Abstract

Expressions of Goos-Hänchen and Imbert-Fedorov shifts of rotational 2-D finite energy Airy beams are introduced in this paper. The influences of the second-order terms of the reflection coefficient on the spatial Goos-Hänchen shift (GHS) and spatial Imbert-Fedorov shift (IFS) of rotational 2-D finite energy Airy beams are theoretically and numerically investigated at the surface between air and weakly absorbing medium for the first time. It is found that the axial symmetry of the initial field of beams has huge influences on GHS and IFS and both of the GHS and IFS can be controlled by adjusting the rotation angle of the initial field distribution.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2019 (4)

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

H. Lin, M. Jiang, L. Zhuo, W. Zhu, H. Guan, J. Yu, H. Lu, J. Tan, J. Zhang, and Z. Chen, “Enhanced imbert-fedorov shifts of higher-order laguerre-gaussian beams by lossy mode resonance,” Opt. Commun. 431, 136–141 (2019).
[Crossref]

H. Li, M. Tang, J. Wang, J. Cao, and X. Li, “Spin hall effect of airy beam in inhomogeneous medium,” Appl. Phys. B 125(3), 51 (2019).
[Crossref]

K. Y. Bliokh, C. Prajapati, C. T. Samlan, N. K. Viswanathan, and F. Nori, “Spin-hall effect of light at a tilted polarizer,” Opt. Lett. 44(19), 4781–4784 (2019).
[Crossref]

2018 (4)

2017 (2)

2016 (2)

V. J. Yallapragada, A. P. Ravishankar, G. L. Mulay, G. S. Agarwal, and V. G. Achanta, “Observation of giant goos-hänchen and angular shifts at designed metasurfaces,” Sci. Rep. 6(1), 19319 (2016).
[Crossref]

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(10), 1039–1047 (2016).
[Crossref]

2015 (2)

2014 (3)

2013 (2)

O. Marco and A. Andrea, “Goos-hänchen and imbert-fedorov shifts for bounded wavepackets of light,” J. Opt. 15(1), 014004 (2013).
[Crossref]

M. C. Beeler, R. A. Williams, K. Jiménez-García, L. J. LeBlanc, A. R. Perry, and I. B. Spielman, “The spin hall effect in a quantum gas,” Nature 498(7453), 201–204 (2013).
[Crossref]

2012 (3)

C. Prajapati and D. Ranganathan, “Goos-hänchen and imbert-fedorov shifts for hermite-gauss beams,” J. Opt. Soc. Am. A 29(7), 1377–1382 (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]

X.-H. Ling, H.-L. Luo, M. Tang, and S.-C. Wen, “Enhanced and tunable spin hall effect of light upon reflection of one-dimensional photonic crystal with a defect layer,” Chin. Phys. Lett. 29(7), 074209 (2012).
[Crossref]

2011 (2)

A. Aiello and J. P. Woerdman, “Goos-hänchen and imbert-fedorov shifts of a nondiffracting bessel beam,” Opt. Lett. 36(4), 543–545 (2011).
[Crossref]

D. Golla and S. D. Gupta, “Goos-hänchen shift for higher-order hermite-gaussian beams,” Pramana 76(4), 603–612 (2011).
[Crossref]

2009 (1)

K. Y. Bliokh and A. S. Desyatnikov, “Spin and orbital hall effects for diffracting optical beams in gradient-index media,” Phys. Rev. A 79(1), 011807 (2009).
[Crossref]

2008 (2)

2007 (2)

C.-F. Li, “Unified theory for goos-hänchen and imbert-fedorov effects,” Phys. Rev. A 76(1), 013811 (2007).
[Crossref]

K. Y. Bliokh and Y. P. Bliokh, “Polarization, transverse shifts, and angular momentum conservation laws in partial reflection and refraction of an electromagnetic wave packet,” Phys. Rev. E 75(6), 066609 (2007).
[Crossref]

2006 (1)

2005 (1)

2002 (1)

2000 (1)

1995 (1)

