Abstract

Tiny but universal beam shifts occur when a polarized light beam is reflected upon a planar interface. Although the beam shifts of Gaussian beams have been measured by the weak measurement technique, the weak measurement for orbital angular momentum (OAM)-induced spatial shifts of vortex beams is still missing. Here, by elaborately choosing the preselection and postselection states, the tiny OAM-induced Goos–Hänchen and Imbert–Fedorov shifts are amplified at an air–prism interface. The maximum shifts along directions both parallel and perpendicular to the incident plane are theoretically predicted and experimentally verified with optimal preselection and postselection states. These maximum shifts can be used to determine the OAM of vortex beams.

© 2019 Chinese Laser Press

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]

2019 (1)

X. Zhou, S. Liu, Y. Ding, L. Min, and Z. Luo, “Precise controlling of positive and negative Goos-Hänchen shifts in graphene,” Carbon 149, 604–608 (2019).
[Crossref]

2018 (5)

H. Lin, B. Chen, S. Yang, W. Zhu, J. Yu, H. Guan, and H. Lu, “Photonic spin Hall effect of monolayer black phosphorus in the terahertz region,” Nanophotonics 7, 1929–1937 (2018).
[Crossref]

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

S. Nechayev, M. Neugebauer, M. Vorndran, G. Leuchs, and P. Banzer, “Weak measurement of elliptical dipole moments by C-point splitting,” Phys. Rev. Lett. 121, 243903 (2018).
[Crossref]

Z. Chen, L. Zhuo, W. Zhu, L. Chen, J. Yu, H. Guan, H. Lu, J. Dong, W. Qiu, and Z. Chen, “Measurement of giant spin splitting of reflected Gaussian beams,” IEEE Photon. J. 10, 4500307 (2018).
[Crossref]

L. Zhuo, W. Long, M. Jiang, W. Zhu, H. Guan, J. Tang, J. Yu, H. Lu, J. Zhang, and Z. Chen, “Graphene-based tunable Imbert-Fedorov shifts and orbital angular momentum sidebands for reflected vortex beams in the terahertz region,” Opt. Lett. 43, 2823–2826 (2018).
[Crossref]

2017 (6)

2016 (3)

2014 (3)

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

B. de L. Bertúlio, S. Azevedo, and A. Rosas, “Simplified algebraic description of weak measurements with Hermite-Gaussian and Laguerre-Gaussian pointer states,” Opt. Commun. 331, 194–197 (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, 051130 (2014).
[Crossref]

2013 (2)

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

G. Jayaswal, G. Mistura, and M. Merano, “Weak measurement of the Goos-Hänchen shift,” Opt. Lett. 38, 1232–1234 (2013).
[Crossref]

2012 (6)

W. Löffler, A. Aiello, and J. P. Woerdman, “Observation of orbital angular momentum sidebands due to optical reflection,” Phys. Rev. Lett. 109, 113602 (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, 33–35 (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, 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, 251602 (2012).
[Crossref]

G. Puentes, N. Hermosa, and J. P. Torres, “Weak measurements with orbital-angular-momentum pointer states,” Phys. Rev. Lett. 109, 040401 (2012).
[Crossref]

H. Kobayashi, G. Puentes, and Y. Shikano, “Extracting joint weak values from two-dimensional spatial displacements,” Phys. Rev. A 86, 053805 (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, 023817 (2010).
[Crossref]

2009 (1)

2008 (1)

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

2006 (1)

X. Yin and L. Hesselink, “Goos-Hänchen shift surface plasmon resonance sensor,” Appl. Phys. Lett. 89, 261108 (2006).
[Crossref]

Aiello, A.

K. Y. Bliokh and A. Aiello, “Goos-Hänchen and Imbert-Fedorov beam shifts: an overview,” J. Opt. 15, 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, 113602 (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, 023817 (2010).
[Crossref]

Azevedo, S.

B. de L. Bertúlio, S. Azevedo, and A. Rosas, “Simplified algebraic description of weak measurements with Hermite-Gaussian and Laguerre-Gaussian pointer states,” Opt. Commun. 331, 194–197 (2014).
[Crossref]

Banzer, P.

