Abstract

Motivated by recent experimental observation of photonic spin Hall effect at metasurfaces, we study lateral Goos-Hänchen (GH) and transverse Imbert-Fedorov (IF) shifts of an arbitrarily polarized light beam totally reflected from metasurfaces, in terms of stationary phase method and energy flux method. The intriguing phenomenon is that the gradient in phase discontinuity results in anomalous reflection and refraction, and the GH and IF shifts can be thus controlled from negative to positive values by changing the sign of phase discontinuity. The tunable GH and IF shifts have potential applications in nano-optics, with the development of novel functionalities and performances of metasurfaces.

© 2019 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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2019 (1)

X. Yin, H. Zhu, H.-J. Guo, M. Deng, T. Xu, Z.-J. Gong, X. Li, Z.-H. Hang, C. Wu, H.-Q. Li, S.-Q. Chen, L. Zhou, and L. Chen, “Hyperbolic Metamaterial Devices for Wavefront Manipulation,” Laser Photonics Rev. 13, 1800081 (2019).
[Crossref]

2018 (1)

2017 (1)

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

2016 (7)

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

Y.-C. Liu, Y.-G. Ke, H.-L. Luo, and S.-C. Wen, “Photonic spin Hall effect in metasurfaces: a brief review,” Nanophotonics 6, 51–70 (2016).
[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, 19319 (2016).
[Crossref]

A. M. Shaltout, A. V. Kildishev, and V. M. Shalaev, “Evolution of photonic metasurfaces: from static to dynamic,” J. Opt. Soc. A. B 33, 501–510 (2016).
[Crossref]

N. M. Estakhri and A. ALú, “Recent progress in gradient metasurfaces,” J. Opt. Soc. A. B 33, A21–A30 (2016).
[Crossref]

Y. Chen, Y. Ban, Q.-B. Zhu, and X. Chen, “Graphene-assisted resonant transmission and enhanced Goos-Hänchen shift in a frustrated total internal reflection configuration, ” Opt. Lett. 41, 4468–4471 (2016).
[Crossref] [PubMed]

X.-X. Zhou and X.-H. Ling, “Enhanced photonic spin Hall effect due to surface plasmon resonance,” IEEE Photon. J. 8, 4801108 (2016).
[Crossref]

2013 (3)

A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar photonics with metasurfaces,” Science 339, 1289 (2013).
[Crossref]

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

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

2012 (3)

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

X. Chen, X. J. Lu, P. L. Zhao, and Q. B. Zhu, “Energy flux and Goos-Hänchen shift in frustrated total internal reflection,” Opt. Lett. 37, 1526–1528 (2012).
[Crossref] [PubMed]

2011 (4)

N. Hermosa, A. M. Nugrowati, A. Aiello, and J. P. Woerdman, “Spin Hall effect of light in metallic reflection,” Opt. Lett. 36, 3200–3202 (2011).
[Crossref] [PubMed]

N.-F. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light Propagation with phase discontinuities: Generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
[Crossref] [PubMed]

J. C. Martinez and M. B. A. Jalil, “Theory of giant Faraday rotation and Goos-Hänchen shift in graphene,” Europhys. Lett. 96, 27008 (2011).
[Crossref]

H.-L. Wang and X.-D. Zhang, “Unusual spin Hall effect of a light beam in chiral metamaterials,” Phys. Rev. A 83, 053820 (2011).
[Crossref]

2009 (3)

H.-L. Luo, S.-C. Wen, W.-X. Shu, Z.-X. Tang, Y.-H. Zou, and D.-Y. Fan, “Spin Hall effect of a light beam in left-handed materials,” Phys. Rev. A 80, 043810 (2009).
[Crossref]

X. Chen, C.-F. Li, R.-R. Wei, and Y. Zhang, “Goos-Hänchen shifts in frustrated total internal reflection studied with wave packet propagation,” Phys. Rev. A 80, 015803 (2009).
[Crossref]

Y. Qin, Y. Li, H.-Y. He, and Q.-H. Gong, “Measurement of spin Hall effect of reflected light,” Opt. Lett.,  34, 2551–2553 (2009).
[Crossref] [PubMed]

2008 (3)

2007 (4)

P. T. Leung, C. W. Chen, and H.-P. Chiang, “Large negative Goos-Hänchen shift at metal surfaces,” Opt. Commun. 276, 206–208 (2007).
[Crossref]

J.-L. Shi, C.-F. Li, and Q. Wang, “Theory of the Goos-Hänchen displacement in total internal reflection,” Int. J. Mod. Phys. B 21, 2777–2791 (2007).
[Crossref]