O. Emile, T. Galstyan, F. A. Le, and F. Bretenaker, “Measurement of the nonlinear goos-hänchen effect for gaussian optical beams,” Phys. Rev. Lett. 75(8), 1511–1513 (1995).
[Crossref]

1987 (1)

M. Player, “Angular momentum balance and transverse shifts on reflection of light,” J. Phys. A: Math. Gen. 20(12), 3667–3678 (1987).
[Crossref]

1972 (1)

O. C. de Beauregard and C. Imbert, “Quantized longitudinal and transverse shifts associated with total internal reflection,” Phys. Rev. Lett. 28(18), 1211–1213 (1972).
[Crossref]

1948 (1)

K. Artmann, “Berechnung der seitenversetzung des totalreflektierten strahles,” Ann. Phys. 437(1-2), 87–102 (1948).
[Crossref]

1947 (1)

F. Goos and H. Hänchen, “Ein neuer und fundamentaler versuch zur totalreflexion,” Ann. Phys. 436(7-8), 333–346 (1947).
[Crossref]

Aceves, A. B.

Achanta, V. G.

V. J. Yallapragada, A. P. Ravishankar, G. L. Mulay, G. S. Agarwal, and V. G. Achanta, “Observation of giant goos-hänchen and angular shifts at designed metasurfaces,” Sci. Rep. 6(1), 19319 (2016).
[Crossref]

Agarwal, G. S.

V. J. Yallapragada, A. P. Ravishankar, G. L. Mulay, G. S. Agarwal, and V. G. Achanta, “Observation of giant goos-hänchen and angular shifts at designed metasurfaces,” Sci. Rep. 6(1), 19319 (2016).
[Crossref]

Aiello, A.

Andrea, A.

O. Marco and A. Andrea, “Goos-hänchen and imbert-fedorov shifts for bounded wavepackets of light,” J. Opt. 15(1), 014004 (2013).
[Crossref]

Artmann, K.

K. Artmann, “Berechnung der seitenversetzung des totalreflektierten strahles,” Ann. Phys. 437(1-2), 87–102 (1948).
[Crossref]

Baida, F. I.

Beeler, M. C.

M. C. Beeler, R. A. Williams, K. Jiménez-García, L. J. LeBlanc, A. R. Perry, and I. B. Spielman, “The spin hall effect in a quantum gas,” Nature 498(7453), 201–204 (2013).
[Crossref]

Bliokh, K. Y.

K. Y. Bliokh, C. Prajapati, C. T. Samlan, N. K. Viswanathan, and F. Nori, “Spin-hall effect of light at a tilted polarizer,” Opt. Lett. 44(19), 4781–4784 (2019).
[Crossref]

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(10), 1039–1047 (2016).
[Crossref]

K. Y. Bliokh and A. S. Desyatnikov, “Spin and orbital hall effects for diffracting optical beams in gradient-index media,” Phys. Rev. A 79(1), 011807 (2009).
[Crossref]

K. Y. Bliokh and Y. P. Bliokh, “Polarization, transverse shifts, and angular momentum conservation laws in partial reflection and refraction of an electromagnetic wave packet,” Phys. Rev. E 75(6), 066609 (2007).
[Crossref]

Bliokh, Y. P.

K. Y. Bliokh and Y. P. Bliokh, “Polarization, transverse shifts, and angular momentum conservation laws in partial reflection and refraction of an electromagnetic wave packet,” Phys. Rev. E 75(6), 066609 (2007).
[Crossref]

Born, M.

M. Born and E. Wolf, Principles of optics: electromagnetic theory of propagation, interference and diffraction of light (Elsevier, 2013).

Bretenaker, F.

O. Emile, T. Galstyan, F. A. Le, and F. Bretenaker, “Measurement of the nonlinear goos-hänchen effect for gaussian optical beams,” Phys. Rev. Lett. 75(8), 1511–1513 (1995).
[Crossref]

Broky, J.

Cai, L.

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]

Cao, J.

H. Li, M. Tang, J. Wang, J. Cao, and X. Li, “Spin hall effect of airy beam in inhomogeneous medium,” Appl. Phys. B 125(3), 51 (2019).
[Crossref]

Cen, H.