S. Nechayev, M. Neugebauer, M. Vorndran, G. Leuchs, and P. Banzer, “Weak measurement of elliptical dipole moments by C-point splitting,” Phys. Rev. Lett. 121, 243903 (2018).
[Crossref]

Bliokh, K. Y.

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, 031105 (2017).
[Crossref]

Chen, B.

H. Lin, B. Chen, S. Yang, W. Zhu, J. Yu, H. Guan, and H. Lu, “Photonic spin Hall effect of monolayer black phosphorus in the terahertz region,” Nanophotonics 7, 1929–1937 (2018).
[Crossref]

Chen, L.

Z. Chen, L. Zhuo, W. Zhu, L. Chen, J. Yu, H. Guan, H. Lu, J. Dong, W. Qiu, and Z. Chen, “Measurement of giant spin splitting of reflected Gaussian beams,” IEEE Photon. J. 10, 4500307 (2018).
[Crossref]

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, 031105 (2017).
[Crossref]

Chen, Z.

de L. Bertúlio, B.

B. de L. Bertúlio, S. Azevedo, and A. Rosas, “Simplified algebraic description of weak measurements with Hermite-Gaussian and Laguerre-Gaussian pointer states,” Opt. Commun. 331, 194–197 (2014).
[Crossref]

Dhara, S.

Ding, Y.

X. Zhou, S. Liu, Y. Ding, L. Min, and Z. Luo, “Precise controlling of positive and negative Goos-Hänchen shifts in graphene,” Carbon 149, 604–608 (2019).
[Crossref]

Dong, J.

Z. Chen, L. Zhuo, W. Zhu, L. Chen, J. Yu, H. Guan, H. Lu, J. Dong, W. Qiu, and Z. Chen, “Measurement of giant spin splitting of reflected Gaussian beams,” IEEE Photon. J. 10, 4500307 (2018).
[Crossref]

Du, J.

Ghosh, N.

Goswami, S.

Guan, H.

Hermosa, N.

G. Puentes, N. Hermosa, and J. P. Torres, “Weak measurements with orbital-angular-momentum pointer states,” Phys. Rev. Lett. 109, 040401 (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, 023817 (2010).
[Crossref]

Hesselink, L.

X. Yin and L. Hesselink, “Goos-Hänchen shift surface plasmon resonance sensor,” Appl. Phys. Lett. 89, 261108 (2006).
[Crossref]

Hosten, O.

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

Huang, K.

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

Jayaswal, G.

Jiang, M.

Kivshar, Y. S.

Kobayashi, H.

H. Kobayashi, G. Puentes, and Y. Shikano, “Extracting joint weak values from two-dimensional spatial displacements,” Phys. Rev. A 86, 053805 (2012).
[Crossref]

Kwiat, P.

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

Leuchs, G.

S. Nechayev, M. Neugebauer, M. Vorndran, G. Leuchs, and P. Banzer, “Weak measurement of elliptical dipole moments by C-point splitting,” Phys. Rev. Lett. 121, 243903 (2018).
[Crossref]

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, 051130 (2014).
[Crossref]

Li, Z.

Lin, H.

H. Lin, B. Chen, S. Yang, W. Zhu, J. Yu, H. Guan, and H. Lu, “Photonic spin Hall effect of monolayer black phosphorus in the terahertz region,” Nanophotonics 7, 1929–1937 (2018).
[Crossref]

Ling, X.

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

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

X. Zhou, X. Ling, H. Luo, and S. Wen, “Identifying graphene layers via spin Hall effect of light,” Appl. Phys. Lett. 101, 251602 (2012).
[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, 031105 (2017).
[Crossref]

Liu, S.

X. Zhou, S. Liu, Y. Ding, L. Min, and Z. Luo, “Precise controlling of positive and negative Goos-Hänchen shifts in graphene,” Carbon 149, 604–608 (2019).
[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, 066401 (2017).
[Crossref]

Löffler, W.