C.-F. Li, “Unified theory for Goos-Hänchen and Imbert-Fedorov effects,” Phys. Rev. A 76, 013811 (2007).
[Crossref]

M. Merano, A. Aiello, G. W. ’t Hooft, M. P. van Exter, E. R. Eliel, and J. P. Woerdman, “Observation of Goos-Hänchen shifts in metallic reflection,” Opt. Express 15, 15928–15934 (2007).
[Crossref] [PubMed]

2006 (2)

K. Yu. 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, 073903 (2006).
[Crossref] [PubMed]

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

2004 (1)

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

2002 (1)

P. R. Berman, “Goos-Hänchen shift in negatively refractive media,” Phys. Rev. E 66, 067603 (2002).
[Crossref]

2000 (2)

T. Sakata, H. Togo, and F. Shimokawa, “Reflection-type 2 × 2 optical waveguide switch using the Goos-Hänchen shift effect,” Appl. Phys. Lett. 76, 2841–2843 (2000).
[Crossref]

H. M. Lai, C. W. Kwok, Y. W. Loo, and B. Y. Xu, “Energy-flux pattern in the Goos-Hänchen effect,” Phys. Rev. E 62, 7330–7739 (2000).
[Crossref]

1983 (1)

K. Yasumoto and Y. Oishi, “A new evaluation of the Goos-Hänchen shift and associated time delay,” J. Appl. Phys. 54, 2170–2176 (1983).
[Crossref]

1973 (1)

O. Costa de Beauregard and C. Imbert, “Quantized longitudinal and transverse shifts associated with total internal reflection,” Phys. Rev. D 7, 3555 (1973).
[Crossref]

1972 (1)

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

1971 (2)

H. K. V. Lotsch, “Beam displacement at total reflection: the Goos-Hänchen effect III,” Optik (Stuttgart) 32, 299–319 (1971).

H. K. V. Lotsch, “Beam displacement at total reflection: the Goos-Hänchen effect IV,” Optik (Stuttgart) 32, 553–569 (1971).

1970 (2)

H. K. V. Lotsch, “Beam displacement at total reflection: the Goos-Hänchen effect I,” Optik (Stuttgart) 32, 116–137 (1970).

H. K. V. Lotsch, “Beam displacement at total reflection: the Goos-Hänchen effect II,” Optik (Stuttgart) 32, 189–204 (1970).

1964 (1)

1955 (1)

F. I. Fedorov, “K teorii polnovo otrazenija,” Dokl. Akad. Nauk SSSR 105, 465–468 (1955).

1948 (1)

K. V. Artmann, “Berechnung der Seitenversetzung des totalreflektierten strahles,” Ann. Phys. (Leipzig) 2, 87–102 (1948).
[Crossref]

1947 (2)

F. Goos and H. Hänchen, “Ein neuer und fundamentaler Versuch zur total reflexion,” Ann. der Phys. 436, 333–346 (1947).
[Crossref]

F. Goos and H. Hänchen, “Neumessung des strahlversetzungseffektes bei total reflexion,” Ann. der Phys. 440, 251–252 (1947).
[Crossref]

’t Hooft, G. W.

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, 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, 19319 (2016).
[Crossref]

Aiello, A.

Aieta, F.

N.-F. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light Propagation with phase discontinuities: Generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
[Crossref] [PubMed]

ALú, A.

N. M. Estakhri and A. ALú, “Recent progress in gradient metasurfaces,” J. Opt. Soc. A. B 33, A21–A30 (2016).
[Crossref]

Artmann, K. V.

K. V. Artmann, “Berechnung der Seitenversetzung des totalreflektierten strahles,” Ann. Phys. (Leipzig) 2, 87–102 (1948).
[Crossref]

Ban, Y.

Berman, P. R.

P. R. Berman, “Goos-Hänchen shift in negatively refractive media,” Phys. Rev. E 66, 067603 (2002).
[Crossref]

Bliokh, K. Y.

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

Bliokh, K. Yu.

K. Yu. 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, 073903 (2006).
[Crossref] [PubMed]

Bliokh, Y. P.

K. Yu. 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, 073903 (2006).
[Crossref] [PubMed]

Boltasseva, A.

A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar photonics with metasurfaces,” Science 339, 1289 (2013).
[Crossref]

Cao, Z.-Q

Capasso, F.

N.-F. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light Propagation with phase discontinuities: Generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
[Crossref] [PubMed]

Chen, C. W.

P. T. Leung, C. W. Chen, and H.-P. Chiang, “Large negative Goos-Hänchen shift at metal surfaces,” Opt. Commun. 276, 206–208 (2007).
[Crossref]

Chen, L.

