PubMed]

Briggs, D. P.

P. Moitra, Y. Yang, Z. Anderson, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Realization of an all-dielectric zero-index optical metamaterial,” Nat. Photonics 7(10), 791–795 (2013).
[Crossref]

Cai, L.

S. Chen, C. Mi, L. Cai, M. Liu, H. Luo, and S. Wen, “Observation of the Goos-Hänchen shift in graphene via weak measurements,” Appl. Phys. Lett. 110, 4974212 (2017).

L. Cai, M. Liu, S. Chen, Y. Liu, W. Shu, H. Luo, and S. Wen, “Quantized photonic spin Hall effect in graphene,” Phys. Rev. A 95(1), 013809 (2017).
[Crossref]

Chan, C. T.

Y. Xu, C. T. Chan, and H. Chen, “Goos-Hänchen effect in epsilon-near-zero metamaterials,” Sci. Rep. 5(1), 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(1), 8681 (2015).
[Crossref] [PubMed]

Chen, S.

L. Cai, M. Liu, S. Chen, Y. Liu, W. Shu, H. Luo, and S. Wen, “Quantized photonic spin Hall effect in graphene,” Phys. Rev. A 95(1), 013809 (2017).
[Crossref]

S. Chen, C. Mi, L. Cai, M. Liu, H. Luo, and S. Wen, “Observation of the Goos-Hänchen shift in graphene via weak measurements,” Appl. Phys. Lett. 110, 4974212 (2017).

Chen, Z.

Dasgupta, R.

R. Dasgupta and P. K. Gupta, “Experimental observation of spin-independent transverse shift of the centre of gravity of a reflected Laguerre-Gaussian light beam,” Opt. Commun. 257(1), 91–96 (2006).
[Crossref]

De Leon, I.

M. Z. Alam, I. De Leon, and R. W. Boyd, “Large optical nonlinearity of indium tin oxide in its epsilon-near-zero region,” Science 352(6287), 795–797 (2016).
[Crossref] [PubMed]

Du, J.

Dumelow, T.

Edwards, B.

I. Liberal, A. M. Mahmoud, Y. Li, B. Edwards, and N. Engheta, “Photonic doping of epsilon-near-zero media,” Science 355(6329), 1058–1062 (2017).
[Crossref] [PubMed]

Engheta, N.

I. Liberal, A. M. Mahmoud, Y. Li, B. Edwards, and N. Engheta, “Photonic doping of epsilon-near-zero media,” Science 355(6329), 1058–1062 (2017).
[Crossref] [PubMed]

Fan, Y.

Y. Fan, N. H. Shen, F. Zhang, Z. Wei, H. Li, Q. Zhao, Q. Fu, P. Zhang, T. Koschny, and C. M. Soukoulis, “Electrically Tunable Goos-Hanchen Effect with Graphene in the Terahertz Regime,” Adv. Opt. Mater. 4(11), 1824–1828 (2016).
[Crossref]

Fedoseyev, V. G.

V. G. Fedoseyev, “Spin-independent transverse shift of the centre of gravity of a reflected and of a refracted light beam,” Opt. Commun. 193(1), 9–18 (2001).
[Crossref]

Fu, Q.

Y. Fan, N. H. Shen, F. Zhang, Z. Wei, H. Li, Q. Zhao, Q. Fu, P. Zhang, T. Koschny, and C. M. Soukoulis, “Electrically Tunable Goos-Hanchen Effect with Graphene in the Terahertz Regime,” Adv. Opt. Mater. 4(11), 1824–1828 (2016).
[Crossref]

Guan, H.

Gupta, P. K.

R. Dasgupta and P. K. Gupta, “Experimental observation of spin-independent transverse shift of the centre of gravity of a reflected Laguerre-Gaussian light beam,” Opt. Commun. 257(1), 91–96 (2006).
[Crossref]

Hermosa, N.

M. Merano, N. Hermosa, J. P. Woerdman, and A. Aiello, “How orbital angular momentum affects beam shifts in optical reflection,” Phys. Rev. A 82(2), 023817 (2010).
[Crossref]

Iorsh, I.

