Abstract

A pure vortex beam carrying m-order orbital angular momentum (OAM) will be deformed when transmitting through a thin slab, and “neighboring” sideband {m + 1} and {m-1} modes will emerge. The emergence of the OAM sideband is accompanied with OAM-dependent Goos–Hänchen (GH) shift. When the energies carried by the {m} mode of the transmitted beam and by the sideband modes are identical, the OAM-dependent shifts reach their upper limits, |m|w0/2(|m| + 1)1/2, where w0 is the incident beam waist. The epsilon-near-zero metamaterial is found to be suitable to achieve the upper-limited OAM-dependent GH shifts. These findings provide a deeper insight into the beam shifts of vortex beams and have potential applications in the optical sensing, detection of OAM, and other OAM-based applications.

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

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References

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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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2018 (1)

X. Zhou, L. Sheng, and X. Ling, “Photonic spin Hall effect enabled refractive index sensor using weak measurements,” Sci. Rep. 8(1), 1221 (2018).
[Crossref] [PubMed]

2017 (8)

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(6), 066401 (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(3), 031105 (2017).
[Crossref]

W. Zhu, M. Jiang, H. Guan, J. Yu, H. Lu, J. Zhang, and Z. Chen, “Tunable spin splitting of Laguerre–Gaussian beams in graphene metamaterials,” Photon. Res. 5(6), 684 (2017).
[Crossref]

Y. Xiang, X. Jiang, Q. You, J. Guo, and X. Dai, “Enhanced spin Hall effect of reflected light with guided-wave surface plasmon resonance,” Photon. Res. 5(5), 467–472 (2017).
[Crossref]

W. Zhu, L. Zhuo, M. Jiang, H. Guan, J. Yu, H. Lu, Y. Luo, J. Zhang, and Z. Chen, “Controllable symmetric and asymmetric spin splitting of Laguerre-Gaussian beams assisted by surface plasmon resonance,” Opt. Lett. 42(23), 4869–4872 (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]

I. Liberal and N. Engheta, “Near-zero refractive index photonics,” Nat. Photonics 11(3), 149–158 (2017).
[Crossref]

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]

2016 (5)

Y. Li, H. T. Jiang, W. W. Liu, J. Ran, Y. Lai, and H. Chen, “Experimental realization of subwavelength flux manipulation in anisotropic near-zero index metamaterials,” Europhys. Lett. 113(5), 57006 (2016).
[Crossref]

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]

J. Qiu, C. Ren, and Z. Zhang, “Precisely measuring the orbital angular momentum of beams via weak measurement,” Phys. Rev. A 93(6), 063841 (2016).
[Crossref]

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 (4)

X.-T. He, Y.-N. Zhong, Y. Zhou, Z. C. Zhong, and J. W. Dong, “Dirac directional emission in anisotropic zero refractive index photonic crystals,” Sci. Rep. 5(1), 13085 (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]

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]

S. Campione, S. Liu, A. Benz, J. F. Klem, M. B. Sinclair, and I. Brener, “Epsilon-near-zero modes for tailored light-matter interaction,” Phys. Rev. Appl. 4(4), 044011 (2015).
[Crossref]

2014 (2)

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Corrigendum: Hyperbolic metamaterials,” Nat. Photonics 8(1), 78 (2014).
[Crossref]

J. Zhang, X. X. Zhou, X. H. Ling, S. Z. Chen, H. L. Luo, and S. C. Wen, “Orbit-orbit interaction and photonic orbital Hall effect in reflection of a light beam,” Chin. Phys. B 23(6), 064215 (2014).
[Crossref]

2013 (2)

J. B. Götte and M. R. Dennis, “Limits to superweak amplification of beam shifts,” Opt. Lett. 38(13), 2295–2297 (2013).
[Crossref] [PubMed]

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

2012 (3)

J. B. Götte and M. R. Dennis, “Generalized shifts and weak values for polarization components of reflected light beams,” New J. Phys. 14(7), 073016 (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), 053822 (2012).
[Crossref]

W. Löffler, A. Aiello, and J. P. Woerdman, “Observation of orbital angular momentum sidebands due to optical reflection,” Phys. Rev. Lett. 109(11), 113602 (2012).
[Crossref] [PubMed]

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)

2008 (2)

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930 (2008).
[Crossref] [PubMed]

O. Hosten and P. Kwiat, “Observation of the spin hall effect of light via weak measurements,” Science 319(5864), 787–790 (2008).
[Crossref] [PubMed]

2007 (1)

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B 75(15), 155410 (2007).
[Crossref]

1992 (1)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref] [PubMed]

Aiello, A.