X. Yin, H. Zhu, H.-J. Guo, M. Deng, T. Xu, Z.-J. Gong, X. Li, Z.-H. Hang, C. Wu, H.-Q. Li, S.-Q. Chen, L. Zhou, and L. Chen, “Hyperbolic Metamaterial Devices for Wavefront Manipulation,” Laser Photonics Rev. 13, 1800081 (2019).
[Crossref]

Chen, S.-Q.

X. Yin, H. Zhu, H.-J. Guo, M. Deng, T. Xu, Z.-J. Gong, X. Li, Z.-H. Hang, C. Wu, H.-Q. Li, S.-Q. Chen, L. Zhou, and L. Chen, “Hyperbolic Metamaterial Devices for Wavefront Manipulation,” Laser Photonics Rev. 13, 1800081 (2019).
[Crossref]

Chen, X.

Chen, Y.

Chiang, H.-P.

P. T. Leung, C. W. Chen, and H.-P. Chiang, “Large negative Goos-Hänchen shift at metal surfaces,” Opt. Commun. 276, 206–208 (2007).
[Crossref]

Costa de Beauregard, O.

O. Costa de Beauregard and C. Imbert, “Quantized longitudinal and transverse shifts associated with total internal reflection,” Phys. Rev. D 7, 3555 (1973).
[Crossref]

Deng, M.

X. Yin, H. Zhu, H.-J. Guo, M. Deng, T. Xu, Z.-J. Gong, X. Li, Z.-H. Hang, C. Wu, H.-Q. Li, S.-Q. Chen, L. Zhou, and L. Chen, “Hyperbolic Metamaterial Devices for Wavefront Manipulation,” Laser Photonics Rev. 13, 1800081 (2019).
[Crossref]

Eliel, E. R.

Estakhri, N. M.

N. M. Estakhri and A. ALú, “Recent progress in gradient metasurfaces,” J. Opt. Soc. A. B 33, A21–A30 (2016).
[Crossref]

Fan, D.-Y.

H.-L. Luo, S.-C. Wen, W.-X. Shu, Z.-X. Tang, Y.-H. Zou, and D.-Y. Fan, “Spin Hall effect of a light beam in left-handed materials,” Phys. Rev. A 80, 043810 (2009).
[Crossref]

Fang, N.

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

Fedorov, F. I.

F. I. Fedorov, “K teorii polnovo otrazenija,” Dokl. Akad. Nauk SSSR 105, 465–468 (1955).

Gaburro, Z.

N.-F. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light Propagation with phase discontinuities: Generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
[Crossref] [PubMed]

Genevet, P.

N.-F. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light Propagation with phase discontinuities: Generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
[Crossref] [PubMed]

Gong, Q.-H.

Gong, Z.-J.

X. Yin, H. Zhu, H.-J. Guo, M. Deng, T. Xu, Z.-J. Gong, X. Li, Z.-H. Hang, C. Wu, H.-Q. Li, S.-Q. Chen, L. Zhou, and L. Chen, “Hyperbolic Metamaterial Devices for Wavefront Manipulation,” Laser Photonics Rev. 13, 1800081 (2019).
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X. Yin, H. Zhu, H.-J. Guo, M. Deng, T. Xu, Z.-J. Gong, X. Li, Z.-H. Hang, C. Wu, H.-Q. Li, S.-Q. Chen, L. Zhou, and L. Chen, “Hyperbolic Metamaterial Devices for Wavefront Manipulation,” Laser Photonics Rev. 13, 1800081 (2019).
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Z.-N. Wang, Y.-Y. Sun, L. Han, and D.-H. Liu, “General laws of reflection and refraction for subwavelength phase grating,” arXiv 1312.3855 (2013).

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F. Goos and H. Hänchen, “Neumessung des strahlversetzungseffektes bei total reflexion,” Ann. der Phys. 440, 251–252 (1947).
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X. Yin, H. Zhu, H.-J. Guo, M. Deng, T. Xu, Z.-J. Gong, X. Li, Z.-H. Hang, C. Wu, H.-Q. Li, S.-Q. Chen, L. Zhou, and L. Chen, “Hyperbolic Metamaterial Devices for Wavefront Manipulation,” Laser Photonics Rev. 13, 1800081 (2019).
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He, Y.

Hermosa, N.

Hesselink, L.

X. B. Yin, L. Hesselink, Z. Liu, N. Fang, and X. Zhang, “Goos-Hänchen shift surface plasmon resonance sensor,” Appl. Phys. Lett. 89, 261108 (2006).
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J. C. Martinez and M. B. A. Jalil, “Theory of giant Faraday rotation and Goos-Hänchen shift in graphene,” Europhys. Lett. 96, 27008 (2011).
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Kats, M. A.

