Abstract

The Goos-Hänchen (GH) shift of light beam incident on graphene ribbon array is investigated by Green’s function method. Due to the resonance effects of leaky surface plasmons on ribbons, the zeroth-order reflection field shows both giant positive and negative GH shifts. By tuning the graphene Fermi level, we can control the shift conveniently. This effect is important to graphene-based metasurface and electro-optical devices.

© 2017 Optical Society of America

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

2017 (3)

X. D. Zeng, L. F. Fan, and M. Suhail Zubairy, “Deep-subwavelength lithography via graphene plasmons,” Phys. Rev. A 95, 053850 (2017).
[Crossref]

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 95013809 (2017).
[Crossref]

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

2016 (4)

A. A. Maradudin, I. Simonsen, J. Polanco, and R. M. Fitzgerald, “Rayleigh and Wood anomalies in the diffraction of light from a perfectly conducting reflection grating,” J. Opt. 18024004 (2016).
[Crossref]

X. D. Zeng, Z. Y. Liao, M. Al-Amri, and M. S. Zubairy, “Controllable waveguide via dielectric cylinder covered with graphene: Tunable entanglement,” Europhys. Lett. 115, 14002 (2016).
[Crossref]

M. Merano, “Optical beam shifts in graphene and single-layer boron-nitride,” Opt. Lett. 41, 5780–5783 (2016).
[Crossref] [PubMed]

S. Asiri, J. Xu, M. Al-Amri, and M. S. Zubairy, “Controlling the Goos-Hänchen and Imbert-Fedorov shifts via pump and driving fields,” Phys. Rev. A 93, 013821 (2016).
[Crossref]

2015 (1)

Z. B. Li, K. Yao, F. N. Xia, S. Shen, J. G. Tian, and Y. M. Liu, “Graphene Plasmonic Metasurfaces to Steer Infrared Light,” Sci. Rep. 5, 12423 (2015).
[Crossref] [PubMed]

2014 (6)

T. Low and P. Avouris, “Graphene Plasmonics for Terahertz to Mid-Infrared Applications,” ACS. Nano 8(2), 1086–1101 (2014).
[Crossref] [PubMed]

X. D. Zeng, M. Al-Amri, and M. S. Zubairy, “Nanometer-scale microscopy via graphene plasmons,” Phys. Rev. B 90, 235418 (2014).
[Crossref]

R. Yang, W. Zhu, and J. Li, “Giant positive and negative Goos-Hänchen shift on dielectric gratings caused by guided mode resonance,” Opt. Express 22(2), 2043–2050 (2014).
[Crossref] [PubMed]

R. Macedo, R. L. Stamps, and T. Dumelow, “Spin canting induced nonreciprocal Goos-Hänchen shifts,” Opt. Express 22(23), 28467–28478 (2014).
[Crossref] [PubMed]

M. Cheng, P. Fu, M. H. Weng, X Y. Chen, X. H. Zeng, S. Y. Feng, and R. Chen, “Spatial and angular shifts of terahertz wave for the graphene metamaterial structure,” J. Phys. D 48, 285105 (2014).
[Crossref]

X. Li, P. Wang, F. Xing, X. D. Chen, Z. B. Liu, and J. G. Tian, “Experimental observation of a giant Goos-Hänchen shift in graphene using a beam splitter scanning method,” Opt. Lett. 39(19), 5574–5577 (2014).
[Crossref] [PubMed]

2013 (4)

W. Wang and J. M. Kinaret, “Plasmons in graphene nanoribbons: Interband transitions and nonlocal effects,” Phys. Rev. B 87, 195424 (2013).
[Crossref]

L. G. Wang, S. Y. Zhu, and M. S. Zubairy, “Goos-Hänchen Shifts of Partially Coherent Light Fields,” Phys. Rev. Lett. 111, 223901 (2013).
[Crossref]

A. Khavasi, “Fast convergent Fourier modal method for the analysis of periodic arrays of graphene ribbons,” Opt. Lett. 38(16), 3009–3012 (2013).
[Crossref] [PubMed]

Z. Fang, S. Thongrattanasiri, A. Schlather, Z. Liu, L. Ma, Y. Wang, P. M. Ajayan, P. Nordlander, N. J. Halas, and F. J. Garcia de Abajo, “Gated Tunability and Hybridization of Localized Plasmons in Nanostructured Graphene,” ACS. Nano 7(3), 2388–2395 (2013).
[Crossref] [PubMed]

2012 (6)

A. N. Grigorenko, M. Polini, and K. S. Novoselov, “Graphene plasmonics,” Nat. Photon. 6, 749–758 (2012).
[Crossref]

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

A. Y. Nikitin, F. Guinea, F. J. Garcia-Vidal, and L. Martin-Moreno, “Surface plasmon enhanced absorption and suppressed transmission in periodic arrays of graphene ribbons,” Phys. Rev. B 85081405 (2012).
[Crossref]

J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. Garcia de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature (London) 487, 77–81 (2012).