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Hyperbolic metamaterials,” Nat. Photonics 7(12), 948–957 (2013).
[Crossref]

Jiang, M.

Kivshar, Y.

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Hyperbolic metamaterials,” Nat. Photonics 7(12), 948–957 (2013).
[Crossref]

Koschny, T.

Y. Fan, N. H. Shen, F. Zhang, Z. Wei, H. Li, Q. Zhao, Q. Fu, P. Zhang, T. Koschny, and C. M. Soukoulis, “Electrically Tunable Goos-Hanchen Effect with Graphene in the Terahertz Regime,” Adv. Opt. Mater. 4(11), 1824–1828 (2016).
[Crossref]

Kravchenko, I. I.

P. Moitra, Y. Yang, Z. Anderson, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Realization of an all-dielectric zero-index optical metamaterial,” Nat. Photonics 7(10), 791–795 (2013).
[Crossref]

Li, C.

Li, H.

Y. Fan, N. H. Shen, F. Zhang, Z. Wei, H. Li, Q. Zhao, Q. Fu, P. Zhang, T. Koschny, and C. M. Soukoulis, “Electrically Tunable Goos-Hanchen Effect with Graphene in the Terahertz Regime,” Adv. Opt. Mater. 4(11), 1824–1828 (2016).
[Crossref]

Li, J.

Li, Y.

I. Liberal, A. M. Mahmoud, Y. Li, B. Edwards, and N. Engheta, “Photonic doping of epsilon-near-zero media,” Science 355(6329), 1058–1062 (2017).
[Crossref] [PubMed]

Liberal, I.

I. Liberal, A. M. Mahmoud, Y. Li, B. Edwards, and N. Engheta, “Photonic doping of epsilon-near-zero media,” Science 355(6329), 1058–1062 (2017).
[Crossref] [PubMed]

Liu, M.

S. Chen, C. Mi, L. Cai, M. Liu, H. Luo, and S. Wen, “Observation of the Goos-Hänchen shift in graphene via weak measurements,” Appl. Phys. Lett. 110, 4974212 (2017).

L. Cai, M. Liu, S. Chen, Y. Liu, W. Shu, H. Luo, and S. Wen, “Quantized photonic spin Hall effect in graphene,” Phys. Rev. A 95(1), 013809 (2017).
[Crossref]

Liu, X.

Liu, Y.

L. Cai, M. Liu, S. Chen, Y. Liu, W. Shu, H. Luo, and S. Wen, “Quantized photonic spin Hall effect in graphene,” Phys. Rev. A 95(1), 013809 (2017).
[Crossref]

Lu, H.

Luo, H.

L. Cai, M. Liu, S. Chen, Y. Liu, W. Shu, H. Luo, and S. Wen, “Quantized photonic spin Hall effect in graphene,” Phys. Rev. A 95(1), 013809 (2017).
[Crossref]

S. Chen, C. Mi, L. Cai, M. Liu, H. Luo, and S. Wen, “Observation of the Goos-Hänchen shift in graphene via weak measurements,” Appl. Phys. Lett. 110, 4974212 (2017).

Z. Xiao, H. Luo, and S. Wen, “Goos-Hanchen and Imbert-Fedorov shifts of vortex beams at air left-handed-material interfaces,” Phys. Rev. A 85(5), 33–35 (2012).
[Crossref]

Luo, L.

L. Luo and T. Tang, “Enhanced Imbert-Fedorov effect of reflected light from an epsilon-near-zero slab,” Superlattices Microstruct. 109, 259–263 (2017).
[Crossref]

X. Qiu, L. Xie, X. Liu, L. Luo, Z. Zhang, and J. Du, “Estimation of optical rotation of chiral molecules with weak measurements,” Opt. Lett. 41(17), 4032–4035 (2016).
[Crossref] [PubMed]

T. Tang, J. Li, Y. Zhang, C. Li, and L. Luo, “Spin Hall effect of transmitted light in a three-layer waveguide with lossy epsilon-near-zero metamaterial,” Opt. Express 24(24), 28113–28121 (2016).
[Crossref] [PubMed]

T. Tang, C. Li, and L. Luo, “Enhanced spin Hall effect of tunneling light in hyperbolic metamaterial waveguide,” Sci. Rep. 6(1), 30762 (2016).
[Crossref] [PubMed]

Luo, Y.