N.-F. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light Propagation with phase discontinuities: Generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
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Y.-C. Liu, Y.-G. Ke, H.-L. Luo, and S.-C. Wen, “Photonic spin Hall effect in metasurfaces: a brief review,” Nanophotonics 6, 51–70 (2016).
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Kildishev, A. V.

A. M. Shaltout, A. V. Kildishev, and V. M. Shalaev, “Evolution of photonic metasurfaces: from static to dynamic,” J. Opt. Soc. A. B 33, 501–510 (2016).
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A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar photonics with metasurfaces,” Science 339, 1289 (2013).
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O. Hosten and P. Kwiat, “Observation of the spin-Hall effect of light via weak measurements,” Science 319, 787–790 (2008).
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H. M. Lai, C. W. Kwok, Y. W. Loo, and B. Y. Xu, “Energy-flux pattern in the Goos-Hänchen effect,” Phys. Rev. E 62, 7330–7739 (2000).
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Lai, H. M.

H. M. Lai, C. W. Kwok, Y. W. Loo, and B. Y. Xu, “Energy-flux pattern in the Goos-Hänchen effect,” Phys. Rev. E 62, 7330–7739 (2000).
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Leung, P. T.

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X. Chen, C.-F. Li, R.-R. Wei, and Y. Zhang, “Goos-Hänchen shifts in frustrated total internal reflection studied with wave packet propagation,” Phys. Rev. A 80, 015803 (2009).
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J.-L. Shi, C.-F. Li, and Q. Wang, “Theory of the Goos-Hänchen displacement in total internal reflection,” Int. J. Mod. Phys. B 21, 2777–2791 (2007).
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C.-F. Li, “Unified theory for Goos-Hänchen and Imbert-Fedorov effects,” Phys. Rev. A 76, 013811 (2007).
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Li, C.-Y.

T. Tang, C.-Y. Li, and L. Luo, “Enhanced spin Hall effect of tunneling light in hyperbolic metamaterial waveguide,” Sci. Rep. 6, 30762 (2016).
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Li, H.-Q.

X. Yin, H. Zhu, H.-J. Guo, M. Deng, T. Xu, Z.-J. Gong, X. Li, Z.-H. Hang, C. Wu, H.-Q. Li, S.-Q. Chen, L. Zhou, and L. Chen, “Hyperbolic Metamaterial Devices for Wavefront Manipulation,” Laser Photonics Rev. 13, 1800081 (2019).
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X. Yin, H. Zhu, H.-J. Guo, M. Deng, T. Xu, Z.-J. Gong, X. Li, Z.-H. Hang, C. Wu, H.-Q. Li, S.-Q. Chen, L. Zhou, and L. Chen, “Hyperbolic Metamaterial Devices for Wavefront Manipulation,” Laser Photonics Rev. 13, 1800081 (2019).
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Ling, X.-H.

X.-H. Ling, X.-X. Zhou, K. Huang, Y.-C. Liu, C.-W. Qiu, H.-L. Luo, and S.-C. Wen, “Recent advances in the spin Hall effect of light,” Rep. Prog. Phys. 80, 066401 (2017).
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X.-X. Zhou and X.-H. Ling, “Enhanced photonic spin Hall effect due to surface plasmon resonance,” IEEE Photon. J. 8, 4801108 (2016).
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X.-X. Zhou, X.-H. Ling, H.-L. Luo, and S.-C. Wen, “Identifying graphene layers via spin Hall effect of light,” Appl. Phys. Lett. 101, 251602 (2012).
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X.-X. Zhou, X.-H. Ling, H.-L. Luo, and S.-C. Wen, “Experimental observation of the spin Hall effect of light on a nanometal film via weak measurements,” Phys. Rev. A 85, 043809 (2012).
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Z.-N. Wang, Y.-Y. Sun, L. Han, and D.-H. Liu, “General laws of reflection and refraction for subwavelength phase grating,” arXiv 1312.3855 (2013).

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X.-H. Ling, X.-X. Zhou, K. Huang, Y.-C. Liu, C.-W. Qiu, H.-L. Luo, and S.-C. Wen, “Recent advances in the spin Hall effect of light,” Rep. Prog. Phys. 80, 066401 (2017).
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X. B. Yin, L. Hesselink, Z. Liu, N. Fang, and X. Zhang, “Goos-Hänchen shift surface plasmon resonance sensor,” Appl. Phys. Lett. 89, 261108 (2006).
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H. M. Lai, C. W. Kwok, Y. W. Loo, and B. Y. Xu, “Energy-flux pattern in the Goos-Hänchen effect,” Phys. Rev. E 62, 7330–7739 (2000).
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Luo, H.-L.