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 (London) 487, 82–85 (2012).

S. Thongrattanasiri, A. Manjavacas, and F. J. Garcia de Abajo, “Quantum Finite-Size Effects in Graphene Plasmons,” ACS Nano 6(2), 1766–1775 (2012).
[Crossref] [PubMed]

2011 (3)

A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332, 1291–1294 (2011).
[Crossref] [PubMed]

F. H. L. Koppens, D. E. Chang, and F. J. Garcia de Abajo, “Graphene Plasmonics: A Platform for Strong LightâĂŞMatter Interactions,” Nano Lett. 11(8), 3370–3377 (2011).
[Crossref] [PubMed]

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotech. 6, 630–634 (2011).
[Crossref]

2009 (3)

M. Jablan, H. Buljan, and M. Soljačič, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80, 245435 (2009).
[Crossref]

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

G.-Y. Oh, D. G. Kim, and Y. -W. Choi, “The characterization of GH shifts of surface plasmon resonance in a waveguide using the FDTD method,” Opt. Express 17(23), 20714–20720 (2009).
[Crossref] [PubMed]

2008 (3)

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320, 1308 (2008).
[Crossref] [PubMed]

L. G. Wang, M. Ikram, and M. S. Zubairy, “Control of the Goos-Hänchen shift of a light beam via a coherent driving field,” Phys. Rev. A 77, 023811 (2008).
[Crossref]

G. W. Hanson, “Dyadic Green’s functions and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys. 103, 064302 (2008)
[Crossref]

2007 (3)

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6, 183–191 (2007).
[Crossref] [PubMed]

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(24), 15928–15934 (2007).
[Crossref] [PubMed]

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

2005 (1)

2004 (1)

X. Yin, L. Hesselink, Z. Liu, N. Fang, and X. Zhang, “Large positive and negative lateral optical beam displacements due to surface plasmon resonance,” Appl. Phys. Lett. 85, 372 (2004).
[Crossref]

2003 (1)

M. Sarrazin, J. P. Vigneron, and J. M. Vigoureux, “Role of Wood anomalies in optical properties of thin metallic films with a bidimensional array of subwavelength holes,” Phys. Rev. B 67, 085415 (2003).
[Crossref]

2001 (1)

1995 (1)

M. S. Tomaš, “Green function for multilayers: Light scattering in planar cavities,” Phys. Rev. A 51, 2545 (1995).
[Crossref]

1989 (1)

S. Zhang and T. Tamir, “Spatial modifications of Gaussian beams diffracted by reflection gratings,” J. Opt. Soc. Am. 6(9), 1368–1381 (1989).
[Crossref]

1971 (1)

1948 (1)

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

1947 (1)

F. Goos and H. Hänchen, “Ein neuer und fundamentaler Versuch zur Totalreflexion,” Ann. Phys. (Leipzig) 1, 333 (1947).
[Crossref]

’t Hooft, G. W.

Aiello, A.

Ajayan, P. M.

Z. Fang, S. Thongrattanasiri, A. Schlather, Z. Liu, L. Ma, Y. Wang, P. M. Ajayan, P. Nordlander, N. J. Halas, and F. J. Garcia de Abajo, “Gated Tunability and Hybridization of Localized Plasmons in Nanostructured Graphene,” ACS. Nano 7(3), 2388–2395 (2013).
[Crossref] [PubMed]

Al-Amri, M.