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

Long, W.

Lu, H.

Luo, H.

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, 031105 (2017).
[Crossref]

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

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

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

X. Zhou, Z. Xiao, H. Luo, and S. Wen, “Experimental observation of the spin Hall effect of light on a nanometal film via weak measurements,” Phys. Rev. A 85, 043809 (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, 33–35 (2012).
[Crossref]

Luo, L.

Luo, Y.

Luo, Z.

X. Zhou, S. Liu, Y. Ding, L. Min, and Z. Luo, “Precise controlling of positive and negative Goos-Hänchen shifts in graphene,” Carbon 149, 604–608 (2019).
[Crossref]

Merano, M.

G. Jayaswal, G. Mistura, and M. Merano, “Weak measurement of the Goos-Hänchen shift,” Opt. Lett. 38, 1232–1234 (2013).
[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, 023817 (2010).
[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, 031105 (2017).
[Crossref]

Min, L.

X. Zhou, S. Liu, Y. Ding, L. Min, and Z. Luo, “Precise controlling of positive and negative Goos-Hänchen shifts in graphene,” Carbon 149, 604–608 (2019).
[Crossref]

Mistura, G.

Nandi, A.

Nechayev, S.

S. Nechayev, M. Neugebauer, M. Vorndran, G. Leuchs, and P. Banzer, “Weak measurement of elliptical dipole moments by C-point splitting,” Phys. Rev. Lett. 121, 243903 (2018).
[Crossref]

Neugebauer, M.

S. Nechayev, M. Neugebauer, M. Vorndran, G. Leuchs, and P. Banzer, “Weak measurement of elliptical dipole moments by C-point splitting,” Phys. Rev. Lett. 121, 243903 (2018).
[Crossref]

Nori, F.

Pal, M.

Panigrahi, P. K.

Prajapati, C.

Puentes, G.

K. Y. Bliokh, C. T. Samlan, C. Prajapati, G. Puentes, N. K. Viswanathan, and F. Nori, “Spin-Hall effect and circular birefringence of a uniaxial crystal plate,” Optica 3, 1039–1047 (2016).
[Crossref]

H. Kobayashi, G. Puentes, and Y. Shikano, “Extracting joint weak values from two-dimensional spatial displacements,” Phys. Rev. A 86, 053805 (2012).
[Crossref]

G. Puentes, N. Hermosa, and J. P. Torres, “Weak measurements with orbital-angular-momentum pointer states,” Phys. Rev. Lett. 109, 040401 (2012).
[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, 066401 (2017).
[Crossref]

Qiu, J.

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

Qiu, W.

Z. Chen, L. Zhuo, W. Zhu, L. Chen, J. Yu, H. Guan, H. Lu, J. Dong, W. Qiu, and Z. Chen, “Measurement of giant spin splitting of reflected Gaussian beams,” IEEE Photon. J. 10, 4500307 (2018).
[Crossref]

Qiu, X.

Ren, C.

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

Rosas, A.

B. de L. Bertúlio, S. Azevedo, and A. Rosas, “Simplified algebraic description of weak measurements with Hermite-Gaussian and Laguerre-Gaussian pointer states,” Opt. Commun. 331, 194–197 (2014).
[Crossref]

Samlan, C. T.

Shadrivov, I. V.

Sheng, L.

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

Shikano, Y.

H. Kobayashi, G. Puentes, and Y. Shikano, “Extracting joint weak values from two-dimensional spatial displacements,” Phys. Rev. A 86, 053805 (2012).
[Crossref]

Tan, J.

Tang, J.

Torres, J. P.

G. Puentes, N. Hermosa, and J. P. Torres, “Weak measurements with orbital-angular-momentum pointer states,” Phys. Rev. Lett. 109, 040401 (2012).
[Crossref]

Viswanathan, N. K.

Vorndran, M.

S. Nechayev, M. Neugebauer, M. Vorndran, G. Leuchs, and P. Banzer, “Weak measurement of elliptical dipole moments by C-point splitting,” Phys. Rev. Lett. 121, 243903 (2018).
[Crossref]

Wen, S.