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

W. Löffler, A. Aiello, and J. P. Woerdman, “Observation of orbital angular momentum sidebands due to optical reflection,” Phys. Rev. Lett. 109(11), 113602 (2012).
[Crossref] [PubMed]

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]

A. Aiello, M. Merano, and J. P. Woerdman, “Brewster cross polarization,” Opt. Lett. 34(8), 1207–1209 (2009).
[Crossref] [PubMed]

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]

Allen, L.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref] [PubMed]

Alù, A.

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B 75(15), 155410 (2007).
[Crossref]

Bartal, G.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930 (2008).
[Crossref] [PubMed]

Beijersbergen, M. W.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref] [PubMed]

Belov, P.

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Corrigendum: Hyperbolic metamaterials,” Nat. Photonics 8(1), 78 (2014).
[Crossref]

Benz, A.

S. Campione, S. Liu, A. Benz, J. F. Klem, M. B. Sinclair, and I. Brener, “Epsilon-near-zero modes for tailored light-matter interaction,” Phys. Rev. Appl. 4(4), 044011 (2015).
[Crossref]

Bliokh, K. Y.

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

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]

Brener, I.

S. Campione, S. Liu, A. Benz, J. F. Klem, M. B. Sinclair, and I. Brener, “Epsilon-near-zero modes for tailored light-matter interaction,” Phys. Rev. Appl. 4(4), 044011 (2015).
[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(3), 031105 (2017).
[Crossref]

Campione, S.

S. Campione, S. Liu, A. Benz, J. F. Klem, M. B. Sinclair, and I. Brener, “Epsilon-near-zero modes for tailored light-matter interaction,” Phys. Rev. Appl. 4(4), 044011 (2015).
[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. Li, H. T. Jiang, W. W. Liu, J. Ran, Y. Lai, and H. Chen, “Experimental realization of subwavelength flux manipulation in anisotropic near-zero index metamaterials,” Europhys. Lett. 113(5), 57006 (2016).
[Crossref]

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.

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(3), 031105 (2017).
[Crossref]

Chen, S. Z.

J. Zhang, X. X. Zhou, X. H. Ling, S. Z. Chen, H. L. Luo, and S. C. Wen, “Orbit-orbit interaction and photonic orbital Hall effect in reflection of a light beam,” Chin. Phys. B 23(6), 064215 (2014).
[Crossref]

Chen, Z.

Dai, X.

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]

Dennis, M. R.

J. B. Götte and M. R. Dennis, “Limits to superweak amplification of beam shifts,” Opt. Lett. 38(13), 2295–2297 (2013).
[Crossref] [PubMed]

J. B. Götte and M. R. Dennis, “Generalized shifts and weak values for polarization components of reflected light beams,” New J. Phys. 14(7), 073016 (2012).
[Crossref]

Dong, J. W.

X.-T. He, Y.-N. Zhong, Y. Zhou, Z. C. Zhong, and J. W. Dong, “Dirac directional emission in anisotropic zero refractive index photonic crystals,” Sci. Rep. 5(1), 13085 (2015).
[Crossref] [PubMed]

Du, J.

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]

I. Liberal and N. Engheta, “Near-zero refractive index photonics,” Nat. Photonics 11(3), 149–158 (2017).
[Crossref]

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B 75(15), 155410 (2007).
[Crossref]

Götte, J. B.

J. B. Götte and M. R. Dennis, “Limits to superweak amplification of beam shifts,” Opt. Lett. 38(13), 2295–2297 (2013).
[Crossref] [PubMed]

J. B. Götte and M. R. Dennis, “Generalized shifts and weak values for polarization components of reflected light beams,” New J. Phys. 14(7), 073016 (2012).
[Crossref]

Guan, H.

Guo, J.

He, X.-T.

X.-T. He, Y.-N. Zhong, Y. Zhou, Z. C. Zhong, and J. W. Dong, “Dirac directional emission in anisotropic zero refractive index photonic crystals,” Sci. Rep. 5(1), 13085 (2015).
[Crossref] [PubMed]

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]

Hosten, O.