Chamorro-Posada, P.

Chan, S. W.

Chen, H.

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]

Chen, Z.

H. Lin, M. Jiang, L. Zhuo, W. Zhu, H. Guan, J. Yu, H. Lu, J. Tan, J. Zhang, and Z. Chen, “Enhanced imbert-fedorov shifts of higher-order laguerre-gaussian beams by lossy mode resonance,” Opt. Commun. 431, 136–141 (2019).
[Crossref]

Chern, R.-L.

Christodoulides, D. N.

Cisowski, C. M.

Conti, C.

Correia, R. R. B.

Dai, X.

L. Jiang, J. Wu, X. Dai, and Y. Xiang, “Comparison of goos-hänchen shifts of the reflected beam from graphene on dielectrics and metals,” Optik 125(23), 7025–7029 (2014).
[Crossref]

de Beauregard, O. C.

O. C. de Beauregard and C. Imbert, “Quantized longitudinal and transverse shifts associated with total internal reflection,” Phys. Rev. Lett. 28(18), 1211–1213 (1972).
[Crossref]

Desyatnikov, A. S.

K. Y. Bliokh and A. S. Desyatnikov, “Spin and orbital hall effects for diffracting optical beams in gradient-index media,” Phys. Rev. A 79(1), 011807 (2009).
[Crossref]

Ding, Y.

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

Dogariu, A.

Dong, H.

Emile, O.

O. Emile, T. Galstyan, F. A. Le, and F. Bretenaker, “Measurement of the nonlinear goos-hänchen effect for gaussian optical beams,” Phys. Rev. Lett. 75(8), 1511–1513 (1995).
[Crossref]

Farmani, A.

Fedorov, F. I.

F. I. Fedorov, “K teorii polnogo otrazheniya,” Doklady Akademii Nauk SSSR 105, 465–468 (1955).

Galstyan, T.

O. Emile, T. Galstyan, F. A. Le, and F. Bretenaker, “Measurement of the nonlinear goos-hänchen effect for gaussian optical beams,” Phys. Rev. Lett. 75(8), 1511–1513 (1995).
[Crossref]

Golla, D.

D. Golla and S. D. Gupta, “Goos-hänchen shift for higher-order hermite-gaussian beams,” Pramana 76(4), 603–612 (2011).
[Crossref]

Goos, F.

F. Goos and H. Hänchen, “Ein neuer und fundamentaler versuch zur totalreflexion,” Ann. Phys. 436(7-8), 333–346 (1947).
[Crossref]

Grosche, S.

Guan, H.

H. Lin, M. Jiang, L. Zhuo, W. Zhu, H. Guan, J. Yu, H. Lu, J. Tan, J. Zhang, and Z. Chen, “Enhanced imbert-fedorov shifts of higher-order laguerre-gaussian beams by lossy mode resonance,” Opt. Commun. 431, 136–141 (2019).
[Crossref]

Gupta, S. D.

D. Golla and S. D. Gupta, “Goos-hänchen shift for higher-order hermite-gaussian beams,” Pramana 76(4), 603–612 (2011).
[Crossref]

Hänchen, H.

F. Goos and H. Hänchen, “Ein neuer und fundamentaler versuch zur totalreflexion,” Ann. Phys. 436(7-8), 333–346 (1947).
[Crossref]

He, J.

He, S.

Imbert, C.

O. C. de Beauregard and C. Imbert, “Quantized longitudinal and transverse shifts associated with total internal reflection,” Phys. Rev. Lett. 28(18), 1211–1213 (1972).
[Crossref]

Jiang, L.

L. Jiang, J. Wu, X. Dai, and Y. Xiang, “Comparison of goos-hänchen shifts of the reflected beam from graphene on dielectrics and metals,” Optik 125(23), 7025–7029 (2014).
[Crossref]

Jiang, M.

H. Lin, M. Jiang, L. Zhuo, W. Zhu, H. Guan, J. Yu, H. Lu, J. Tan, J. Zhang, and Z. Chen, “Enhanced imbert-fedorov shifts of higher-order laguerre-gaussian beams by lossy mode resonance,” Opt. Commun. 431, 136–141 (2019).
[Crossref]

Jiménez-García, K.