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

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, 031105 (2017).
[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, 051130 (2014).
[Crossref]

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

X. Zhou, Z. Xiao, H. Luo, and S. Wen, “Experimental observation of the spin Hall effect of light on a nanometal film via weak measurements,” Phys. Rev. A 85, 043809 (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, 33–35 (2012).
[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, 113602 (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, 023817 (2010).
[Crossref]

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, 33–35 (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, 043809 (2012).
[Crossref]

Xie, L.

Yang, S.

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Figures (8)

Fig. 1.
Fig. 1. (a) Incident (green arrow), preselection (red arrow), and postselection (blue arrow) states of weak-value amplification represented in Poincare sphere. (b) Corresponding polarization angles.
Fig. 2.
Fig. 2. GH and IF shifts of the reflected vortex beam as functions of polarization angles ϕ1 and ϕ2. In the numerical calculation, θ=45°, w0=125  μm.
Fig. 3.
Fig. 3. Comparisons of the contributions of the OAM-dependent and OAM-independent terms in (a) GH and (b) IF shifts when =4, ϕ2=44°.
Fig. 4.
Fig. 4. Maximum OAM-induced (a) GH and (b) IF shifts changing with the incident angle. (c) Polarization angle ϕ0 and (d) optimized angle Δ changing with the incident angle.
Fig. 5.
Fig. 5. Experiment setup for the measurement of OAM-induced shifts by weak technique. Insets show the intensity distributions of the generated vortex beam after aperture and the beam in the image plane of CCD with GH and IF shifts.
Fig. 6.
Fig. 6. Experimental (dots) and theoretical (lines) results of the amplified OAM-induced (a) GH and (b) IF shifts changing with the angle of GLP1 ϕ1.
Fig. 7.
Fig. 7. (a) Comparisons of the experimental (first and third rows) and theoretical (second and fourth rows) intensity patterns of the transmitted beam from GLP2. The amplified OAM-induced (b) GH and (c) IF shifts changing with the incident OAM for ϕ1=179.7° and 180.7°.
Fig. 8.
Fig. 8. Experimental (dots) and theoretical (lines) results of the amplified OAM-induced (a), (c) GH and (b), (d) IF shifts changing with (a), (b) ϕ1 for ϕ2=45° and (c), (d) ϕ2 for ϕ1=163.3°.

Equations (12)

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GH=[0χpχs0],
IF=[γp00γs],
|φf=ψpost|exp[ig(GHP^x+IFP^y)]|ψpre|φi.
Xw=φf|X^|φf=g[Re(AwGH)+Im(AwIF)],
Yw=φf|Y^|φf=g[Re(AwIF)Im(AwIF)],
Xw=k0rp2Im(γp)rs2Im(γs)Δ(rp2+rs2),
Yw=k0rsrp[Im(χp)Im(χs)]Δ(rp2+rs2),
E˜={[α(rpkxk0rp)+βMkyk0]|H+[β(rskxk0rs)+αMkyk0]|V}φ˜,
E˜{[α(rpkxk0rp)+βMkyk0]i[β(rskxk0rs)+αMkyk0]ei2ϕ}φ˜(cosϕ2|H+sinϕ2|V).
Xw={αβrprs[Im(γpei2ϕ2)Im(γsei2ϕ2)]+αβ[rp2Im(γp)+rs2Im(γs)]+rprs[α2Re(γpei2ϕ2)β2Re(γsei2ϕ2)]}/k0W,
Yw={rprs[α2Im(γsei2ϕ2)β2Im(γpei2ϕ2)]+[α2rp2Im(χp)+β2rs2Im(χs)]+αβrprs[Re(χsei2ϕ2)+Re(χpei2ϕ2)]}/k0W,
W=α2rp2+β2rs2+2αβrprssin2ϕ2+(||+1)[(αrpχp)2+(βrsχs)2+2αrpβrsIm(χp*χse2iϕ2)+rp2γp2(α2+β22αβrsin2ϕ)]/k02w02.