O. Hosten and P. Kwiat, “Observation of the spin hall effect of light via weak measurements,” Science 319(5864), 787–790 (2008).
[Crossref] [PubMed]

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(6), 066401 (2017).
[Crossref] [PubMed]

Iorsh, I.

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Corrigendum: Hyperbolic metamaterials,” Nat. Photonics 8(1), 78 (2014).
[Crossref]

Jiang, H. T.

Y. Li, H. T. Jiang, W. W. Liu, J. Ran, Y. Lai, and H. Chen, “Experimental realization of subwavelength flux manipulation in anisotropic near-zero index metamaterials,” Europhys. Lett. 113(5), 57006 (2016).
[Crossref]

Jiang, M.

Jiang, X.

Kivshar, Y.

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Corrigendum: Hyperbolic metamaterials,” Nat. Photonics 8(1), 78 (2014).
[Crossref]

Klem, J. F.

S. Campione, S. Liu, A. Benz, J. F. Klem, M. B. Sinclair, and I. Brener, “Epsilon-near-zero modes for tailored light-matter interaction,” Phys. Rev. Appl. 4(4), 044011 (2015).
[Crossref]

Kwiat, P.

O. Hosten and P. Kwiat, “Observation of the spin hall effect of light via weak measurements,” Science 319(5864), 787–790 (2008).
[Crossref] [PubMed]

Lai, Y.

Y. Li, H. T. Jiang, W. W. Liu, J. Ran, Y. Lai, and H. Chen, “Experimental realization of subwavelength flux manipulation in anisotropic near-zero index metamaterials,” Europhys. Lett. 113(5), 57006 (2016).
[Crossref]

Li, C.

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]

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]

Y. Li, H. T. Jiang, W. W. Liu, J. Ran, Y. Lai, and H. Chen, “Experimental realization of subwavelength flux manipulation in anisotropic near-zero index metamaterials,” Europhys. Lett. 113(5), 57006 (2016).
[Crossref]

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]

I. Liberal and N. Engheta, “Near-zero refractive index photonics,” Nat. Photonics 11(3), 149–158 (2017).
[Crossref]

Ling, X.

X. Zhou, L. Sheng, and X. Ling, “Photonic spin Hall effect enabled refractive index sensor using weak measurements,” Sci. Rep. 8(1), 1221 (2018).
[Crossref] [PubMed]

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(6), 066401 (2017).
[Crossref] [PubMed]

Ling, X. H.

J. Zhang, X. X. Zhou, X. H. Ling, S. Z. Chen, H. L. Luo, and S. C. Wen, “Orbit-orbit interaction and photonic orbital Hall effect in reflection of a light beam,” Chin. Phys. B 23(6), 064215 (2014).
[Crossref]

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(3), 031105 (2017).
[Crossref]

Liu, S.

S. Campione, S. Liu, A. Benz, J. F. Klem, M. B. Sinclair, and I. Brener, “Epsilon-near-zero modes for tailored light-matter interaction,” Phys. Rev. Appl. 4(4), 044011 (2015).
[Crossref]

Liu, W. W.

Y. Li, H. T. Jiang, W. W. Liu, J. Ran, Y. Lai, and H. Chen, “Experimental realization of subwavelength flux manipulation in anisotropic near-zero index metamaterials,” Europhys. Lett. 113(5), 57006 (2016).
[Crossref]

Liu, X.

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(6), 066401 (2017).
[Crossref] [PubMed]

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930 (2008).
[Crossref] [PubMed]

Liu, Z.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930 (2008).
[Crossref] [PubMed]

Löffler, W.

W. Löffler, A. Aiello, and J. P. Woerdman, “Observation of orbital angular momentum sidebands due to optical reflection,” Phys. Rev. Lett. 109(11), 113602 (2012).
[Crossref] [PubMed]

Lu, H.

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(6), 066401 (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(3), 031105 (2017).
[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), 053822 (2012).
[Crossref]

Luo, H. L.

J. Zhang, X. X. Zhou, X. H. Ling, S. Z. Chen, H. L. Luo, and S. C. Wen, “Orbit-orbit interaction and photonic orbital Hall effect in reflection of a light beam,” Chin. Phys. B 23(6), 064215 (2014).
[Crossref]

Luo, L.

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, 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.

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]

A. Aiello, M. Merano, and J. P. Woerdman, “Brewster cross polarization,” Opt. Lett. 34(8), 1207–1209 (2009).
[Crossref] [PubMed]

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(3), 031105 (2017).
[Crossref]

Poddubny, A.

