Abstract

We theoretically calculated the Goos-Hänchen (G-H) shift of the beam that reflected from and transmitted through an epsilon-near-zero (ENZ) slab, which was covered by the different number of layers of graphene and also realized tunable G-H shifts with electrically controllable graphene in terahertz regime. It is shown that besides the impact of the thickness of the slab and the number of layers of graphene, Fermi energy (chemical potential),which can be electrically controlled through electrical modification of the charge density of graphene by gate voltage, also plays an important role in adjusting G-H shifts. In this work we achieved about 200 times the incident wavelength of the adjustment range which can be used in measuring the doping level of graphene due to the dependence of Fermi energy on G-H shifts. Furthermore, our results provide a richer control on G-H shifts in ENZ slab and also provide potential applications for ENZ metamaterials-based devices than semi-infinite structures.

© 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] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]

2017 (3)

2016 (3)

M. Lobet, B. Majerus, L. Henrard, and P. Lambin, “Perfect electromagnetic absorption using graphene and epsilon-near-zero metamaterials,” Phys. Rev. B 93(23), 235424 (2016).
[Crossref]

Y. Ziauddin, S. Q. Chuang, and R. K. Lee, “Goos-Hanchen shift of partially coherent light fields in epsilion-near-zero metamaterials,” Sci. Rep. 6, 26504 (2016).

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

2015 (3)

Y. Xu, C. Chan, and H. Chen, “Goos-Hanchen shift in epsilon-near-zero metamaterials,” Sci. Rep. 5, 8681 (2015).

V. Ginis, P. Tassin, T. Koschny, and C. M. Soukoulis, “Tunable terahertz frequency comb generation using time-dependent graphene sheets,” Phys. Rev. B 91(16), 161403 (2015).
[Crossref]

S. Grosche, M. Ornigotti, and A. Szameit, “Goos-Hänchen and Imbert-Fedorov shifts for Gaussian beams impinging on graphene-coated surfaces,” Opt. Express 23(23), 30195–30203 (2015).
[Crossref] [PubMed]

2013 (3)

D. A. Smirnova, A. V. Gorbach, I. V. Iorsh, I. V. Shadrivov, and Y. S. Kivshar, “Nonlinear switching with a graphene coupler,” Phys. Rev. B 88(4), 045443 (2013).
[Crossref]

Y. Fan, Z. Wei, H. Li, H. Chen, and C. M. Soukoulis, “Photonic band gap of a graphene-embedded quarter-wave stack,” Phys. Rev. B 88(24), 241403 (2013).
[Crossref]

T. Zhan, X. Shi, Y. Dai, X. Liu, and J. Zi, “Transfer matrix method for optics in graphene layers,” J. Phys. Condens. Matter 25(21), 215301 (2013).
[Crossref] [PubMed]

2012 (2)

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref] [PubMed]

Y. Song, H. Wu, and Y. Guo, “Gaint Goos-Hanchen shift in graphene double-barrier structures,” Appl. Phys. Lett. 100(25), 253116 (2012).
[Crossref]

2011 (3)

F. H. L. Koppens, D. E. Chang, and F. J. García de Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11(8), 3370–3377 (2011).
[Crossref] [PubMed]

S. D. Sarma, S. Adam, E. H. Hwang, and E. Rossi, “Electronic transport in two dimensional graphene,” Rev. Mod. Phys. 83(2), 407–470 (2011).
[Crossref]

F. H. L. Koppens, D. E. Chang, and F. J. García de Abajo, “Graphene plasmonics: A platform for strong light-matter interactions,” Nano Lett. 11(8), 3370–3377 (2011).
[Crossref] [PubMed]

2010 (1)

2009 (4)

B. Zhao and L. Gao, “Temperature-dependent Goos-Hänchen shift on the interface of metal/dielectric composites,” Opt. Express 17(24), 21433–21441 (2009).
[Crossref] [PubMed]