M. C. Beeler, R. A. Williams, K. Jiménez-García, L. J. LeBlanc, A. R. Perry, and I. B. Spielman, “The spin hall effect in a quantum gas,” Nature 498(7453), 201–204 (2013).
[Crossref]

Lai, H. M.

Le, F. A.

O. Emile, T. Galstyan, F. A. Le, and F. Bretenaker, “Measurement of the nonlinear goos-hänchen effect for gaussian optical beams,” Phys. Rev. Lett. 75(8), 1511–1513 (1995).
[Crossref]

LeBlanc, L. J.

M. C. Beeler, R. A. Williams, K. Jiménez-García, L. J. LeBlanc, A. R. Perry, and I. B. Spielman, “The spin hall effect in a quantum gas,” Nature 498(7453), 201–204 (2013).
[Crossref]

Li, C.-F.

C.-F. Li, “Unified theory for goos-hänchen and imbert-fedorov effects,” Phys. Rev. A 76(1), 013811 (2007).
[Crossref]

Li, H.

H. Li, M. Tang, J. Wang, J. Cao, and X. Li, “Spin hall effect of airy beam in inhomogeneous medium,” Appl. Phys. B 125(3), 51 (2019).
[Crossref]

Li, X.

H. Li, M. Tang, J. Wang, J. Cao, and X. Li, “Spin hall effect of airy beam in inhomogeneous medium,” Appl. Phys. B 125(3), 51 (2019).
[Crossref]

Liang, R.

Lin, H.

H. Lin, M. Jiang, L. Zhuo, W. Zhu, H. Guan, J. Yu, H. Lu, J. Tan, J. Zhang, and Z. Chen, “Enhanced imbert-fedorov shifts of higher-order laguerre-gaussian beams by lossy mode resonance,” Opt. Commun. 431, 136–141 (2019).
[Crossref]

Lin, N.

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]

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]

Ling, X.-H.

X.-H. Ling, H.-L. Luo, M. Tang, and S.-C. Wen, “Enhanced and tunable spin hall effect of light upon reflection of one-dimensional photonic crystal with a defect layer,” Chin. Phys. Lett. 29(7), 074209 (2012).
[Crossref]

Liu, M.

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, S.

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

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.

H. Lin, M. Jiang, L. Zhuo, W. Zhu, H. Guan, J. Yu, H. Lu, J. Tan, J. Zhang, and Z. Chen, “Enhanced imbert-fedorov shifts of higher-order laguerre-gaussian beams by lossy mode resonance,” Opt. Commun. 431, 136–141 (2019).
[Crossref]

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]

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]

Luo, H.-L.

X.-H. Ling, H.-L. Luo, M. Tang, and S.-C. Wen, “Enhanced and tunable spin hall effect of light upon reflection of one-dimensional photonic crystal with a defect layer,” Chin. Phys. Lett. 29(7), 074209 (2012).
[Crossref]

Luo, Z.

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

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[Crossref]

McDonald, G. S.

Meng, H.

Min, L.

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

Miri, M.

Mulay, G. L.

V. J. Yallapragada, A. P. Ravishankar, G. L. Mulay, G. S. Agarwal, and V. G. Achanta, “Observation of giant goos-hänchen and angular shifts at designed metasurfaces,” Sci. Rep. 6(1), 19319 (2016).
[Crossref]

Nori, F.

Ornigotti, M.

Perry, A. R.

M. C. Beeler, R. A. Williams, K. Jiménez-García, L. J. LeBlanc, A. R. Perry, and I. B. Spielman, “The spin hall effect in a quantum gas,” Nature 498(7453), 201–204 (2013).
[Crossref]

Player, M.

M. Player, “Angular momentum balance and transverse shifts on reflection of light,” J. Phys. A: Math. Gen. 20(12), 3667–3678 (1987).
[Crossref]

Prajapati, C.

Puentes, G.

Ranganathan, D.

Ravishankar, A. P.