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Corrigendum: Hyperbolic metamaterials,” Nat. Photonics 8(1), 78 (2014).
[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, 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(6), 066401 (2017).
[Crossref] [PubMed]

Qiu, J.

J. Qiu, C. Ren, and Z. Zhang, “Precisely measuring the orbital angular momentum of beams via weak measurement,” Phys. Rev. A 93(6), 063841 (2016).
[Crossref]

Qiu, X.

Ran, J.

Y. Li, H. T. Jiang, W. W. Liu, J. Ran, Y. Lai, and H. Chen, “Experimental realization of subwavelength flux manipulation in anisotropic near-zero index metamaterials,” Europhys. Lett. 113(5), 57006 (2016).
[Crossref]

Ren, C.

J. Qiu, C. Ren, and Z. Zhang, “Precisely measuring the orbital angular momentum of beams via weak measurement,” Phys. Rev. A 93(6), 063841 (2016).
[Crossref]

Salandrino, A.

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B 75(15), 155410 (2007).
[Crossref]

She, W.

Sheng, L.

X. Zhou, L. Sheng, and X. Ling, “Photonic spin Hall effect enabled refractive index sensor using weak measurements,” Sci. Rep. 8(1), 1221 (2018).
[Crossref] [PubMed]

Silveirinha, M. G.

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B 75(15), 155410 (2007).
[Crossref]

Sinclair, M. B.

S. Campione, S. Liu, A. Benz, J. F. Klem, M. B. Sinclair, and I. Brener, “Epsilon-near-zero modes for tailored light-matter interaction,” Phys. Rev. Appl. 4(4), 044011 (2015).
[Crossref]

Spreeuw, R. J. C.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref] [PubMed]

Stacy, A. M.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930 (2008).
[Crossref] [PubMed]

Sun, C.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930 (2008).
[Crossref] [PubMed]

Tang, T.

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]

Wang, Y.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930 (2008).
[Crossref] [PubMed]

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(6), 066401 (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(3), 031105 (2017).
[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), 053822 (2012).
[Crossref]

Wen, S. C.

J. Zhang, X. X. Zhou, X. H. Ling, S. Z. Chen, H. L. Luo, and S. C. Wen, “Orbit-orbit interaction and photonic orbital Hall effect in reflection of a light beam,” Chin. Phys. B 23(6), 064215 (2014).
[Crossref]

Woerdman, J. P.

W. Löffler, A. Aiello, and J. P. Woerdman, “Observation of orbital angular momentum sidebands due to optical reflection,” Phys. Rev. Lett. 109(11), 113602 (2012).
[Crossref] [PubMed]

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]

A. Aiello, M. Merano, and J. P. Woerdman, “Brewster cross polarization,” Opt. Lett. 34(8), 1207–1209 (2009).
[Crossref] [PubMed]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref] [PubMed]

Xiang, Y.

Xiao, Z.

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), 053822 (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).
[Crossref] [PubMed]

Yao, J.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930 (2008).
[Crossref] [PubMed]

You, Q.

Yu, J.

Zhang, J.

Zhang, X.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930 (2008).
[Crossref] [PubMed]

Zhang, Z.

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]

J. Qiu, C. Ren, and Z. Zhang, “Precisely measuring the orbital angular momentum of beams via weak measurement,” Phys. Rev. A 93(6), 063841 (2016).
[Crossref]

Zhong, Y.-N.

X.-T. He, Y.-N. Zhong, Y. Zhou, Z. C. Zhong, and J. W. Dong, “Dirac directional emission in anisotropic zero refractive index photonic crystals,” Sci. Rep. 5(1), 13085 (2015).
[Crossref] [PubMed]

Zhong, Z. C.

X.-T. He, Y.-N. Zhong, Y. Zhou, Z. C. Zhong, and J. W. Dong, “Dirac directional emission in anisotropic zero refractive index photonic crystals,” Sci. Rep. 5(1), 13085 (2015).
[Crossref] [PubMed]

Zhou, X.

X. Zhou, L. Sheng, and X. Ling, “Photonic spin Hall effect enabled refractive index sensor using weak measurements,” Sci. Rep. 8(1), 1221 (2018).
[Crossref] [PubMed]

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(6), 066401 (2017).
[Crossref] [PubMed]

Zhou, X. X.