A. H. C. Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[Crossref]

A. K. Geim, “Graphene: Status and Prospects,” Science 324(5934), 1530–1534 (2009).
[Crossref] [PubMed]

C. W. J. Beenakker, R. A. Sepkhanov, A. R. Akhmerov, and J. Tworzydło, “Quantum Goos-Hänchen effect in graphene,” Phys. Rev. Lett. 102(14), 146804 (2009).
[Crossref] [PubMed]

2008 (4)

2007 (1)

D. S. L. Abergel and V. I. Fal’ko, “Optical and magneto-optical far-infrared properties of bilayer graphene,” Phys. Rev. B 75(15), 155430 (2007).
[Crossref]

2005 (2)

Y. Zhang, Y. W. Tan, H. L. Stormer, and P. Kim, “Experimental observation of the quantum Hall effect and Berry’s phase in graphene,” Nature 438(7065), 201–204 (2005).
[Crossref] [PubMed]

L. G. Wang, H. Chen, and S. Y. Zhu, “Large negative Goos-Hänchen shift from a weakly absorbing dielectric slab,” Opt. Lett. 30(21), 2936–2938 (2005).
[Crossref] [PubMed]

2004 (1)

2003 (1)

1972 (1)

K. W. Chiu and J. J. Quinn, “On the Goos-Hanchen effect: A simple example of time delay scatting process,” Am. J. Phys. 40(12), 1847–1851 (1972).
[Crossref]

1964 (1)

1947 (1)

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

Abergel, D. S. L.

D. S. L. Abergel and V. I. Fal’ko, “Optical and magneto-optical far-infrared properties of bilayer graphene,” Phys. Rev. B 75(15), 155430 (2007).
[Crossref]

Adam, S.

S. D. Sarma, S. Adam, E. H. Hwang, and E. Rossi, “Electronic transport in two dimensional graphene,” Rev. Mod. Phys. 83(2), 407–470 (2011).
[Crossref]

Aiello, A.

Akhmerov, A. R.

C. W. J. Beenakker, R. A. Sepkhanov, A. R. Akhmerov, and J. Tworzydło, “Quantum Goos-Hänchen effect in graphene,” Phys. Rev. Lett. 102(14), 146804 (2009).
[Crossref] [PubMed]

Andreev, G. O.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref] [PubMed]

Bao, W.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref] [PubMed]

Basov, D. N.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref] [PubMed]

Beenakker, C. W. J.

C. W. J. Beenakker, R. A. Sepkhanov, A. R. Akhmerov, and J. Tworzydło, “Quantum Goos-Hänchen effect in graphene,” Phys. Rev. Lett. 102(14), 146804 (2009).
[Crossref] [PubMed]

Cai, L.

S. Chen, C. Mi, L. Cai, M. Liu, H. Luo, and S. Wen, “Observation of the Goos-Hanchen shift in graphene via weak measurement,” Appl. Phys. Lett. 110(3), 031105 (2017).
[Crossref]

Cao, Z.

Castro Neto, A. H.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref] [PubMed]

Chan, C.

Y. Xu, C. Chan, and H. Chen, “Goos-Hanchen shift in epsilon-near-zero metamaterials,” Sci. Rep. 5, 8681 (2015).

Chang, D. E.

F. H. L. Koppens, D. E. Chang, and F. J. García de Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11(8), 3370–3377 (2011).
[Crossref] [PubMed]

F. H. L. Koppens, D. E. Chang, and F. J. García de Abajo, “Graphene plasmonics: A platform for strong light-matter interactions,” Nano Lett. 11(8), 3370–3377 (2011).
[Crossref] [PubMed]

Chen, G.

Chen, H.

Y. Xu, C. Chan, and H. Chen, “Goos-Hanchen shift in epsilon-near-zero metamaterials,” Sci. Rep. 5, 8681 (2015).

Y. Fan, Z. Wei, H. Li, H. Chen, and C. M. Soukoulis, “Photonic band gap of a graphene-embedded quarter-wave stack,” Phys. Rev. B 88(24), 241403 (2013).
[Crossref]

L. G. Wang, H. Chen, and S. Y. Zhu, “Large negative Goos-Hänchen shift from a weakly absorbing dielectric slab,” Opt. Lett. 30(21), 2936–2938 (2005).
[Crossref] [PubMed]

Chen, S.