W. Zhu, J. Yu, H. Guan, H. Lu, J. Tang, J. Zhang, Y. Luo, and Z. Chen, “The upper limit of the in-plane spin splitting of Gaussian beam reflected from a glass-air interface,” Sci. Rep. 7(1), 1150 (2017).
[Crossref] [PubMed]

W. Zhu, J. Yu, H. Guan, H. Lu, J. Tang, Y. Luo, and Z. Chen, “Large spatial and angular spin splitting in a thin anisotropic ε-near-zero metamaterial,” Opt. Express 25(5), 5196–5205 (2017).
[Crossref] [PubMed]

Macêdo, R.

Mahmoud, A. M.

I. Liberal, A. M. Mahmoud, Y. Li, B. Edwards, and N. Engheta, “Photonic doping of epsilon-near-zero media,” Science 355(6329), 1058–1062 (2017).
[Crossref] [PubMed]

Merano, M.

M. Merano, N. Hermosa, J. P. Woerdman, and A. Aiello, “How orbital angular momentum affects beam shifts in optical reflection,” Phys. Rev. A 82(2), 023817 (2010).
[Crossref]

M. Merano, A. Aiello, M. P. van Exter, and J. P. Woerdman, “Observing angular deviations in the specular reflection of a light beam,” Nat. Photonics 3(6), 337–340 (2009).
[Crossref]

Mi, C.

S. Chen, C. Mi, L. Cai, M. Liu, H. Luo, and S. Wen, “Observation of the Goos-Hänchen shift in graphene via weak measurements,” Appl. Phys. Lett. 110, 4974212 (2017).

Moitra, P.

P. Moitra, Y. Yang, Z. Anderson, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Realization of an all-dielectric zero-index optical metamaterial,” Nat. Photonics 7(10), 791–795 (2013).
[Crossref]

Paterson, C.

C. Paterson, “Atmospheric turbulence and orbital angular momentum of single photons for optical communication,” Phys. Rev. Lett. 94(15), 153901 (2005).
[Crossref] [PubMed]

Poddubny, A.

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Hyperbolic metamaterials,” Nat. Photonics 7(12), 948–957 (2013).
[Crossref]

Prajapati, C.

C. Prajapati, “Numerical calculation of beam shifts for higher-order Laguerre-Gaussian beams upon transmission,” Opt. Commun. 389, 290–296 (2017).
[Crossref]

Qiu, X.

She, W.

Shen, N. H.

Y. Fan, N. H. Shen, F. Zhang, Z. Wei, H. Li, Q. Zhao, Q. Fu, P. Zhang, T. Koschny, and C. M. Soukoulis, “Electrically Tunable Goos-Hanchen Effect with Graphene in the Terahertz Regime,” Adv. Opt. Mater. 4(11), 1824–1828 (2016).
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Shu, W.

L. Cai, M. Liu, S. Chen, Y. Liu, W. Shu, H. Luo, and S. Wen, “Quantized photonic spin Hall effect in graphene,” Phys. Rev. A 95(1), 013809 (2017).
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Soukoulis, C. M.

Y. Fan, N. H. Shen, F. Zhang, Z. Wei, H. Li, Q. Zhao, Q. Fu, P. Zhang, T. Koschny, and C. M. Soukoulis, “Electrically Tunable Goos-Hanchen Effect with Graphene in the Terahertz Regime,” Adv. Opt. Mater. 4(11), 1824–1828 (2016).
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Stamps, R. L.

Tan, J.

Tang, J.

W. Zhu, J. Yu, H. Guan, H. Lu, J. Tang, Y. Luo, and Z. Chen, “Large spatial and angular spin splitting in a thin anisotropic ε-near-zero metamaterial,” Opt. Express 25(5), 5196–5205 (2017).
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W. Zhu, J. Yu, H. Guan, H. Lu, J. Tang, J. Zhang, Y. Luo, and Z. Chen, “The upper limit of the in-plane spin splitting of Gaussian beam reflected from a glass-air interface,” Sci. Rep. 7(1), 1150 (2017).
[Crossref] [PubMed]

Tang, T.