J. Zhang, X. X. Zhou, X. H. Ling, S. Z. Chen, H. L. Luo, and S. C. Wen, “Orbit-orbit interaction and photonic orbital Hall effect in reflection of a light beam,” Chin. Phys. B 23(6), 064215 (2014).
[Crossref]

Zhou, Y.

X.-T. He, Y.-N. Zhong, Y. Zhou, Z. C. Zhong, and J. W. Dong, “Dirac directional emission in anisotropic zero refractive index photonic crystals,” Sci. Rep. 5(1), 13085 (2015).
[Crossref] [PubMed]

Zhu, W.

Zhuo, L.

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(3), 031105 (2017).
[Crossref]

Chin. Phys. B (1)

J. Zhang, X. X. Zhou, X. H. Ling, S. Z. Chen, H. L. Luo, and S. C. Wen, “Orbit-orbit interaction and photonic orbital Hall effect in reflection of a light beam,” Chin. Phys. B 23(6), 064215 (2014).
[Crossref]

Europhys. Lett. (1)

Y. Li, H. T. Jiang, W. W. Liu, J. Ran, Y. Lai, and H. Chen, “Experimental realization of subwavelength flux manipulation in anisotropic near-zero index metamaterials,” Europhys. Lett. 113(5), 57006 (2016).
[Crossref]

J. Opt. (1)

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

Nat. Photonics (2)

I. Liberal and N. Engheta, “Near-zero refractive index photonics,” Nat. Photonics 11(3), 149–158 (2017).
[Crossref]

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Corrigendum: Hyperbolic metamaterials,” Nat. Photonics 8(1), 78 (2014).
[Crossref]

New J. Phys. (1)

J. B. Götte and M. R. Dennis, “Generalized shifts and weak values for polarization components of reflected light beams,” New J. Phys. 14(7), 073016 (2012).
[Crossref]

Opt. Commun. (1)

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

Opt. Lett. (5)

Photon. Res. (2)

Phys. Rev. A (4)

J. Qiu, C. Ren, and Z. Zhang, “Precisely measuring the orbital angular momentum of beams via weak measurement,” Phys. Rev. A 93(6), 063841 (2016).
[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), 053822 (2012).
[Crossref]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref] [PubMed]

Phys. Rev. Appl. (1)

S. Campione, S. Liu, A. Benz, J. F. Klem, M. B. Sinclair, and I. Brener, “Epsilon-near-zero modes for tailored light-matter interaction,” Phys. Rev. Appl. 4(4), 044011 (2015).
[Crossref]

Phys. Rev. B (1)

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B 75(15), 155410 (2007).
[Crossref]

Phys. Rev. Lett. (1)

W. Löffler, A. Aiello, and J. P. Woerdman, “Observation of orbital angular momentum sidebands due to optical reflection,” Phys. Rev. Lett. 109(11), 113602 (2012).
[Crossref] [PubMed]

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(6), 066401 (2017).
[Crossref] [PubMed]

Sci. Rep. (4)

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. Zhou, L. Sheng, and X. Ling, “Photonic spin Hall effect enabled refractive index sensor using weak measurements,” Sci. Rep. 8(1), 1221 (2018).
[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]

X.-T. He, Y.-N. Zhong, Y. Zhou, Z. C. Zhong, and J. W. Dong, “Dirac directional emission in anisotropic zero refractive index photonic crystals,” Sci. Rep. 5(1), 13085 (2015).
[Crossref] [PubMed]

Science (4)

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]

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]

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930 (2008).
[Crossref] [PubMed]

O. Hosten and P. Kwiat, “Observation of the spin hall effect of light via weak measurements,” Science 319(5864), 787–790 (2008).
[Crossref] [PubMed]

Other (1)

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Figures (6)