S. Chen, C. Mi, L. Cai, M. Liu, H. Luo, and S. Wen, “Observation of the Goos-Hanchen shift in graphene via weak measurement,” Appl. Phys. Lett. 110(3), 031105 (2017).
[Crossref]

Chiu, K. W.

K. W. Chiu and J. J. Quinn, “On the Goos-Hanchen effect: A simple example of time delay scatting process,” Am. J. Phys. 40(12), 1847–1851 (1972).
[Crossref]

Chuang, S. Q.

Y. Ziauddin, S. Q. Chuang, and R. K. Lee, “Goos-Hanchen shift of partially coherent light fields in epsilion-near-zero metamaterials,” Sci. Rep. 6, 26504 (2016).

Dai, Y.

T. Zhan, X. Shi, Y. Dai, X. Liu, and J. Zi, “Transfer matrix method for optics in graphene layers,” J. Phys. Condens. Matter 25(21), 215301 (2013).
[Crossref] [PubMed]

Dominguez, G.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref] [PubMed]

Fal’ko, V. I.

D. S. L. Abergel and V. I. Fal’ko, “Optical and magneto-optical far-infrared properties of bilayer graphene,” Phys. Rev. B 75(15), 155430 (2007).
[Crossref]

Falkovsky, L. A.

L. A. Falkovsky, “Optical properties of graphene,” J. Phys. Conf. Ser. 129(1), 012004 (2008).

Fan, Y.

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

Y. Fan, Z. Wei, H. Li, H. Chen, and C. M. Soukoulis, “Photonic band gap of a graphene-embedded quarter-wave stack,” Phys. Rev. B 88(24), 241403 (2013).
[Crossref]

Farani, A.

Fei, Z.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref] [PubMed]

Felbacq, D.

Fogler, M. M.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref] [PubMed]

Fu, Q.

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

Gao, L.

García de Abajo, F. J.

F. H. L. Koppens, D. E. Chang, and F. J. García de Abajo, “Graphene plasmonics: A platform for strong light-matter interactions,” Nano Lett. 11(8), 3370–3377 (2011).
[Crossref] [PubMed]

F. H. L. Koppens, D. E. Chang, and F. J. García de Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11(8), 3370–3377 (2011).
[Crossref] [PubMed]

Geim, A. K.

A. K. Geim, “Graphene: Status and Prospects,” Science 324(5934), 1530–1534 (2009).
[Crossref] [PubMed]

A. H. C. Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[Crossref]

Ginis, V.

V. Ginis, P. Tassin, T. Koschny, and C. M. Soukoulis, “Tunable terahertz frequency comb generation using time-dependent graphene sheets,” Phys. Rev. B 91(16), 161403 (2015).
[Crossref]

Gong, Y.

Goos, F.

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

Gorbach, A. V.

D. A. Smirnova, A. V. Gorbach, I. V. Iorsh, I. V. Shadrivov, and Y. S. Kivshar, “Nonlinear switching with a graphene coupler,” Phys. Rev. B 88(4), 045443 (2013).
[Crossref]

Götte, J. B.

Grosche, S.

Guinea, F.

A. H. C. Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[Crossref]

Guo, Y.

Y. Song, H. Wu, and Y. Guo, “Gaint Goos-Hanchen shift in graphene double-barrier structures,” Appl. Phys. Lett. 100(25), 253116 (2012).
[Crossref]

Hanchen, H.

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

He, Y.

Henrard, L.

M. Lobet, B. Majerus, L. Henrard, and P. Lambin, “Perfect electromagnetic absorption using graphene and epsilon-near-zero metamaterials,” Phys. Rev. B 93(23), 235424 (2016).
[Crossref]

Hwang, E. H.

S. D. Sarma, S. Adam, E. H. Hwang, and E. Rossi, “Electronic transport in two dimensional graphene,” Rev. Mod. Phys. 83(2), 407–470 (2011).
[Crossref]

Iorsh, I. V.