L. Luo and T. Tang, “Enhanced Imbert-Fedorov effect of reflected light from an epsilon-near-zero slab,” Superlattices Microstruct. 109, 259–263 (2017).
[Crossref]

T. Tang, J. Li, Y. Zhang, C. Li, and L. Luo, “Spin Hall effect of transmitted light in a three-layer waveguide with lossy epsilon-near-zero metamaterial,” Opt. Express 24(24), 28113–28121 (2016).
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T. Tang, C. Li, and L. Luo, “Enhanced spin Hall effect of tunneling light in hyperbolic metamaterial waveguide,” Sci. Rep. 6(1), 30762 (2016).
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Valentine, J.

P. Moitra, Y. Yang, Z. Anderson, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Realization of an all-dielectric zero-index optical metamaterial,” Nat. Photonics 7(10), 791–795 (2013).
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van Exter, M. P.

M. Merano, A. Aiello, M. P. van Exter, and J. P. Woerdman, “Observing angular deviations in the specular reflection of a light beam,” Nat. Photonics 3(6), 337–340 (2009).
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Wei, Z.

Y. Fan, N. H. Shen, F. Zhang, Z. Wei, H. Li, Q. Zhao, Q. Fu, P. Zhang, T. Koschny, and C. M. Soukoulis, “Electrically Tunable Goos-Hanchen Effect with Graphene in the Terahertz Regime,” Adv. Opt. Mater. 4(11), 1824–1828 (2016).
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Wen, S.

S. Chen, C. Mi, L. Cai, M. Liu, H. Luo, and S. Wen, “Observation of the Goos-Hänchen shift in graphene via weak measurements,” Appl. Phys. Lett. 110, 4974212 (2017).

L. Cai, M. Liu, S. Chen, Y. Liu, W. Shu, H. Luo, and S. Wen, “Quantized photonic spin Hall effect in graphene,” Phys. Rev. A 95(1), 013809 (2017).
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Z. Xiao, H. Luo, and S. Wen, “Goos-Hanchen and Imbert-Fedorov shifts of vortex beams at air left-handed-material interfaces,” Phys. Rev. A 85(5), 33–35 (2012).
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M. Merano, N. Hermosa, J. P. Woerdman, and A. Aiello, “How orbital angular momentum affects beam shifts in optical reflection,” Phys. Rev. A 82(2), 023817 (2010).
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M. Merano, A. Aiello, M. P. van Exter, and J. P. Woerdman, “Observing angular deviations in the specular reflection of a light beam,” Nat. Photonics 3(6), 337–340 (2009).
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Z. Xiao, H. Luo, and S. Wen, “Goos-Hanchen and Imbert-Fedorov shifts of vortex beams at air left-handed-material interfaces,” Phys. Rev. A 85(5), 33–35 (2012).
[Crossref]

Xie, L.

Xu, Y.

Y. Xu, C. T. Chan, and H. Chen, “Goos-Hänchen effect in epsilon-near-zero metamaterials,” Sci. Rep. 5(1), 8681 (2015).
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Yang, Y.

P. Moitra, Y. Yang, Z. Anderson, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Realization of an all-dielectric zero-index optical metamaterial,” Nat. Photonics 7(10), 791–795 (2013).
[Crossref]

Yu, J.

Zhang, F.

Y. Fan, N. H. Shen, F. Zhang, Z. Wei, H. Li, Q. Zhao, Q. Fu, P. Zhang, T. Koschny, and C. M. Soukoulis, “Electrically Tunable Goos-Hanchen Effect with Graphene in the Terahertz Regime,” Adv. Opt. Mater. 4(11), 1824–1828 (2016).
[Crossref]

Zhang, J.