V. J. Yallapragada, A. P. Ravishankar, G. L. Mulay, G. S. Agarwal, and V. G. Achanta, “Observation of giant goos-hänchen and angular shifts at designed metasurfaces,” Sci. Rep. 6(1), 19319 (2016).
[Crossref]

Samlan, C. T.

Sánchez-Curto, J.

Sheikhi, M. H.

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]

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).
[Crossref]

Siviloglou, G. A.

Spielman, I. B.

M. C. Beeler, R. A. Williams, K. Jiménez-García, L. J. LeBlanc, A. R. Perry, and I. B. Spielman, “The spin hall effect in a quantum gas,” Nature 498(7453), 201–204 (2013).
[Crossref]

Szameit, A.

Tan, J.

H. Lin, M. Jiang, L. Zhuo, W. Zhu, H. Guan, J. Yu, H. Lu, J. Tan, J. Zhang, and Z. Chen, “Enhanced imbert-fedorov shifts of higher-order laguerre-gaussian beams by lossy mode resonance,” Opt. Commun. 431, 136–141 (2019).
[Crossref]

Tang, M.

H. Li, M. Tang, J. Wang, J. Cao, and X. Li, “Spin hall effect of airy beam in inhomogeneous medium,” Appl. Phys. B 125(3), 51 (2019).
[Crossref]

X.-H. Ling, H.-L. Luo, M. Tang, and S.-C. Wen, “Enhanced and tunable spin hall effect of light upon reflection of one-dimensional photonic crystal with a defect layer,” Chin. Phys. Lett. 29(7), 074209 (2012).
[Crossref]

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Vigoureux, J.-M.

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H. Li, M. Tang, J. Wang, J. Cao, and X. Li, “Spin hall effect of airy beam in inhomogeneous medium,” Appl. Phys. B 125(3), 51 (2019).
[Crossref]

Wang, L.

Wei, Z.

Wen, 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]

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).
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X.-H. Ling, H.-L. Luo, M. Tang, and S.-C. Wen, “Enhanced and tunable spin hall effect of light upon reflection of one-dimensional photonic crystal with a defect layer,” Chin. Phys. Lett. 29(7), 074209 (2012).
[Crossref]

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M. C. Beeler, R. A. Williams, K. Jiménez-García, L. J. LeBlanc, A. R. Perry, and I. B. Spielman, “The spin hall effect in a quantum gas,” Nature 498(7453), 201–204 (2013).
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A. Aiello and H. Woerdman, “The reflection of a maxwell-gaussian beam by a planar surface,” arXiv preprint arXiv:0710.1643 (2007).

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A. Aiello and J. Woerdman, “Theory of angular goos-hänchen shift near brewster incidence,” arXiv preprint arXiv:0903.3730 (2009).

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L. Mandel and E. Wolf, Optical coherence and quantum optics (Cambridge University Press, 1995).

M. Born and E. Wolf, Principles of optics: electromagnetic theory of propagation, interference and diffraction of light (Elsevier, 2013).

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L. Jiang, J. Wu, X. Dai, and Y. Xiang, “Comparison of goos-hänchen shifts of the reflected beam from graphene on dielectrics and metals,” Optik 125(23), 7025–7029 (2014).
[Crossref]

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L. Jiang, J. Wu, X. Dai, and Y. Xiang, “Comparison of goos-hänchen shifts of the reflected beam from graphene on dielectrics and metals,” Optik 125(23), 7025–7029 (2014).
[Crossref]

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V. J. Yallapragada, A. P. Ravishankar, G. L. Mulay, G. S. Agarwal, and V. G. Achanta, “Observation of giant goos-hänchen and angular shifts at designed metasurfaces,” Sci. Rep. 6(1), 19319 (2016).
[Crossref]

Yi, J.

Yu, J.