D. A. Smirnova, A. V. Gorbach, I. V. Iorsh, I. V. Shadrivov, and Y. S. Kivshar, “Nonlinear switching with a graphene coupler,” Phys. Rev. B 88(4), 045443 (2013).
[Crossref]

Keilmann, F.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref] [PubMed]

Kim, P.

Y. Zhang, Y. W. Tan, H. L. Stormer, and P. Kim, “Experimental observation of the quantum Hall effect and Berry’s phase in graphene,” Nature 438(7065), 201–204 (2005).
[Crossref] [PubMed]

Kivshar, Y. S.

D. A. Smirnova, A. V. Gorbach, I. V. Iorsh, I. V. Shadrivov, and Y. S. Kivshar, “Nonlinear switching with a graphene coupler,” Phys. Rev. B 88(4), 045443 (2013).
[Crossref]

Koppens, F. H. L.

F. H. L. Koppens, D. E. Chang, and F. J. García de Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11(8), 3370–3377 (2011).
[Crossref] [PubMed]

F. H. L. Koppens, D. E. Chang, and F. J. García de Abajo, “Graphene plasmonics: A platform for strong light-matter interactions,” Nano Lett. 11(8), 3370–3377 (2011).
[Crossref] [PubMed]

Koschny, T.

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

V. Ginis, P. Tassin, T. Koschny, and C. M. Soukoulis, “Tunable terahertz frequency comb generation using time-dependent graphene sheets,” Phys. Rev. B 91(16), 161403 (2015).
[Crossref]

Lambin, P.

M. Lobet, B. Majerus, L. Henrard, and P. Lambin, “Perfect electromagnetic absorption using graphene and epsilon-near-zero metamaterials,” Phys. Rev. B 93(23), 235424 (2016).
[Crossref]

Lau, C. N.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref] [PubMed]

Lee, R. K.

Y. Ziauddin, S. Q. Chuang, and R. K. Lee, “Goos-Hanchen shift of partially coherent light fields in epsilion-near-zero metamaterials,” Sci. Rep. 6, 26504 (2016).

Li, H.

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

Y. Fan, Z. Wei, H. Li, H. Chen, and C. M. Soukoulis, “Photonic band gap of a graphene-embedded quarter-wave stack,” Phys. Rev. B 88(24), 241403 (2013).
[Crossref]

T. Yu, H. Li, Z. Cao, Y. Wang, Q. Shen, and Y. He, “Oscillating wave displacement sensor using the enhanced Goos-Hänchen effect in a symmetrical metal-cladding optical waveguide,” Opt. Lett. 33(9), 1001–1003 (2008).
[Crossref] [PubMed]

Y. Wang, H. Li, Z. Cao, T. Yu, Q. Shen, and Y. He, “Oscillating wave sensor based on the Goos–Hänchen effect,” Appl. Phys. Lett. 92(6), 061117 (2008).
[Crossref]

Liu, M.

S. Chen, C. Mi, L. Cai, M. Liu, H. Luo, and S. Wen, “Observation of the Goos-Hanchen shift in graphene via weak measurement,” Appl. Phys. Lett. 110(3), 031105 (2017).
[Crossref]

Liu, X.

T. Zhan, X. Shi, Y. Dai, X. Liu, and J. Zi, “Transfer matrix method for optics in graphene layers,” J. Phys. Condens. Matter 25(21), 215301 (2013).
[Crossref] [PubMed]

H. Lu, X. Liu, D. Mao, L. Wang, and Y. Gong, “Tunable band-pass plasmonic waveguide filters with nanodisk resonators,” Opt. Express 18(17), 17922–17927 (2010).
[Crossref] [PubMed]

Lobet, M.

M. Lobet, B. Majerus, L. Henrard, and P. Lambin, “Perfect electromagnetic absorption using graphene and epsilon-near-zero metamaterials,” Phys. Rev. B 93(23), 235424 (2016).
[Crossref]

Lu, H.

Luo, H.

S. Chen, C. Mi, L. Cai, M. Liu, H. Luo, and S. Wen, “Observation of the Goos-Hanchen shift in graphene via weak measurement,” Appl. Phys. Lett. 110(3), 031105 (2017).
[Crossref]

Majerus, B.