X. D. Zeng, Z. Y. Liao, M. Al-Amri, and M. S. Zubairy, “Controllable waveguide via dielectric cylinder covered with graphene: Tunable entanglement,” Europhys. Lett. 115, 14002 (2016).
[Crossref]

S. Asiri, J. Xu, M. Al-Amri, and M. S. Zubairy, “Controlling the Goos-Hänchen and Imbert-Fedorov shifts via pump and driving fields,” Phys. Rev. A 93, 013821 (2016).
[Crossref]

X. D. Zeng, M. Al-Amri, and M. S. Zubairy, “Nanometer-scale microscopy via graphene plasmons,” Phys. Rev. B 90, 235418 (2014).
[Crossref]

Alonso-González, P.

J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. Garcia de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature (London) 487, 77–81 (2012).

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 (London) 487, 82–85 (2012).

Artmann, K.

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

Asiri, S.

S. Asiri, J. Xu, M. Al-Amri, and M. S. Zubairy, “Controlling the Goos-Hänchen and Imbert-Fedorov shifts via pump and driving fields,” Phys. Rev. A 93, 013821 (2016).
[Crossref]

Avouris, P.

T. Low and P. Avouris, “Graphene Plasmonics for Terahertz to Mid-Infrared Applications,” ACS. Nano 8(2), 1086–1101 (2014).
[Crossref] [PubMed]

Badioli, M.

J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. Garcia de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature (London) 487, 77–81 (2012).

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 (London) 487, 82–85 (2012).

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 (London) 487, 82–85 (2012).

Bechtel, H. A.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotech. 6, 630–634 (2011).
[Crossref]

Bertoni, H. L.

Blake, P.

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320, 1308 (2008).
[Crossref] [PubMed]

Bonnet, C.

Booth, T. J.

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320, 1308 (2008).
[Crossref] [PubMed]

Bretenaker, F.

Buljan, H.

M. Jablan, H. Buljan, and M. Soljačič, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80, 245435 (2009).
[Crossref]

Cai, L.

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Pesquera, A.

J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. Garcia de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature (London) 487, 77–81 (2012).

Polanco, J.

A. A. Maradudin, I. Simonsen, J. Polanco, and R. M. Fitzgerald, “Rayleigh and Wood anomalies in the diffraction of light from a perfectly conducting reflection grating,” J. Opt. 18024004 (2016).
[Crossref]

Polini, M.

A. N. Grigorenko, M. Polini, and K. S. Novoselov, “Graphene plasmonics,” Nat. Photon. 6, 749–758 (2012).
[Crossref]

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 (London) 487, 82–85 (2012).

Sarrazin, M.

M. Sarrazin, J. P. Vigneron, and J. M. Vigoureux, “Role of Wood anomalies in optical properties of thin metallic films with a bidimensional array of subwavelength holes,” Phys. Rev. B 67, 085415 (2003).
[Crossref]

Schlather, A.

Z. Fang, S. Thongrattanasiri, A. Schlather, Z. Liu, L. Ma, Y. Wang, P. M. Ajayan, P. Nordlander, N. J. Halas, and F. J. Garcia de Abajo, “Gated Tunability and Hybridization of Localized Plasmons in Nanostructured Graphene,” ACS. Nano 7(3), 2388–2395 (2013).
[Crossref] [PubMed]

Shen, S.

Z. B. Li, K. Yao, F. N. Xia, S. Shen, J. G. Tian, and Y. M. Liu, “Graphene Plasmonic Metasurfaces to Steer Infrared Light,” Sci. Rep. 5, 12423 (2015).
[Crossref] [PubMed]

Shen, Y. R.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotech. 6, 630–634 (2011).
[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 95013809 (2017).
[Crossref]

Simonsen, I.

A. A. Maradudin, I. Simonsen, J. Polanco, and R. M. Fitzgerald, “Rayleigh and Wood anomalies in the diffraction of light from a perfectly conducting reflection grating,” J. Opt. 18024004 (2016).
[Crossref]

Soljacic, M.

M. Jablan, H. Buljan, and M. Soljačič, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80, 245435 (2009).
[Crossref]

Spasenovic, M.

J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. Garcia de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature (London) 487, 77–81 (2012).

Stamps, R. L.

Stauber, T.

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320, 1308 (2008).
[Crossref] [PubMed]

Suhail Zubairy, M.

X. D. Zeng, L. F. Fan, and M. Suhail Zubairy, “Deep-subwavelength lithography via graphene plasmons,” Phys. Rev. A 95, 053850 (2017).
[Crossref]

Tamir, T.