X.-H. Ling, X.-X. Zhou, K. Huang, Y.-C. Liu, C.-W. Qiu, H.-L. Luo, and S.-C. Wen, “Recent advances in the spin Hall effect of light,” Rep. Prog. Phys. 80, 066401 (2017).
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Y.-C. Liu, Y.-G. Ke, H.-L. Luo, and S.-C. Wen, “Photonic spin Hall effect in metasurfaces: a brief review,” Nanophotonics 6, 51–70 (2016).
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X.-X. Zhou, X.-H. Ling, H.-L. Luo, and S.-C. Wen, “Experimental observation of the spin Hall effect of light on a nanometal film via weak measurements,” Phys. Rev. A 85, 043809 (2012).
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X.-X. Zhou, X.-H. Ling, H.-L. Luo, and S.-C. Wen, “Identifying graphene layers via spin Hall effect of light,” Appl. Phys. Lett. 101, 251602 (2012).
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H.-L. Luo, S.-C. Wen, W.-X. Shu, Z.-X. Tang, Y.-H. Zou, and D.-Y. Fan, “Spin Hall effect of a light beam in left-handed materials,” Phys. Rev. A 80, 043810 (2009).
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T. Tang, C.-Y. Li, and L. Luo, “Enhanced spin Hall effect of tunneling light in hyperbolic metamaterial waveguide,” Sci. Rep. 6, 30762 (2016).
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Martinez, J. C.

J. C. Martinez and M. B. A. Jalil, “Theory of giant Faraday rotation and Goos-Hänchen shift in graphene,” Europhys. Lett. 96, 27008 (2011).
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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, 19319 (2016).
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X.-H. Ling, X.-X. Zhou, K. Huang, Y.-C. Liu, C.-W. Qiu, H.-L. Luo, and S.-C. Wen, “Recent advances in the spin Hall effect of light,” Rep. Prog. Phys. 80, 066401 (2017).
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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, 19319 (2016).
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Rho, J.

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T. Sakata, H. Togo, and F. Shimokawa, “Reflection-type 2 × 2 optical waveguide switch using the Goos-Hänchen shift effect,” Appl. Phys. Lett. 76, 2841–2843 (2000).
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A. M. Shaltout, A. V. Kildishev, and V. M. Shalaev, “Evolution of photonic metasurfaces: from static to dynamic,” J. Opt. Soc. A. B 33, 501–510 (2016).
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A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar photonics with metasurfaces,” Science 339, 1289 (2013).
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A. M. Shaltout, A. V. Kildishev, and V. M. Shalaev, “Evolution of photonic metasurfaces: from static to dynamic,” J. Opt. Soc. A. B 33, 501–510 (2016).
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Shi, J.-L.

J.-L. Shi, C.-F. Li, and Q. Wang, “Theory of the Goos-Hänchen displacement in total internal reflection,” Int. J. Mod. Phys. B 21, 2777–2791 (2007).
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T. Sakata, H. Togo, and F. Shimokawa, “Reflection-type 2 × 2 optical waveguide switch using the Goos-Hänchen shift effect,” Appl. Phys. Lett. 76, 2841–2843 (2000).
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H.-L. Luo, S.-C. Wen, W.-X. Shu, Z.-X. Tang, Y.-H. Zou, and D.-Y. Fan, “Spin Hall effect of a light beam in left-handed materials,” Phys. Rev. A 80, 043810 (2009).
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Sun, Y.-Y.

Z.-N. Wang, Y.-Y. Sun, L. Han, and D.-H. Liu, “General laws of reflection and refraction for subwavelength phase grating,” arXiv 1312.3855 (2013).

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Tang, T.

T. Tang, C.-Y. Li, and L. Luo, “Enhanced spin Hall effect of tunneling light in hyperbolic metamaterial waveguide,” Sci. Rep. 6, 30762 (2016).
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Tang, Z.-X.

H.-L. Luo, S.-C. Wen, W.-X. Shu, Z.-X. Tang, Y.-H. Zou, and D.-Y. Fan, “Spin Hall effect of a light beam in left-handed materials,” Phys. Rev. A 80, 043810 (2009).
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N.-F. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light Propagation with phase discontinuities: Generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
[Crossref] [PubMed]

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T. Sakata, H. Togo, and F. Shimokawa, “Reflection-type 2 × 2 optical waveguide switch using the Goos-Hänchen shift effect,” Appl. Phys. Lett. 76, 2841–2843 (2000).
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Wang, H.-L.