M. Lobet, B. Majerus, L. Henrard, and P. Lambin, “Perfect electromagnetic absorption using graphene and epsilon-near-zero metamaterials,” Phys. Rev. B 93(23), 235424 (2016).
[Crossref]

Mao, D.

McLeod, A. S.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref] [PubMed]

Mi, C.

S. Chen, C. Mi, L. Cai, M. Liu, H. Luo, and S. Wen, “Observation of the Goos-Hanchen shift in graphene via weak measurement,” Appl. Phys. Lett. 110(3), 031105 (2017).
[Crossref]

Miri, M.

Moreau, A.

Neto, A. H. C.

A. H. C. Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[Crossref]

Novoselov, K. S.

A. H. C. Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[Crossref]

Ornigotti, M.

Peres, N. M. R.

A. H. C. Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[Crossref]

Qing, D. K.

Quinn, J. J.

K. W. Chiu and J. J. Quinn, “On the Goos-Hanchen effect: A simple example of time delay scatting process,” Am. J. Phys. 40(12), 1847–1851 (1972).
[Crossref]

Renard, R. H.

Rodin, A. S.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref] [PubMed]

Rossi, E.

S. D. Sarma, S. Adam, E. H. Hwang, and E. Rossi, “Electronic transport in two dimensional graphene,” Rev. Mod. Phys. 83(2), 407–470 (2011).
[Crossref]

Sarma, S. D.

S. D. Sarma, S. Adam, E. H. Hwang, and E. Rossi, “Electronic transport in two dimensional graphene,” Rev. Mod. Phys. 83(2), 407–470 (2011).
[Crossref]

Sepkhanov, R. A.

C. W. J. Beenakker, R. A. Sepkhanov, A. R. Akhmerov, and J. Tworzydło, “Quantum Goos-Hänchen effect in graphene,” Phys. Rev. Lett. 102(14), 146804 (2009).
[Crossref] [PubMed]

Shadrivov, I. V.

D. A. Smirnova, A. V. Gorbach, I. V. Iorsh, I. V. Shadrivov, and Y. S. Kivshar, “Nonlinear switching with a graphene coupler,” Phys. Rev. B 88(4), 045443 (2013).
[Crossref]

Sheikhi, M. H.

Shen, N.

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

Shen, Q.

Shi, X.

T. Zhan, X. Shi, Y. Dai, X. Liu, and J. Zi, “Transfer matrix method for optics in graphene layers,” J. Phys. Condens. Matter 25(21), 215301 (2013).
[Crossref] [PubMed]

Smaâli, R.

Smirnova, D. A.

D. A. Smirnova, A. V. Gorbach, I. V. Iorsh, I. V. Shadrivov, and Y. S. Kivshar, “Nonlinear switching with a graphene coupler,” Phys. Rev. B 88(4), 045443 (2013).
[Crossref]

Song, Y.

Y. Song, H. Wu, and Y. Guo, “Gaint Goos-Hanchen shift in graphene double-barrier structures,” Appl. Phys. Lett. 100(25), 253116 (2012).
[Crossref]

Soukoulis, C. M.

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

V. Ginis, P. Tassin, T. Koschny, and C. M. Soukoulis, “Tunable terahertz frequency comb generation using time-dependent graphene sheets,” Phys. Rev. B 91(16), 161403 (2015).
[Crossref]

Y. Fan, Z. Wei, H. Li, H. Chen, and C. M. Soukoulis, “Photonic band gap of a graphene-embedded quarter-wave stack,” Phys. Rev. B 88(24), 241403 (2013).
[Crossref]

Stormer, H. L.

Y. Zhang, Y. W. Tan, H. L. Stormer, and P. Kim, “Experimental observation of the quantum Hall effect and Berry’s phase in graphene,” Nature 438(7065), 201–204 (2005).
[Crossref] [PubMed]

Szameit, A.

Tan, Y. W.