S. Zhang and T. Tamir, “Spatial modifications of Gaussian beams diffracted by reflection gratings,” J. Opt. Soc. Am. 6(9), 1368–1381 (1989).
[Crossref]

T. Tamir and H. L. Bertoni, “"Lateral Displacement of Optical Beams at Multilayered and Periodic Structures,” J. Opt. Soc. Am. 61(10), 1397–1413 (1971).
[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 (London) 487, 82–85 (2012).

Thongrattanasiri, S.

Z. Fang, S. Thongrattanasiri, A. Schlather, Z. Liu, L. Ma, Y. Wang, P. M. Ajayan, P. Nordlander, N. J. Halas, and F. J. Garcia de Abajo, “Gated Tunability and Hybridization of Localized Plasmons in Nanostructured Graphene,” ACS. Nano 7(3), 2388–2395 (2013).
[Crossref] [PubMed]

J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. Garcia de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature (London) 487, 77–81 (2012).

S. Thongrattanasiri, A. Manjavacas, and F. J. Garcia de Abajo, “Quantum Finite-Size Effects in Graphene Plasmons,” ACS Nano 6(2), 1766–1775 (2012).
[Crossref] [PubMed]

Thyagarajan, K.

A. K. Ghatak and K. Thyagarajan, Contemporary Optics (Plenum, New York, 1978).
[Crossref]

Tian, J. G.

Tomaš, M. S.

M. S. Tomaš, “Green function for multilayers: Light scattering in planar cavities,” Phys. Rev. A 51, 2545 (1995).
[Crossref]

Vakil, A.

A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332, 1291–1294 (2011).
[Crossref] [PubMed]

van Exter, M. P.

Vigneron, J. P.

M. Sarrazin, J. P. Vigneron, and J. M. Vigoureux, “Role of Wood anomalies in optical properties of thin metallic films with a bidimensional array of subwavelength holes,” Phys. Rev. B 67, 085415 (2003).
[Crossref]

Vigoureux, J. M.

M. Sarrazin, J. P. Vigneron, and J. M. Vigoureux, “Role of Wood anomalies in optical properties of thin metallic films with a bidimensional array of subwavelength holes,” Phys. Rev. B 67, 085415 (2003).
[Crossref]

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 (London) 487, 82–85 (2012).

Wang, F.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotech. 6, 630–634 (2011).
[Crossref]

Wang, L. G.

L. G. Wang, S. Y. Zhu, and M. S. Zubairy, “Goos-Hänchen Shifts of Partially Coherent Light Fields,” Phys. Rev. Lett. 111, 223901 (2013).
[Crossref]

L. G. Wang, M. Ikram, and M. S. Zubairy, “Control of the Goos-Hänchen shift of a light beam via a coherent driving field,” Phys. Rev. A 77, 023811 (2008).
[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]

Wang, P.

Wang, W.

W. Wang and J. M. Kinaret, “Plasmons in graphene nanoribbons: Interband transitions and nonlocal effects,” Phys. Rev. B 87, 195424 (2013).
[Crossref]

Wang, Y.

Z. Fang, S. Thongrattanasiri, A. Schlather, Z. Liu, L. Ma, Y. Wang, P. M. Ajayan, P. Nordlander, N. J. Halas, and F. J. Garcia de Abajo, “Gated Tunability and Hybridization of Localized Plasmons in Nanostructured Graphene,” ACS. Nano 7(3), 2388–2395 (2013).
[Crossref] [PubMed]

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 95013809 (2017).
[Crossref]

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

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

Weng, M. H.

M. Cheng, P. Fu, M. H. Weng, X Y. Chen, X. H. Zeng, S. Y. Feng, and R. Chen, “Spatial and angular shifts of terahertz wave for the graphene metamaterial structure,” J. Phys. D 48, 285105 (2014).
[Crossref]

Woerdman, J. P.

Xia, F. N.

Z. B. Li, K. Yao, F. N. Xia, S. Shen, J. G. Tian, and Y. M. Liu, “Graphene Plasmonic Metasurfaces to Steer Infrared Light,” Sci. Rep. 5, 12423 (2015).
[Crossref] [PubMed]

Xing, F.

Xu, J.

S. Asiri, J. Xu, M. Al-Amri, and M. S. Zubairy, “Controlling the Goos-Hänchen and Imbert-Fedorov shifts via pump and driving fields,” Phys. Rev. A 93, 013821 (2016).
[Crossref]

Yang, R.

Yao, K.