H.-L. Wang and X.-D. Zhang, “Unusual spin Hall effect of a light beam in chiral metamaterials,” Phys. Rev. A 83, 053820 (2011).
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J.-L. Shi, C.-F. Li, and Q. Wang, “Theory of the Goos-Hänchen displacement in total internal reflection,” Int. J. Mod. Phys. B 21, 2777–2791 (2007).
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Wang, Z.-N.

Z.-N. Wang, Y.-Y. Sun, L. Han, and D.-H. Liu, “General laws of reflection and refraction for subwavelength phase grating,” arXiv 1312.3855 (2013).

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X. Chen, C.-F. Li, R.-R. Wei, and Y. Zhang, “Goos-Hänchen shifts in frustrated total internal reflection studied with wave packet propagation,” Phys. Rev. A 80, 015803 (2009).
[Crossref]

Wen, S.-C.

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

Y.-C. Liu, Y.-G. Ke, H.-L. Luo, and S.-C. Wen, “Photonic spin Hall effect in metasurfaces: a brief review,” Nanophotonics 6, 51–70 (2016).
[Crossref]

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

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

H.-L. Luo, S.-C. Wen, W.-X. Shu, Z.-X. Tang, Y.-H. Zou, and D.-Y. Fan, “Spin Hall effect of a light beam in left-handed materials,” Phys. Rev. A 80, 043810 (2009).
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Wu, C.

X. Yin, H. Zhu, H.-J. Guo, M. Deng, T. Xu, Z.-J. Gong, X. Li, Z.-H. Hang, C. Wu, H.-Q. Li, S.-Q. Chen, L. Zhou, and L. Chen, “Hyperbolic Metamaterial Devices for Wavefront Manipulation,” Laser Photonics Rev. 13, 1800081 (2019).
[Crossref]

Xu, B. Y.

H. M. Lai, C. W. Kwok, Y. W. Loo, and B. Y. Xu, “Energy-flux pattern in the Goos-Hänchen effect,” Phys. Rev. E 62, 7330–7739 (2000).
[Crossref]

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X. Yin, H. Zhu, H.-J. Guo, M. Deng, T. Xu, Z.-J. Gong, X. Li, Z.-H. Hang, C. Wu, H.-Q. Li, S.-Q. Chen, L. Zhou, and L. Chen, “Hyperbolic Metamaterial Devices for Wavefront Manipulation,” Laser Photonics Rev. 13, 1800081 (2019).
[Crossref]

Yallapragada, V. J.

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, 19319 (2016).
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K. Yasumoto and Y. Oishi, “A new evaluation of the Goos-Hänchen shift and associated time delay,” J. Appl. Phys. 54, 2170–2176 (1983).
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X.-B. Yin, Z.-L. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin Hall effect at metasurfaces,” Science 339, 1405–1407 (2013).
[Crossref] [PubMed]

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X. Yin, H. Zhu, H.-J. Guo, M. Deng, T. Xu, Z.-J. Gong, X. Li, Z.-H. Hang, C. Wu, H.-Q. Li, S.-Q. Chen, L. Zhou, and L. Chen, “Hyperbolic Metamaterial Devices for Wavefront Manipulation,” Laser Photonics Rev. 13, 1800081 (2019).
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X. B. Yin, L. Hesselink, Z. Liu, N. Fang, and X. Zhang, “Goos-Hänchen shift surface plasmon resonance sensor,” Appl. Phys. Lett. 89, 261108 (2006).
[Crossref]

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

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N.-F. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light Propagation with phase discontinuities: Generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
[Crossref] [PubMed]

Yu, T.-Y.

Zhang, X.

X.-B. Yin, Z.-L. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin Hall effect at metasurfaces,” Science 339, 1405–1407 (2013).
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X. B. Yin, L. Hesselink, Z. Liu, N. Fang, and X. Zhang, “Goos-Hänchen shift surface plasmon resonance sensor,” Appl. Phys. Lett. 89, 261108 (2006).
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Zhang, X.-D.

H.-L. Wang and X.-D. Zhang, “Unusual spin Hall effect of a light beam in chiral metamaterials,” Phys. Rev. A 83, 053820 (2011).
[Crossref]

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X. Chen, C.-F. Li, R.-R. Wei, and Y. Zhang, “Goos-Hänchen shifts in frustrated total internal reflection studied with wave packet propagation,” Phys. Rev. A 80, 015803 (2009).
[Crossref]

Zhao, P. L.

Zhou, L.

X. Yin, H. Zhu, H.-J. Guo, M. Deng, T. Xu, Z.-J. Gong, X. Li, Z.-H. Hang, C. Wu, H.-Q. Li, S.-Q. Chen, L. Zhou, and L. Chen, “Hyperbolic Metamaterial Devices for Wavefront Manipulation,” Laser Photonics Rev. 13, 1800081 (2019).
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Zhou, X.-X.