Y. Zhang, Y. W. Tan, H. L. Stormer, and P. Kim, “Experimental observation of the quantum Hall effect and Berry’s phase in graphene,” Nature 438(7065), 201–204 (2005).
[Crossref] [PubMed]

Tassin, P.

V. Ginis, P. Tassin, T. Koschny, and C. M. Soukoulis, “Tunable terahertz frequency comb generation using time-dependent graphene sheets,” Phys. Rev. B 91(16), 161403 (2015).
[Crossref]

Thiemens, M.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref] [PubMed]

Tworzydlo, J.

C. W. J. Beenakker, R. A. Sepkhanov, A. R. Akhmerov, and J. Tworzydło, “Quantum Goos-Hänchen effect in graphene,” Phys. Rev. Lett. 102(14), 146804 (2009).
[Crossref] [PubMed]

Wagner, M.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref] [PubMed]

Wang, L.

Wang, L. G.

Wang, Y.

Wei, Z.

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

Y. Fan, Z. Wei, H. Li, H. Chen, and C. M. Soukoulis, “Photonic band gap of a graphene-embedded quarter-wave stack,” Phys. Rev. B 88(24), 241403 (2013).
[Crossref]

Wen, J. S.

Wen, S.

S. Chen, C. Mi, L. Cai, M. Liu, H. Luo, and S. Wen, “Observation of the Goos-Hanchen shift in graphene via weak measurement,” Appl. Phys. Lett. 110(3), 031105 (2017).
[Crossref]

Woerdman, J. P.

Wu, H.

Y. Song, H. Wu, and Y. Guo, “Gaint Goos-Hanchen shift in graphene double-barrier structures,” Appl. Phys. Lett. 100(25), 253116 (2012).
[Crossref]

Xu, Y.

Y. Xu, C. Chan, and H. Chen, “Goos-Hanchen shift in epsilon-near-zero metamaterials,” Sci. Rep. 5, 8681 (2015).

Yu, T.

Zhan, T.

T. Zhan, X. Shi, Y. Dai, X. Liu, and J. Zi, “Transfer matrix method for optics in graphene layers,” J. Phys. Condens. Matter 25(21), 215301 (2013).
[Crossref] [PubMed]

Zhang, F.

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

Zhang, J. X.

Zhang, L. M.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref] [PubMed]

Zhang, P.

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

Zhang, Y.

Y. Zhang, Y. W. Tan, H. L. Stormer, and P. Kim, “Experimental observation of the quantum Hall effect and Berry’s phase in graphene,” Nature 438(7065), 201–204 (2005).
[Crossref] [PubMed]

Zhao, B.

Zhao, Q.

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

Zhao, Z.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref] [PubMed]

Zhu, S. Y.

Zi, J.

T. Zhan, X. Shi, Y. Dai, X. Liu, and J. Zi, “Transfer matrix method for optics in graphene layers,” J. Phys. Condens. Matter 25(21), 215301 (2013).
[Crossref] [PubMed]

Ziauddin, Y.

Y. Ziauddin, S. Q. Chuang, and R. K. Lee, “Goos-Hanchen shift of partially coherent light fields in epsilion-near-zero metamaterials,” Sci. Rep. 6, 26504 (2016).

Adv. Opt. Mater (1)

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

Am. J. Phys. (1)

K. W. Chiu and J. J. Quinn, “On the Goos-Hanchen effect: A simple example of time delay scatting process,” Am. J. Phys. 40(12), 1847–1851 (1972).
[Crossref]

Ann. Phys. (1)

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

Appl. Phys. Lett. (3)

Y. Wang, H. Li, Z. Cao, T. Yu, Q. Shen, and Y. He, “Oscillating wave sensor based on the Goos–Hänchen effect,” Appl. Phys. Lett. 92(6), 061117 (2008).
[Crossref]

S. Chen, C. Mi, L. Cai, M. Liu, H. Luo, and S. Wen, “Observation of the Goos-Hanchen shift in graphene via weak measurement,” Appl. Phys. Lett. 110(3), 031105 (2017).
[Crossref]