H. Lin, M. Jiang, L. Zhuo, W. Zhu, H. Guan, J. Yu, H. Lu, J. Tan, J. Zhang, and Z. Chen, “Enhanced imbert-fedorov shifts of higher-order laguerre-gaussian beams by lossy mode resonance,” Opt. Commun. 431, 136–141 (2019).
[Crossref]

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H. Lin, M. Jiang, L. Zhuo, W. Zhu, H. Guan, J. Yu, H. Lu, J. Tan, J. Zhang, and Z. Chen, “Enhanced imbert-fedorov shifts of higher-order laguerre-gaussian beams by lossy mode resonance,” Opt. Commun. 431, 136–141 (2019).
[Crossref]

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

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]

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]

Zhu, S.

Zhu, W.

H. Lin, M. Jiang, L. Zhuo, W. Zhu, H. Guan, J. Yu, H. Lu, J. Tan, J. Zhang, and Z. Chen, “Enhanced imbert-fedorov shifts of higher-order laguerre-gaussian beams by lossy mode resonance,” Opt. Commun. 431, 136–141 (2019).
[Crossref]

Zhuo, L.

H. Lin, M. Jiang, L. Zhuo, W. Zhu, H. Guan, J. Yu, H. Lu, J. Tan, J. Zhang, and Z. Chen, “Enhanced imbert-fedorov shifts of higher-order laguerre-gaussian beams by lossy mode resonance,” Opt. Commun. 431, 136–141 (2019).
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Appl. Phys. B (1)

H. Li, M. Tang, J. Wang, J. Cao, and X. Li, “Spin hall effect of airy beam in inhomogeneous medium,” Appl. Phys. B 125(3), 51 (2019).
[Crossref]

Appl. Phys. Lett. (1)

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]

Carbon (1)

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

Chin. Phys. Lett. (1)

X.-H. Ling, H.-L. Luo, M. Tang, and S.-C. Wen, “Enhanced and tunable spin hall effect of light upon reflection of one-dimensional photonic crystal with a defect layer,” Chin. Phys. Lett. 29(7), 074209 (2012).
[Crossref]

J. Opt. (1)

O. Marco and A. Andrea, “Goos-hänchen and imbert-fedorov shifts for bounded wavepackets of light,” J. Opt. 15(1), 014004 (2013).
[Crossref]

J. Opt. Soc. Am. A (2)

J. Opt. Soc. Am. B (2)

J. Phys. A: Math. Gen. (1)

M. Player, “Angular momentum balance and transverse shifts on reflection of light,” J. Phys. A: Math. Gen. 20(12), 3667–3678 (1987).
[Crossref]

Nature (1)

M. C. Beeler, R. A. Williams, K. Jiménez-García, L. J. LeBlanc, A. R. Perry, and I. B. Spielman, “The spin hall effect in a quantum gas,” Nature 498(7453), 201–204 (2013).
[Crossref]

Opt. Commun. (1)

H. Lin, M. Jiang, L. Zhuo, W. Zhu, H. Guan, J. Yu, H. Lu, J. Tan, J. Zhang, and Z. Chen, “Enhanced imbert-fedorov shifts of higher-order laguerre-gaussian beams by lossy mode resonance,” Opt. Commun. 431, 136–141 (2019).
[Crossref]

Opt. Express (2)

Opt. Lett. (10)

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A. Aiello and J. P. Woerdman, “Role of beam propagation in goos-hänchen and imbert-fedorov shifts,” Opt. Lett. 33(13), 1437–1439 (2008).
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A. Aiello and J. P. Woerdman, “Goos-hänchen and imbert-fedorov shifts of a nondiffracting bessel beam,” Opt. Lett. 36(4), 543–545 (2011).
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C. M. Cisowski and R. R. B. Correia, “Splitting an optical vortex beam to study photonic orbit-orbit interactions,” Opt. Lett. 43(3), 499–502 (2018).
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M. Ornigotti, “Goos-hänchen and imbert-fedorov shifts for airy beams,” Opt. Lett. 43(6), 1411–1414 (2018).
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Opt. Mater. Express (1)

Optica (1)

Optik (1)

L. Jiang, J. Wu, X. Dai, and Y. Xiang, “Comparison of goos-hänchen shifts of the reflected beam from graphene on dielectrics and metals,” Optik 125(23), 7025–7029 (2014).
[Crossref]

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]