X.-H. Ling, X.-X. Zhou, K. Huang, Y.-C. Liu, C.-W. Qiu, H.-L. Luo, and S.-C. Wen, “Recent advances in the spin Hall effect of light,” Rep. Prog. Phys. 80, 066401 (2017).
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X.-X. Zhou and X.-H. Ling, “Enhanced photonic spin Hall effect due to surface plasmon resonance,” IEEE Photon. J. 8, 4801108 (2016).
[Crossref]

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

X.-X. Zhou, X.-H. Ling, H.-L. Luo, and S.-C. Wen, “Experimental observation of the spin Hall effect of light on a nanometal film via weak measurements,” Phys. Rev. A 85, 043809 (2012).
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X. Yin, H. Zhu, H.-J. Guo, M. Deng, T. Xu, Z.-J. Gong, X. Li, Z.-H. Hang, C. Wu, H.-Q. Li, S.-Q. Chen, L. Zhou, and L. Chen, “Hyperbolic Metamaterial Devices for Wavefront Manipulation,” Laser Photonics Rev. 13, 1800081 (2019).
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Zhu, Q.-B.

Zou, Y.-H.

H.-L. Luo, S.-C. Wen, W.-X. Shu, Z.-X. Tang, Y.-H. Zou, and D.-Y. Fan, “Spin Hall effect of a light beam in left-handed materials,” Phys. Rev. A 80, 043810 (2009).
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F. Goos and H. Hänchen, “Neumessung des strahlversetzungseffektes bei total reflexion,” Ann. der Phys. 440, 251–252 (1947).
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T. Sakata, H. Togo, and F. Shimokawa, “Reflection-type 2 × 2 optical waveguide switch using the Goos-Hänchen shift effect,” Appl. Phys. Lett. 76, 2841–2843 (2000).
[Crossref]

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

X.-X. Zhou, X.-H. Ling, H.-L. Luo, and S.-C. Wen, “Identifying graphene layers via spin Hall effect of light,” Appl. Phys. Lett. 101, 251602 (2012).
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IEEE Photon. J. (1)

X.-X. Zhou and X.-H. Ling, “Enhanced photonic spin Hall effect due to surface plasmon resonance,” IEEE Photon. J. 8, 4801108 (2016).
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J.-L. Shi, C.-F. Li, and Q. Wang, “Theory of the Goos-Hänchen displacement in total internal reflection,” Int. J. Mod. Phys. B 21, 2777–2791 (2007).
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Figures (5)

Fig. 1
Fig. 1 Schematic diagram of the lateral GH (lGH) and transverse IF (lIF) shifts of reflected light beam at a single gradient metasurface, fabricated by the femtosecond laser self-assembly of nanostructures in silicon substrate, with different refractive indies, n1 and n2, where θi, ki, kr, kt stand for incidence angle, incident, reflected, and transmitted wave vectors. ∇Φx denotes the phase discontinuity.
Fig. 2
Fig. 2 Reflection coefficients, Rs,p, for s-polarization (a) and p-polarization (b). Parameters: θi = 2°, n1 = 3.5 and n2 = 1 represent the refractive indices for silcon and air.
Fig. 3
Fig. 3 Dependence of GH shifts on the wavelength (a) and the phase gradient (b), where their positive (negative) values correspond the positive (negative) phase gradient. The red solid and blue dashed lines are plotted with energy flux method and stationary phase method respectively. Parameters: (a) dΦ/dx = ±3.6 rad/μm, (b) λ0 = 2 μm, θi = 2°, | c s | = | c p | = 1 / 2, n1 = 3.5 and n2 = 1.
Fig. 4
Fig. 4 Dependence of IF shifts on the wavelength (a,b) and the phase gradient (c). (a) The red solid and blue dashed lines are plotted with energy flux method and stationary phase method respectively, where the positive (negative) values correspond to Δ = π/2 (Δ = −π/2) and incidence angle is θi = 2°. (b) The red solid and blue dashed lines are plotted with energy flux method and stationary phase method respectively, where the positive (negative) values correspond to Δ = π/2 (Δ = −π/2) and incidence angle is θi = 30°. (c) The example given by stationary phase approach, in which the red solid line (Δ = π/2) and the blue dashed line (Δ = −π/2). Parameters: (a) dΦ/dx = −2π/15 rad/μm, (b) θi = 2°, and other parameters are the same as those in Fig. 3.
Fig. 5
Fig. 5 Dependence of energy flux on the wavelength with a positive/negative phase gradient in x-(a) and z-(b) directions. Parameters: dΦ/dx = 3.6 rad/μm (solid red), dΦ/dx = 3rad/μm (dotted purple), dΦ/dx = −3.6 rad/μm (dashed blue), dΦ/dx = −3 rad/μm (dashed green), Δ = π/2. Other parameters are the same as those in Fig. 3.