Y. Song, H. Wu, and Y. Guo, “Gaint Goos-Hanchen shift in graphene double-barrier structures,” Appl. Phys. Lett. 100(25), 253116 (2012).
[Crossref]

J. Opt. Soc. Am. (1)

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

J. Phys. Condens. Matter (1)

T. Zhan, X. Shi, Y. Dai, X. Liu, and J. Zi, “Transfer matrix method for optics in graphene layers,” J. Phys. Condens. Matter 25(21), 215301 (2013).
[Crossref] [PubMed]

J. Phys. Conf. Ser. (1)

L. A. Falkovsky, “Optical properties of graphene,” J. Phys. Conf. Ser. 129(1), 012004 (2008).

Nano Lett. (2)

F. H. L. Koppens, D. E. Chang, and F. J. García de Abajo, “Graphene plasmonics: A platform for strong light-matter interactions,” Nano Lett. 11(8), 3370–3377 (2011).
[Crossref] [PubMed]

F. H. L. Koppens, D. E. Chang, and F. J. García de Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11(8), 3370–3377 (2011).
[Crossref] [PubMed]

Nature (2)

Y. Zhang, Y. W. Tan, H. L. Stormer, and P. Kim, “Experimental observation of the quantum Hall effect and Berry’s phase in graphene,” Nature 438(7065), 201–204 (2005).
[Crossref] [PubMed]

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref] [PubMed]

Opt. Express (4)

Opt. Lett. (4)

Phys. Rev. B (5)

D. A. Smirnova, A. V. Gorbach, I. V. Iorsh, I. V. Shadrivov, and Y. S. Kivshar, “Nonlinear switching with a graphene coupler,” Phys. Rev. B 88(4), 045443 (2013).
[Crossref]

V. Ginis, P. Tassin, T. Koschny, and C. M. Soukoulis, “Tunable terahertz frequency comb generation using time-dependent graphene sheets,” Phys. Rev. B 91(16), 161403 (2015).
[Crossref]

D. S. L. Abergel and V. I. Fal’ko, “Optical and magneto-optical far-infrared properties of bilayer graphene,” Phys. Rev. B 75(15), 155430 (2007).
[Crossref]

M. Lobet, B. Majerus, L. Henrard, and P. Lambin, “Perfect electromagnetic absorption using graphene and epsilon-near-zero metamaterials,” Phys. Rev. B 93(23), 235424 (2016).
[Crossref]

Y. Fan, Z. Wei, H. Li, H. Chen, and C. M. Soukoulis, “Photonic band gap of a graphene-embedded quarter-wave stack,” Phys. Rev. B 88(24), 241403 (2013).
[Crossref]

Phys. Rev. Lett. (1)

C. W. J. Beenakker, R. A. Sepkhanov, A. R. Akhmerov, and J. Tworzydło, “Quantum Goos-Hänchen effect in graphene,” Phys. Rev. Lett. 102(14), 146804 (2009).
[Crossref] [PubMed]

Rev. Mod. Phys. (2)

S. D. Sarma, S. Adam, E. H. Hwang, and E. Rossi, “Electronic transport in two dimensional graphene,” Rev. Mod. Phys. 83(2), 407–470 (2011).
[Crossref]

A. H. C. Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[Crossref]

Sci. Rep. (2)

Y. Xu, C. Chan, and H. Chen, “Goos-Hanchen shift in epsilon-near-zero metamaterials,” Sci. Rep. 5, 8681 (2015).

Y. Ziauddin, S. Q. Chuang, and R. K. Lee, “Goos-Hanchen shift of partially coherent light fields in epsilion-near-zero metamaterials,” Sci. Rep. 6, 26504 (2016).