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K. Y. Bliokh and Y. P. Bliokh, “Polarization, transverse shifts, and angular momentum conservation laws in partial reflection and refraction of an electromagnetic wave packet,” Phys. Rev. E 75(6), 066609 (2007).
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Sci. Rep. (2)

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]

V. J. Yallapragada, A. P. Ravishankar, G. L. Mulay, G. S. Agarwal, and V. G. Achanta, “Observation of giant goos-hänchen and angular shifts at designed metasurfaces,” Sci. Rep. 6(1), 19319 (2016).
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A. Aiello and J. Woerdman, “Theory of angular goos-hänchen shift near brewster incidence,” arXiv preprint arXiv:0903.3730 (2009).

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A. Aiello and H. Woerdman, “The reflection of a maxwell-gaussian beam by a planar surface,” arXiv preprint arXiv:0710.1643 (2007).

L. Mandel and E. Wolf, Optical coherence and quantum optics (Cambridge University Press, 1995).

M. Born and E. Wolf, Principles of optics: electromagnetic theory of propagation, interference and diffraction of light (Elsevier, 2013).

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Figures (6)

Fig. 1.
Fig. 1. Schematic diagram of GH and IF shifts reflecting from the surface between air and weakly absorbing medium. $\varepsilon _0$ and $\varepsilon _1$ represent the dielectric constant of air and weakly absorbing medium respectively.
Fig. 2.
Fig. 2. The influence of high order Taylor expansion terms in denominator on GH and IF shifts for $\alpha =\beta = 0.1$(solid line), $0.01$(dashed line) and $0.001$(dotted line).
Fig. 3.
Fig. 3. (a) Analytic GHS of finite energy Airy beams(solid line), numerical GHS of finite energy Airy beams(’$\times$’ symbol) and analytic GHS of Gaussian beams(dashed line). (b) Analytic IFS of finite energy Airy beams(solid line) and numerical IFS of finite energy Airy beams (’$\times$’ symbol).
Fig. 4.
Fig. 4. (a)-(d) Intensity of finite energy Airy beams at the initial incident plane rotated around the origin for $0^\circ$, $45^\circ$, $-45^\circ$ and $-90^\circ$, respectively. (e) Dependence of GH shifts on the incident angle for different rotation angles of $0^\circ$(solid line), $45^\circ$(dash line), $-45^\circ$(dotted line) and $-90^\circ$(dash-dotted line) respectively.
Fig. 5.
Fig. 5. (a)-(d) Intensity of finite energy Airy beams at the initial incident plane rotated around the origin for $0^\circ$, $-45^\circ$, $90^\circ$ and $135^\circ$ respectively. (e) Dependence of GH shifts on the incident angle for different rotation angles of $0^\circ$(solid line), $-45^\circ$(dashed line), $90^\circ$(dotted line) and $135^\circ$(dash-dotted line) respectively.
Fig. 6.
Fig. 6. The GHS (a) and IFS (b) as a function of the rotation angle when the incident angle is the Brewster angle.

Equations (30)