Equations (28)

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E i = [ c s z ^ + c p ( sin θ i y ^ cos θ i x ^ ) ] e i ( k x i x + k y i y ) ,
E r = [ r s c s z ^ + r p c p ( sin θ r y ^ + cos θ r x ^ ) ] e i ( k x r x k y r y ) ,
E t = [ t s c s z ^ + t p c p ( sin θ t y ^ cos θ t x ^ ) ] e i ( k x t x + k y t y ) ,
n 2 sin θ t n 1 sin θ i = λ 0 2 π d Φ d x ,
n 1 sin θ r n 1 sin θ i = λ 0 2 π d Φ d x ,
d ϕ d x 2 π n 1 λ 0 sin θ i ,
θ c = arcsin ( ± n 2 n 1 λ 0 2 π n 1 d Φ d x ) .
θ i arcsin ( n 2 n 1 λ 0 2 π n 1 d Φ d x ) , or θ i arcsin ( n 2 n 1 λ 0 2 π n 1 d Φ d x ) .
θ c = arcsin ( ± 1 λ 0 2 π n 1 d Φ d x ) ,
θ i arcsin ( 1 λ 0 2 π n 1 d Φ d x ) , or θ i arcsin ( 1 λ 0 2 π n 1 d Φ d x ) .
arcsin ( n 2 n 1 λ 0 2 π n 1 d Φ d x ) θ i arcsin ( 1 λ 0 2 π n 1 d Φ d x ) ,
arcsin ( 1 λ 0 2 π n 1 d Φ d x ) θ i arcsin ( n 2 n 1 λ 0 2 π n 1 d Φ d x ) ,
r s , p = χ k y i k y t χ k y r + k y t e i d Φ d x x ,
t s , p = χ μ 2 μ 1 k y i + k y r χ k y r + k y t e i d Φ d x x ,
S y r = k y r 2 μ 1 ω 0 ( | c p | 2 R p 2 + | c s | 2 R s 2 ) ,
S x t = k x t e 2 κ y 2 μ 2 ω 0 ( | c p | 2 T p 2 + | c s | 2 T s 2 ) ,
S z t = k x t κ e 2 κ y n 2 μ 2 ω 0 k 0 | c p | | c s | T p T s sin ( ϕ p t ϕ s t + Δ ) ,
S x ir = k x i + k x r 2 μ 1 ω 0 { R p | c p | 2 cos [ ( k y i + k y r ) y ϕ p r ] + R s | c s | 2 cos [ ( k y i + k y r ) y ϕ s r ] } .
P x t = k x t 4 μ 2 ω 0 κ ( | c p | 2 T p 2 + | c s | 2 T s 2 ) ,
P z t = | c p | | c s | k x t 2 n 2 μ 2 ω 0 k 0 T p T s sin ( ϕ p t ϕ s t + Δ ) ,
P x ir = ( k x i + k x r ) ( R p | c p | 2 sin ϕ p r + R s | c s | 2 sin ϕ s r ) 2 μ 1 ω 0 ( k y i + k y r ) .
l GH = k x t 2 κ k y r | c s | 2 T s 2 + | c p | 2 T p 2 | c s | 2 R s 2 + | c p | 2 R p 2 k x i + k x r k y r ( k y i + k y r ) R s | c s | 2 sin ϕ s r + R p | c p | 2 sin ϕ p r | c s | 2 R s 2 + | c p | 2 R p 2 .
l GH s = k x t 2 κ k y r T s 2 R s 2 k x i + k x r k y r ( k y i + k y r ) sin ϕ s r R s ,
l GH p = k x t 2 κ k y r T p 2 R p 2 k x i + k x r k y r ( k y i + k y r ) sin ϕ p r R p .
l GH = | c s | 2 R s 2 l GH s + | c p | 2 R p 2 l GH p | c s | 2 R s 2 + | c p | 2 R p 2 ,
l IF = μ 1 k x t | c p | | c s | T p T s sin ( ϕ p t ϕ s t + Δ ) n 2 μ 2 k 0 k y r ( | c s | 2 R s 2 + | c p | 2 R p 2 ) .
l GH = | c s | 2 ϕ s r k x | c p | 2 ϕ p r k x ,
l IF = sin ( ϕ s r ϕ p r + Δ ) n 1 k 0 tan θ i 2 π n 1 λ 0 tan θ i .