Z. B. Li, K. Yao, F. N. Xia, S. Shen, J. G. Tian, and Y. M. Liu, “Graphene Plasmonic Metasurfaces to Steer Infrared Light,” Sci. Rep. 5, 12423 (2015).
[Crossref] [PubMed]

Yin, X.

X. Yin, L. Hesselink, Z. Liu, N. Fang, and X. Zhang, “Large positive and negative lateral optical beam displacements due to surface plasmon resonance,” Appl. Phys. Lett. 85, 372 (2004).
[Crossref]

Zeng, X. D.

X. D. Zeng, L. F. Fan, and M. Suhail Zubairy, “Deep-subwavelength lithography via graphene plasmons,” Phys. Rev. A 95, 053850 (2017).
[Crossref]

X. D. Zeng, Z. Y. Liao, M. Al-Amri, and M. S. Zubairy, “Controllable waveguide via dielectric cylinder covered with graphene: Tunable entanglement,” Europhys. Lett. 115, 14002 (2016).
[Crossref]

X. D. Zeng, M. Al-Amri, and M. S. Zubairy, “Nanometer-scale microscopy via graphene plasmons,” Phys. Rev. B 90, 235418 (2014).
[Crossref]

Zeng, X. H.

M. Cheng, P. Fu, M. H. Weng, X Y. Chen, X. H. Zeng, S. Y. Feng, and R. Chen, “Spatial and angular shifts of terahertz wave for the graphene metamaterial structure,” J. Phys. D 48, 285105 (2014).
[Crossref]

Zettl, A.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotech. 6, 630–634 (2011).
[Crossref]

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 (London) 487, 82–85 (2012).

Zhang, S.

S. Zhang and T. Tamir, “Spatial modifications of Gaussian beams diffracted by reflection gratings,” J. Opt. Soc. Am. 6(9), 1368–1381 (1989).
[Crossref]

Zhang, X.

X. Yin, L. Hesselink, Z. Liu, N. Fang, and X. Zhang, “Large positive and negative lateral optical beam displacements due to surface plasmon resonance,” Appl. Phys. Lett. 85, 372 (2004).
[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 (London) 487, 82–85 (2012).

Zhou, X.

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

Zhu, S. Y.

L. G. Wang, S. Y. Zhu, and M. S. Zubairy, “Goos-Hänchen Shifts of Partially Coherent Light Fields,” Phys. Rev. Lett. 111, 223901 (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]

Zhu, W.

Zubairy, M. S.

S. Asiri, J. Xu, M. Al-Amri, and M. S. Zubairy, “Controlling the Goos-Hänchen and Imbert-Fedorov shifts via pump and driving fields,” Phys. Rev. A 93, 013821 (2016).
[Crossref]

X. D. Zeng, Z. Y. Liao, M. Al-Amri, and M. S. Zubairy, “Controllable waveguide via dielectric cylinder covered with graphene: Tunable entanglement,” Europhys. Lett. 115, 14002 (2016).
[Crossref]

X. D. Zeng, M. Al-Amri, and M. S. Zubairy, “Nanometer-scale microscopy via graphene plasmons,” Phys. Rev. B 90, 235418 (2014).
[Crossref]

L. G. Wang, S. Y. Zhu, and M. S. Zubairy, “Goos-Hänchen Shifts of Partially Coherent Light Fields,” Phys. Rev. Lett. 111, 223901 (2013).
[Crossref]

L. G. Wang, M. Ikram, and M. S. Zubairy, “Control of the Goos-Hänchen shift of a light beam via a coherent driving field,” Phys. Rev. A 77, 023811 (2008).
[Crossref]

ACS Nano (1)

S. Thongrattanasiri, A. Manjavacas, and F. J. Garcia de Abajo, “Quantum Finite-Size Effects in Graphene Plasmons,” ACS Nano 6(2), 1766–1775 (2012).
[Crossref] [PubMed]

ACS. Nano (2)

T. Low and P. Avouris, “Graphene Plasmonics for Terahertz to Mid-Infrared Applications,” ACS. Nano 8(2), 1086–1101 (2014).
[Crossref] [PubMed]

Z. Fang, S. Thongrattanasiri, A. Schlather, Z. Liu, L. Ma, Y. Wang, P. M. Ajayan, P. Nordlander, N. J. Halas, and F. J. Garcia de Abajo, “Gated Tunability and Hybridization of Localized Plasmons in Nanostructured Graphene,” ACS. Nano 7(3), 2388–2395 (2013).
[Crossref] [PubMed]