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

E μ ( r μ ) = 1 2 π E ~ μ ( k μ ) e i ( k μ r μ ) d k x μ d k y μ ,
E I ( k 0 r I ) = k 0 2 2 π E ~ I ( U , V ; θ ) e i ( U X ^ I + V Y ^ I + W Z ^ I ) d U d V ,
E R ( k 0 r R ) = k 0 2 2 π E ~ R ( U , V ; θ ) e i ( U X ^ R + V Y ^ R + W Z ^ R ) d U d V ,
E ~ μ ( U , V ; θ ) = λ p , s e ^ λ ( k μ ) α λ ( U , V ; θ ) A ~ μ ( U , V ; θ ) ,
e ^ p ( k μ ) = e ^ s ( k μ ) × k μ | e ^ s ( k μ ) × k μ | , e ^ s ( k μ ) = z ^ × k μ | z ^ × k μ | .
r λ ( U , V ; θ ) r λ + U r λ + 1 2 U 2 r λ + 1 2 V 2 r λ ,
X ¯ = X R | E R ( k 0 r R ) | 2 d X R d Y R | E R ( k 0 r R ) | 2 d X R d Y R X I | E I ( k 0 r I ) | 2 d X I d Y I | E I ( k 0 r I ) | 2 d X I d Y I ,
Y ¯ = Y R | E R ( k 0 r R ) | 2 d X R d Y R | E R ( k 0 r R ) | 2 d X R d Y R Y I | E I ( k 0 r I ) | 2 d X I d Y I | E I ( k 0 r I ) | 2 d X I d Y I .
X ¯ R = I m [ E ~ R U E ~ R ] d U d V | E ~ R | 2 d U d V ( Z R + Z I ) U W | E ~ R | 2 d U d V | E ~ R | 2 d U d V ,
X ¯ I = I m [ E ~ I U E ~ I ] d U d V | E ~ I | 2 d U d V Z I U W | E ~ I | 2 d U d V | E ~ I | 2 d U d V ,
Y ¯ R = I m [ E ~ R V E ~ R ] d U d V | E ~ R | 2 d U d V + ( Z R + Z I ) V W | E ~ R | 2 d U d V | E ~ R | 2 d U d V ,
Y ¯ I = I m [ E ~ I V E ~ I ] d U d V | E ~ I | 2 d U d V + Z I V W | E ~ I | 2 d U d V | E ~ I | 2 d U d V .
k 0 Δ G H = I m [ E ~ R U E ~ R ] d U d V | E ~ R | 2 d U d V + I m [ E ~ I V E ~ I ] d U d V | E ~ I | 2 d U d V ,
k 0 Δ I F = I m [ E ~ R V E ~ R ] d U d V | E ~ R | 2 d U d V + I m [ E ~ I V E ~ I ] d U d V | E ~ I | 2 d U d V .
A ~ ( U , V ) = w 0 2 2 π e x p ( α 3 + β 3 3 ) e x p ( α U 2 + β V 2 ϑ 2 ) × e x p [ i ( U 3 + V 3 3 ϑ 3 α 2 U + β 2 V ϑ ) ] .
x ¯ R r = 1 Λ k 0 Δ G H g ,
x ¯ I A = α 2 ϑ 1 4 α ϑ ,
x ¯ R A = x ¯ I A + 1 Λ ϑ 8 α 2 λ p , s ω λ 1 ,
k 0 Δ G H A i r y = 1 Λ ( k 0 Δ G H g + ϑ 8 α 2 λ p , s ω λ 1 ) .
Θ G H A i r y = 1 4 α Λ Θ G H g ,
y ¯ R p = 1 Λ 2 a p a s s i n η c o t θ a p 2 R p 2 + a s 2 R s 2 ( R p 2 + R s 2 ) ,
y ¯ R e = 1 Λ 2 a p a s c o t θ a p 2 R p 2 + a s 2 R s 2 R p R s s i n ( ϕ p ϕ s η ) ,
y ¯ I A = β 2 ϑ 1 4 β ϑ ,
y ¯ R A = y ¯ I A + ϑ 8 β 2 Λ λ p , s ω λ 2 ,
y ¯ R r = 1 Λ ϑ 2 4 β 2 a p a s s i n η c o t 2 θ a p 2 R p 2 + a s 2 R s 2 ( R p 2 ϕ p R s 2 ϕ s ) ,
y ¯ I p = y ¯ I e = 2 a p a s s i n η c o t θ a p 2 + a s 2 .
k 0 Δ I F A i r y = 1 Λ ( k 0 Δ I F g + ϑ 8 β 2 λ p , s ω λ 2 ) ,
Θ I F A i r y = 1 4 β Λ Θ I F g ,
A ~ ( ρ , ϕ + θ 0 ) = A ( r , θ + θ 0 ) e x p { i ρ r c o s [ ( θ + θ 0 ) ( ϕ + θ 0 ) ] } r d r d θ ,
A ~ o ( U , V ) = w 0 2 2 π e x p ( α 3 + β 3 3 ) e x p ( α U o 2 + β V o 2 ϑ 2 ) e x p [ i ( U o 3 + V o 3 3 ϑ 3 α 2 U o + β 2 V o ϑ ) ] ,

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