W. Zhu, J. Yu, H. Guan, H. Lu, J. Tang, J. Zhang, Y. Luo, and Z. Chen, “The upper limit of the in-plane spin splitting of Gaussian beam reflected from a glass-air interface,” Sci. Rep. 7(1), 1150 (2017).
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Zhang, P.

Y. Fan, N. H. Shen, F. Zhang, Z. Wei, H. Li, Q. Zhao, Q. Fu, P. Zhang, T. Koschny, and C. M. Soukoulis, “Electrically Tunable Goos-Hanchen Effect with Graphene in the Terahertz Regime,” Adv. Opt. Mater. 4(11), 1824–1828 (2016).
[Crossref]

Zhang, Y.

Zhang, Z.

Zhao, Q.

Y. Fan, N. H. Shen, F. Zhang, Z. Wei, H. Li, Q. Zhao, Q. Fu, P. Zhang, T. Koschny, and C. M. Soukoulis, “Electrically Tunable Goos-Hanchen Effect with Graphene in the Terahertz Regime,” Adv. Opt. Mater. 4(11), 1824–1828 (2016).
[Crossref]

Zhu, W.

Adv. Opt. Mater. (1)

Y. Fan, N. H. Shen, F. Zhang, Z. Wei, H. Li, Q. Zhao, Q. Fu, P. Zhang, T. Koschny, and C. M. Soukoulis, “Electrically Tunable Goos-Hanchen Effect with Graphene in the Terahertz Regime,” Adv. Opt. Mater. 4(11), 1824–1828 (2016).
[Crossref]

Appl. Phys. Lett. (1)

S. Chen, C. Mi, L. Cai, M. Liu, H. Luo, and S. Wen, “Observation of the Goos-Hänchen shift in graphene via weak measurements,” Appl. Phys. Lett. 110, 4974212 (2017).

J. Opt. (1)

K. Y. Bliokh and A. Aiello, “Goos-Hächen and Imbert-Fedorov beam shifts: an overview,” J. Opt. 15(1), 014001 (2013).
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Nat. Photonics (3)

M. Merano, A. Aiello, M. P. van Exter, and J. P. Woerdman, “Observing angular deviations in the specular reflection of a light beam,” Nat. Photonics 3(6), 337–340 (2009).
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A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Hyperbolic metamaterials,” Nat. Photonics 7(12), 948–957 (2013).
[Crossref]

P. Moitra, Y. Yang, Z. Anderson, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Realization of an all-dielectric zero-index optical metamaterial,” Nat. Photonics 7(10), 791–795 (2013).
[Crossref]

New J. Phys. (1)

A. Aiello, “Goos–Hänchen and Imbert–Fedorov shifts: a novel perspective,” New J. Phys. 14(1), 013058 (2012).
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Opt. Commun. (3)

C. Prajapati, “Numerical calculation of beam shifts for higher-order Laguerre-Gaussian beams upon transmission,” Opt. Commun. 389, 290–296 (2017).
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V. G. Fedoseyev, “Spin-independent transverse shift of the centre of gravity of a reflected and of a refracted light beam,” Opt. Commun. 193(1), 9–18 (2001).
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R. Dasgupta and P. K. Gupta, “Experimental observation of spin-independent transverse shift of the centre of gravity of a reflected Laguerre-Gaussian light beam,” Opt. Commun. 257(1), 91–96 (2006).
[Crossref]

Opt. Express (3)

Opt. Lett. (3)

Phys. Rev. A (3)

L. Cai, M. Liu, S. Chen, Y. Liu, W. Shu, H. Luo, and S. Wen, “Quantized photonic spin Hall effect in graphene,” Phys. Rev. A 95(1), 013809 (2017).
[Crossref]

M. Merano, N. Hermosa, J. P. Woerdman, and A. Aiello, “How orbital angular momentum affects beam shifts in optical reflection,” Phys. Rev. A 82(2), 023817 (2010).
[Crossref]

Z. Xiao, H. Luo, and S. Wen, “Goos-Hanchen and Imbert-Fedorov shifts of vortex beams at air left-handed-material interfaces,” Phys. Rev. A 85(5), 33–35 (2012).
[Crossref]

Phys. Rev. Lett. (2)