Ann. Phys. (Leipzig) (2)

F. Goos and H. Hänchen, “Ein neuer und fundamentaler Versuch zur Totalreflexion,” Ann. Phys. (Leipzig) 1, 333 (1947).
[Crossref]

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

Appl. Phys. Lett. (3)

X. Yin, L. Hesselink, Z. Liu, N. Fang, and X. Zhang, “Large positive and negative lateral optical beam displacements due to surface plasmon resonance,” Appl. Phys. Lett. 85, 372 (2004).
[Crossref]

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

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

Europhys. Lett. (1)

X. D. Zeng, Z. Y. Liao, M. Al-Amri, and M. S. Zubairy, “Controllable waveguide via dielectric cylinder covered with graphene: Tunable entanglement,” Europhys. Lett. 115, 14002 (2016).
[Crossref]

J. Appl. Phys. (1)

G. W. Hanson, “Dyadic Green’s functions and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys. 103, 064302 (2008)
[Crossref]

J. Opt. (1)

A. A. Maradudin, I. Simonsen, J. Polanco, and R. M. Fitzgerald, “Rayleigh and Wood anomalies in the diffraction of light from a perfectly conducting reflection grating,” J. Opt. 18024004 (2016).
[Crossref]

J. Opt. Soc. Am. (2)

T. Tamir and H. L. Bertoni, “"Lateral Displacement of Optical Beams at Multilayered and Periodic Structures,” J. Opt. Soc. Am. 61(10), 1397–1413 (1971).
[Crossref]

S. Zhang and T. Tamir, “Spatial modifications of Gaussian beams diffracted by reflection gratings,” J. Opt. Soc. Am. 6(9), 1368–1381 (1989).
[Crossref]

J. Phys. D (1)

M. Cheng, P. Fu, M. H. Weng, X Y. Chen, X. H. Zeng, S. Y. Feng, and R. Chen, “Spatial and angular shifts of terahertz wave for the graphene metamaterial structure,” J. Phys. D 48, 285105 (2014).
[Crossref]

Nano Lett. (1)

F. H. L. Koppens, D. E. Chang, and F. J. Garcia de Abajo, “Graphene Plasmonics: A Platform for Strong LightâĂŞMatter Interactions,” Nano Lett. 11(8), 3370–3377 (2011).
[Crossref] [PubMed]

Nat. Mater. (1)

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6, 183–191 (2007).
[Crossref] [PubMed]

Nat. Nanotech. (1)

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotech. 6, 630–634 (2011).
[Crossref]

Nat. Photon. (1)

A. N. Grigorenko, M. Polini, and K. S. Novoselov, “Graphene plasmonics,” Nat. Photon. 6, 749–758 (2012).
[Crossref]

Nature (London) (2)

J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. Garcia de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature (London) 487, 77–81 (2012).

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 (London) 487, 82–85 (2012).

Opt. Express (4)

Opt. Lett. (5)

Phys. Rev. A (6)

M. S. Tomaš, “Green function for multilayers: Light scattering in planar cavities,” Phys. Rev. A 51, 2545 (1995).
[Crossref]

X. D. Zeng, L. F. Fan, and M. Suhail Zubairy, “Deep-subwavelength lithography via graphene plasmons,” Phys. Rev. A 95, 053850 (2017).
[Crossref]

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 95013809 (2017).
[Crossref]

L. G. Wang, M. Ikram, and M. S. Zubairy, “Control of the Goos-Hänchen shift of a light beam via a coherent driving field,” Phys. Rev. A 77, 023811 (2008).
[Crossref]

S. Asiri, J. Xu, M. Al-Amri, and M. S. Zubairy, “Controlling the Goos-Hänchen and Imbert-Fedorov shifts via pump and driving fields,” Phys. Rev. A 93, 013821 (2016).
[Crossref]

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

Phys. Rev. B (5)

X. D. Zeng, M. Al-Amri, and M. S. Zubairy, “Nanometer-scale microscopy via graphene plasmons,” Phys. Rev. B 90, 235418 (2014).
[Crossref]

M. Sarrazin, J. P. Vigneron, and J. M. Vigoureux, “Role of Wood anomalies in optical properties of thin metallic films with a bidimensional array of subwavelength holes,” Phys. Rev. B 67, 085415 (2003).
[Crossref]