Science (1)

A. K. Geim, “Graphene: Status and Prospects,” Science 324(5934), 1530–1534 (2009).
[Crossref] [PubMed]

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Figures (6)

Fig. 1
Fig. 1 (a) The schematic diagram of lateral shifts of transmitted and reflected beams from graphene-covered ENZ slab. (b) Multilayer graphene sheets surrounded by two different dielectrics that with dielectric constants ε1 and ε2, graphene sheets are characterized by conductivity σ' at z = 0. Arrows in different directions indicate incoming and outgoing light, respectively.(c) The calculation model for Fig. 1(a) used in transfer matrix method, in this structure we set ε1 and ε3 indicate the permittivity of air, d is the thickness of ENZ metamaterials.
Fig. 2
Fig. 2 G-H shift at different temperatures(s polarization). Here we set that Ef = 0.2ev, the thickness of the slab d/λ = 18.55 and τ = 100fs.
Fig. 3
Fig. 3 The effect of different ε2 on G-H shift in the case of reflection(s polarizatons). Here we set Ef = 0.2ev, N = 7 and τ = 100fs as well as θ = 1° in (a) and d/λ = 18.55 in (b).
Fig. 4
Fig. 4 The effect of incident beam with different frequencies on G-H shifts (s polarization). (a) and (b) are reflected conditions, (c) and (d) are transmitted conditions, respectively. We choose the incident angle with θ = 1° in (a) and (c), then with the same thickness of ENZ metamaterial slab (d/λ = 18.55) in (b) and (d). The number of layers of graphene (N) is 7.
Fig. 5
Fig. 5 Reflected beam’s G-H shifts with s polarized incident beam in different conditions. (a) is the dependence of G-H shifts on the thickness of ENZ slab at different Fermi energy and the number of layers of graphene as well as the incident angle θ = 1°. The solid line and dash line represent Ef = 0.8ev and Ef = 0.2ev respectively, the different number of layers of graphene are marked with different colors. (b) is the dependence of G-H shifts on the angle of incident beam θ with the thickness of ENZ slab of d/λ = 18.55, other parameters are the same as (a). (c)describes the effect of different τ on G-H shift with Ef = 0.2ev and d/λ = 18.55. (d)The curve of G-H shifts as the function of Fermi energy, and we set that θ = 1°,the thickness of ENZ slab d/λ = 18.55 . Here we set that τ = 100fs in (a) (c) and (d), N represent the number of layers of graphene.
Fig. 6
Fig. 6 Transmitted beam’s G-H shifts with s polarized incident beam in different conditions. (a) is dependence of G-H shifts on the thickness of ENZ slab at different Fermi energy and layers of graphene as well as the incident angle θ = 1°.The solid line and dash line represent Ef = 0.8ev and Ef = 0.2ev respectively, different layers of graphenes are marked with different colors. (b) is the dependence of G-H shifts on the angle of incident beam θ with the thickness of ENZ slab of d/λ = 18.55, other parameters are the same as (a). (c)The curve of G-H shifts as the function of Fermi energy, with θ = 1°, the thickness of ENZ slab d/λ = 18.55 . Here we also set that τ = 100fs.

Equations (12)

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

E y1 = A 1 e i k z1 z e i k x1 x + B 1 e i k z1 z e i k x1 x ,Z<0
E y2 = A 2 e i k z2 z e i k x2 x + B 2 e i k z2 z e i k x2 x ,Z>0
[ A 1 B 1 ]= T 12,s [ A 2 B 2 ]
[ A 1 B 1 ]= T 12,p [ A 2 B 2 ]
P(d)=[ e i k z d 0 0 e i k z d ]
[ A Ι B Ι ]= T 12,s(p) P(d) T 23,s(p) [ A ΙΙΙ B ΙΙΙ ]=D[ A ΙΙΙ B ΙΙΙ ]
r= D 21 D 11 ,t= 1 D 11 .
σ(ω)= e 2 E f π 2 i ω+ i τ + e 2 4 2 [ θ(ω2 E f )+ i π log| ω2 E f ω+2 E f | ]
r(d,θ,ω)=| r(d,θ,ω) | e i ϕ m r (d,θ,ω)
t(d,θ,ω)=| t(d,θ,ω) | e i ϕ m t (d,θ,ω)
D m r(t) = λ 2π d ϕ m r(t) dθ
D m r(t) = λ 2π 1 | r (t) m | 2 [ Re(r (t) m ) dIm(r (t) m ) dθ Im(r (t) m ) dRe(r (t) m ) dθ ]

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