Fig. 1
Fig. 1 (a) The centroid of a vortex beam will shift along x axis when transmitted through a three-layer barrier structure. (b) When transmitted through the three-layer barrier structure, a linearly polarized LG beam | ϕ 0 3 will be distorted, and the transmitted beam can be considered as a superposition of LG | ϕ 0 4 , | ϕ 0 3 , | ϕ 0 2 , and | ϕ 1 2 modes.
Fig. 2
Fig. 2 (a) The normalized m-GH shift ΔXm up changing with the incident angle θ and initial amplitude ratio β when m = 1. (b) The m-GH shift ΔXm up changing with β for m = ± 1 when θ = 5° (red), 10° (blue), 30° (green), respectively.
Fig. 3
Fig. 3 The normalized m-GH shifts ΔXm up (a) and energies of LG modes of the transmitted beam (b) changing with the thickness of ENZ metamaterial d when θ = 10°, β = −0.07, m = 3. The energies of different LG modes normalized by the total energy of the transmitted beam.
Fig. 4
Fig. 4 (a) The spatial GH shift X shift changing with incident OAM m when θ = 6°, β = 0 (red circles), θ = 6°, β = 0.3 (green circles), and θ = 10°, β = −0.052 (blue circles), respectively. (b) The intensity profiles of the transmitted beam along x axis for m = −5:5, when θ = 10°, β = −0.052.
Fig. 5
Fig. 5 The energies of OAM modes of the transmitted beam for different incident OAM m when θ = 10° and β = −0.052. (a) Three-dimensional bar graph, (b) Two-dimensional pseudocolor plot.
Fig. 6
Fig. 6 The Numerical verification of the theoretically predicted m-GH shifts. The normalized intensity distributions in xgzg plane for m = 1, and β = 0.2 (a) and −0.2 (b), respectively. (c) The comparison of the analytical results (solid lines) and numerical results (circles) on the GH shifts ΔX. The two insets in (c) are the intensity distributions in xy plane for θ = 8° and β = ± 0.2, respectively.

Equations (12)

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

E ˜ t = γ = p , s α γ t γ [ | ϕ ˜ 0 m ( X γ k x + Y γ k y ) / k d | ϕ ˜ 0 m ] | Γ γ . ,
t p = 4 k z e k z d ε o ε d exp [ i k z e d ] [ k z e ε d + k z d ε o ] 2 [ k z e ε d k z d ε o ] 2 exp [ i 2 k z e d ] ,
t s = 4 k z o k z d exp [ i k z o d ] [ k z o + k z d ] 2 [ k z o k z d ] 2 exp [ i 2 k z o d ] ,
E t = γ = p , s α γ t γ { ϕ 0 m + θ 0 2 2 ( | m | + 1 ) [ ( | m | + 1 ) Z γ sgn [ m ] | ϕ 0 sgn [ m ] ( | m | + 1 ) | m | Z γ sgn [ m ] | ϕ 0 sgn [ m ] ( | m | 1 ) Z γ sgn [ m ] | ϕ 1 sgn [ m ] ( | m | 1 ) ] } | Γ γ ,
Δ X = γ = p , s | α γ t γ | 2 [ Re ( X γ ) + m Im ( Y γ ) ] / ( k 0 W ) ,
W = γ = p , s | α γ t γ | 2 { 1 + θ 0 2 [ | X γ | 2 + | Y γ | 2 ] / 4 } ,
Δ X m = 1 k d β cos δ [ | t p | 2 | t s | 2 ] cot θ | t p | 2 + β 2 | t s | 2 + θ 0 2 4 [ | t p ' | 2 + β 2 | t s ' | 2 + ( 1 + β 2 ) | M | 2 ] .
Δ X m , p k ± = ± m ( | t p | 2 | t s | 2 ) cot θ 2 k d | t p | 2 + θ 0 2 [ | t p ' | 2 + | M | 2 ] / 4 | t s | 2 + θ 0 2 [ | t s ' | 2 + | M | 2 ] / 4 ,
β p k ± ( θ ) = ± | t p | 2 + θ 0 2 [ | t p ' | 2 + | M | 2 ] / 4 | t s | 2 + θ 0 2 [ | t s ' | 2 + | M | 2 ] / 4 .
Δ X m , p k ± m w 0 2 | m | + 1 1 1 + | t p ' / t s cot θ | 2 .
E t = α p k d w 0 { | t s cot θ | | m | + 1 | ϕ 0 m sgn [ m ] t s cot θ [ | m | + 1 | ϕ 0 sgn [ m ] ( | m + 1 ) + | m | | ϕ 0 sgn [ m ] ( | m | 1 ) + | ϕ 1 sgn [ m ] ( | m | 1 ) ] / 2 } | V .
C m , 0 m , 0 = 2 C m , 0 sgn [ m ] ( | m | + 1 ) , 0 = 2 [ C m , 0 sgn [ m ] ( | m | 1 ) , 1 + C m , 0 sgn [ m ] ( | m | 1 ) , 0 ] .

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