M. Jablan, H. Buljan, and M. Soljačič, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80, 245435 (2009).
[Crossref]

A. Y. Nikitin, F. Guinea, F. J. Garcia-Vidal, and L. Martin-Moreno, “Surface plasmon enhanced absorption and suppressed transmission in periodic arrays of graphene ribbons,” Phys. Rev. B 85081405 (2012).
[Crossref]

W. Wang and J. M. Kinaret, “Plasmons in graphene nanoribbons: Interband transitions and nonlocal effects,” Phys. Rev. B 87, 195424 (2013).
[Crossref]

Phys. Rev. Lett. (1)

L. G. Wang, S. Y. Zhu, and M. S. Zubairy, “Goos-Hänchen Shifts of Partially Coherent Light Fields,” Phys. Rev. Lett. 111, 223901 (2013).
[Crossref]

Rev, Mod. Phys. (1)

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

Sci. Rep. (1)

Z. B. Li, K. Yao, F. N. Xia, S. Shen, J. G. Tian, and Y. M. Liu, “Graphene Plasmonic Metasurfaces to Steer Infrared Light,” Sci. Rep. 5, 12423 (2015).
[Crossref] [PubMed]

Science (2)

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320, 1308 (2008).
[Crossref] [PubMed]

A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332, 1291–1294 (2011).
[Crossref] [PubMed]

Other (1)

A. K. Ghatak and K. Thyagarajan, Contemporary Optics (Plenum, New York, 1978).
[Crossref]

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Figures (6)

Fig. 1
Fig. 1

A Gaussian beam is incident on the periodic graphene ribbon array. The Fermi level of the ribbons can be tuned by the gate voltage.

Fig. 2
Fig. 2

The zeroth-order reflection spectrum for the ribbon array with different Fermi levels.

Fig. 3
Fig. 3

(a) The zeroth-order reflectivities of TM waves with φ = 0 at different Fermi levels. The labels (1) and (2) represent the plus first and minus second-order diffraction positions. The wavelength of the incident beam is 45.2μm and the other parameters are the same as Fig. 2. (b) The arguments ϕ of the zeroth-order reflection field. (c) and (d) The corresponding GH shifts.

Fig. 4
Fig. 4

(The GH shifts versus the Fermi level under different ε2 and τ. The parameters are the same as the Fig. 3(a) and θ = 0.0769.

Fig. 5
Fig. 5

(a) The zeroth-order reflectivity of TE wave along y direction asa function the incidence angle at different Fermi levels. (b) The corresponding GH shifts.

Fig. 6
Fig. 6

(a) The normalized field intensity distribution of the incident TM-polarized Gaussian beam on the z = 0 plane. (b, c) The normalized field distributions of the zeroth-order reflection fields for the cases that EF = 0.6eV and 0.5eV.

Equations (22)