C. Paterson, “Atmospheric turbulence and orbital angular momentum of single photons for optical communication,” Phys. Rev. Lett. 94(15), 153901 (2005).
[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]

Sci. Rep. (3)

W. Zhu, J. Yu, H. Guan, H. Lu, J. Tang, J. Zhang, Y. Luo, and Z. Chen, “The upper limit of the in-plane spin splitting of Gaussian beam reflected from a glass-air interface,” Sci. Rep. 7(1), 1150 (2017).
[Crossref] [PubMed]

T. Tang, C. Li, and L. Luo, “Enhanced spin Hall effect of tunneling light in hyperbolic metamaterial waveguide,” Sci. Rep. 6(1), 30762 (2016).
[Crossref] [PubMed]

Y. Xu, C. T. Chan, and H. Chen, “Goos-Hänchen effect in epsilon-near-zero metamaterials,” Sci. Rep. 5(1), 8681 (2015).
[Crossref] [PubMed]

Science (2)

M. Z. Alam, I. De Leon, and R. W. Boyd, “Large optical nonlinearity of indium tin oxide in its epsilon-near-zero region,” Science 352(6287), 795–797 (2016).
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I. Liberal, A. M. Mahmoud, Y. Li, B. Edwards, and N. Engheta, “Photonic doping of epsilon-near-zero media,” Science 355(6329), 1058–1062 (2017).
[Crossref] [PubMed]

Superlattices Microstruct. (1)

L. Luo and T. Tang, “Enhanced Imbert-Fedorov effect of reflected light from an epsilon-near-zero slab,” Superlattices Microstruct. 109, 259–263 (2017).
[Crossref]

Other (1)

R. Macêdo and T. Dumelow, “Beam shifts on reflection of electromagnetic radiation off anisotropic crystals at optic phonon frequencies,” J. Opt. (United Kingdom) 15, (2013).

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Figures (7)

Fig. 1
Fig. 1 The schematic of beam shifts of reflected vortex beam. When reflected by air-metamaterial interface, a horizontally polarized vortex beam will undergo spatial shifts ΔY along yr direction and angular shift Θx along xr direction.
Fig. 2
Fig. 2 The dependences of spatial GH (ΔX) and IF (ΔY) shifts (a) and angular GH (Θx) and IF (Θy) shifts (b) on the incident angle θ for w0 = 40λ, = 3, and εm = 0.1.
Fig. 3
Fig. 3 The changes of normalized spatial shifts ΔYYup as a function of incident angle θ and εm.
Fig. 4
Fig. 4 The changes of normalized spatial shifts ΔYYup as a function of the incident angle θ and the image part of permittivity of the metamaterial Im[εm] when Re[εm] = 0.1.
Fig. 5
Fig. 5 The spatial IF ΔY and angular GH Θx shifts changing with the vortex charge . The inset shows the normalized spatial ΔYYup and angular Θxup shifts.
Fig. 6
Fig. 6 (a) The comparisons of the centroid shifts along xr (δX) and yr (δY) axes of the reflected LG beam with the spot size D/2 of standard LG beam for = 3. (b) The parameter F as a function of zr/z0 for = 0, 1, 3, 5, respectively. Intensity patterns at zr = 0 (c,f), 0.75z0 (d,g), 5z0 (e,h) planes for = 3 (c-e) and 1 (f-h), where green dotted lines represent the xr axis, and the white dotted lines denote the rotation the intensity patterns.
Fig. 7
Fig. 7 Dependence of parameter F on the vortex charge for zr = 0 (red dots) and ∞ (blue dots), when the incident angles θ = 15°(a) and 18.14° (b), respectively.

Equations (5)

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E ˜ r ( z r =0)={( r p k rx k 0 r p θ ) e ^ rx k ry k 1 [( r p + r s )cotθ] e ^ ry } ϕ ˜ l
ΔX= Im[ r p * r p θ ] k 0 W r ,
ΔY=l Re[ r p * r p θ ] k 0 W r ,
Θ x =(|l|+1) Re[ r p * r p θ ] k 0 Z 0 W r ,
Θ y =0,

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