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σ ( ω ) = i e 2 E F π 2 ( ω + i τ 1 )
η x ( x , y ) σ ( x , y ) = E x 0 ( x , y , 0 ) + 1 2 ( 2 π ) 3 i ω d k x d k y d x d y 2 π i β k 0 2 ε 1 { [ k y 2 ρ 2 ( 1 + r s ) + 1 k 0 2 k x 2 β 2 ρ 2 ( 1 r p ) ] η x ( x , y ) + [ k x k y ρ 2 ( 1 + r s ) + 1 k 0 2 k x k y β 2 ρ 2 ( 1 r p ) ] η y ( x , y ) } e i [ k x ( x x ) + k y ( y y ) ] ;
η y ( x , y ) σ ( x , y ) = E y 0 ( x , y , 0 ) + 1 2 ( 2 π ) 3 i ω d k x d k y d x d y 2 π i β k 0 2 ε 1 { [ k x k y ρ 2 ( 1 + r s ) + 1 k 0 2 k x k y β 2 ρ 2 ( 1 r p ) ] η x ( x , y ) + [ k x 2 ρ 2 ( 1 + r s ) + 1 k 0 2 k y 2 β 2 ρ 2 ( 1 r p ) ] η y ( x , y ) } e i [ k x ( x x ) + k y ( y y ) ] ,
σ ( x , y ) = n σ n e i g n x ,
η x , y ( x , y ) = n η x , y n e i [ ( k x 0 + g n ) x + k y 0 y ] ,
η x n = 1 a 0 b d x E x 0 ( x , y , 0 ) σ e i ( k x x + k y y ) 1 2 ω n k 0 2 ε 1 β { [ k y 2 ρ 2 ( 1 + r s ) + 1 k 0 2 k x 2 β 2 ρ 2 ( 1 r p ) ] η x n σ n n + [ k x k y ρ 2 ( 1 + r s ) + 1 k 0 2 k x k y β 2 ρ 2 ( 1 r p ) ] η y n σ n n } ;
η y n = 1 a 0 b d x E y 0 ( x , y , 0 ) σ e i ( k x x + k y y ) 1 2 ω n k 0 2 ε 1 β { [ k x k y ρ 2 ( 1 + r s ) + 1 k 0 2 k x k y β 2 ρ 2 ( 1 r p ) ] η x n σ n n + [ k x 2 ρ 2 ( 1 + r s ) + 1 k 0 2 k y 2 β 2 ρ 2 ( 1 r p ) ] η y n σ n n } .
E x ( x , y , z ) = E x r ( x , y , z ) i 2 ω k 0 2 ε 1 β e i [ k x 0 x + k y 0 y + β z ] { [ k y 0 2 ρ 2 ( 1 + r s ) + 1 k 0 2 k x 0 2 β 2 ρ 2 ( 1 r p ) ] η x 0 + [ k x 0 k y 0 ρ 2 ( 1 + r s ) + 1 k 0 2 k x 0 k y 0 β 2 ρ 2 ( 1 r p ) ] η y 0 } = | r x | e i ϕ E x 0 ( x , y , z ) e 2 i β z ;
E y ( x , y , z ) = E y r ( x , y , z ) i 2 ω k 0 2 ε 1 β e i [ k x 0 x + k y 0 y + β z ] { [ k x 0 k y 0 ρ 2 ( 1 + r s ) + 1 k 0 2 k x 0 k y 0 β 2 ρ 2 ( 1 r p ) ] η x 0 + [ k x 0 2 ρ 2 ( 1 + r s ) + 1 k 0 2 k y 0 2 β 2 ρ 2 ( 1 r p ) ] η y 0 } = | r y | e i ϕ E y 0 ( x , y , z ) e 2 i β z .
S = λ 0 2 π d ϕ d θ ,
n π b ( 1 + ε 2 ) ω 2 4 α 0 c ω F .
ϕ = A r g ( η x 0 ) .
E ( r ) = A ( k x 0 , k y 0 ) e i k r d k x 0 d k 0 ,
A ( k x 0 , k y 0 ) = ( w x w y π ) 1 / 2 exp [ w x 2 2 ( k x 0 x 0 G ) 2 w y 2 2 k y 0 2 ] ,
( × × ε ( r , ω ) ω 2 c 2 ) E ( r , ω ) = i ω η ( r , ω ) .
E ( r , ω ) = i ω d 3 r G ( r , r ; ω ) η ( r , ω ) .
G x x ( r , r ; ω ) = 1 2 ( 2 π ) 3 d k x d k y 2 π i ε 1 β [ k y 2 ρ 2 ( 1 + r s ) + k x 2 β 2 k 0 2 ρ 2 ( 1 r p ) ] e i [ k x ( x x ) + k y ( y y ) ] ;
G x y ( r , r ; ω ) = 1 2 ( 2 π ) 3 d k x d k y 2 π i ε 1 β [ k x k y ρ 2 ( 1 + r s ) + k x k y β 2 k 0 2 ρ 2 ( 1 r p ) ] e i [ k x ( x x ) + k y ( y y ) ] ;
G y x ( r , r ; ω ) = G x y ( r , r ; ω ) ;
G y y ( r , r ; ω ) = 1 2 ( 2 π ) 3 d k x d k y 2 π i ε 1 β [ k x 2 ρ 2 ( 1 + r s ) + k y 2 β 2 k 0 2 ρ 2 ( 1 r p ) ] e i [ k x ( x x ) + k y ( y y ) ] .
r s = ( β ε 2 k 0 2 ρ 2 ) / ( β + ε 2 k 0 2 ρ 2 ) ;
r p = ( ε 2 β ε 1 ε 2 k 0 2 ρ 2 ) / ( ε 2 β + ε 1 ε 2 k 0 2 ρ 2 ) .