Abstract

We present a theoretical study of the Goos-Hänchen and Imbert-Fedorov shifts for a fundamental Gaussian beam impinging on a surface coated with a single layer of graphene. We show that the graphene surface conductivity σ(ω) is responsible for the appearance of a giant and negative spatial Goos-Hänchen shift.

© 2015 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  6. K. Y. Bliokh and A. Aiello, “Goos-Hänchen and Imbert-Fedorov shifts: an overwiev,” J. Opt. 15, 014001 (2013).
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
  9. M. A. Player, “Angular momentum balance and transverse shift on reflection of light,” J. Phys. A: Math. Gen. 20, 3667 (1987).
    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
  13. A. Aiello and J. P. Woerdman, “Role of beam propagation in Goos-Hänchen and Imbert-Fedorov shifts,” Opt. Lett. 33, 1437 (2008).
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    [Crossref] [PubMed]
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    [Crossref]
  16. M. Merano, A. Aiello, G. W. ’t Hooft, M. P. von Exter, E. R. Eliel, and J. P. Woerdman, “Observation of Goos-Hänchen shifts in metallic reflection,” Opt. Express 15, 15928 (2007).
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  23. A. Aiello and J. P. Woerdman, “Goos-Hänchen and Imbert-Fedorov shifts of a non diffracting Bessel beam,” Opt. Lett 36, 543 (2010).
    [Crossref]
  24. I. V. Shadrivov, A. A. Zharov, and Yu S. Kivshar, “Giant Goos-Hänchen effect at the reflection from left-handed metamaterials,” Appl. Whys. Let. 83, 2713 (2003).
    [Crossref]
  25. J. He, J. Yi, and S. He, “Giant negative Goos-Hänchen shift for a photonic crystal with a negative effective index,” Opt. Express 14, 3024 (2006).
    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
  28. A. H. CastroNeto, 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]
  29. M. I. Katsnelson, Graphene: Carbon in Two Dimensions (Cambridge University Press, 2012).
    [Crossref]
  30. A. Calogeracos and N. Dombey, “History and physics of the Klein paradox,” Contemp. Phys. 40, 313 (1999).
    [Crossref]
  31. C. Itzykson and J. B. Zuber, Quantum Field Theory (Dover, 2006).
  32. 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, 201 (2005).
    [Crossref] [PubMed]
  33. M. I. Katsnelson, “Zitterbewegung, chirality, and minimal conductivity in graphene,” Eur. Phys. J. B. 51, 157 (2006).
    [Crossref]
  34. 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]
  35. T. Stauber, N. M. R. Peres, and A. K. Geim, “Optical conductivity of graphene in the visible region of the spectrum,” Phys. Rev. B 78, 085432 (2008).
    [Crossref]
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    [Crossref] [PubMed]
  37. A. Jellala, I. Redouanic, Y. Zahidic, and H. Bahloulia, “Goos-Hänchen like shifts in graphene double barriers,” Physica E 58, 30 (2014).
    [Crossref]
  38. J. C. Martinez and M. B. A. Janil, “Theory of giant Faraday rotation and Goos-Hänchen shift in graphene,” Europhys. Lett. 96, 27008 (2011).
    [Crossref]
  39. M. Merano, A. Aiello, and J. P. Woerdman, “Duality between spatial and angular shift in optical reflection,” Phys. Rev. A 80, 061801 (2009).
    [Crossref]
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  44. T. Zhan, X. Shi, Y. Dai, X. Liu, and J. Zi, “Transfer matrix method for optics in graphene layers,” J. Phys.: Conden. Matt. 25, 215301 (2013).
  45. M. Ornigotti and A. Aiello, “Goos-Hänchen and Imbert-Fedorov for bounded wave packets of light,” J. Opt. 15, 014004 (2013).
    [Crossref]

2015 (1)

2014 (2)

2013 (3)

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

T. Zhan, X. Shi, Y. Dai, X. Liu, and J. Zi, “Transfer matrix method for optics in graphene layers,” J. Phys.: Conden. Matt. 25, 215301 (2013).

M. Ornigotti and A. Aiello, “Goos-Hänchen and Imbert-Fedorov for bounded wave packets of light,” J. Opt. 15, 014004 (2013).
[Crossref]

2011 (2)

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

S. Longhi, G. Della Valle, and K. Staliunas, “Goos-Hänchen shift in complex crystals,” Phys. Rev. A 84, 042119 (2011).
[Crossref]

2010 (2)

M. Merano, N. Hermosa, J.P. Woerdman, and A. Aiello, “How orbital angular momentum affects beam shifts in optical reflection,” Phys. Rev. A 82, 023817 (2010).
[Crossref]

A. Aiello and J. P. Woerdman, “Goos-Hänchen and Imbert-Fedorov shifts of a non diffracting Bessel beam,” Opt. Lett 36, 543 (2010).
[Crossref]

2009 (2)

A. H. CastroNeto, 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]

M. Merano, A. Aiello, and J. P. Woerdman, “Duality between spatial and angular shift in optical reflection,” Phys. Rev. A 80, 061801 (2009).
[Crossref]

2008 (4)

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]

T. Stauber, N. M. R. Peres, and A. K. Geim, “Optical conductivity of graphene in the visible region of the spectrum,” Phys. Rev. B 78, 085432 (2008).
[Crossref]

A. Aiello and J. P. Woerdman, “Role of beam propagation in Goos-Hänchen and Imbert-Fedorov shifts,” Opt. Lett. 33, 1437 (2008).
[Crossref] [PubMed]

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

2007 (2)

2006 (3)

K. Y. 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]

J. He, J. Yi, and S. He, “Giant negative Goos-Hänchen shift for a photonic crystal with a negative effective index,” Opt. Express 14, 3024 (2006).
[Crossref] [PubMed]

M. I. Katsnelson, “Zitterbewegung, chirality, and minimal conductivity in graphene,” Eur. Phys. J. B. 51, 157 (2006).
[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, 201 (2005).
[Crossref] [PubMed]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438, 197 (2005).
[Crossref] [PubMed]

2004 (1)

2003 (1)

I. V. Shadrivov, A. A. Zharov, and Yu S. Kivshar, “Giant Goos-Hänchen effect at the reflection from left-handed metamaterials,” Appl. Whys. Let. 83, 2713 (2003).
[Crossref]

1999 (1)

A. Calogeracos and N. Dombey, “History and physics of the Klein paradox,” Contemp. Phys. 40, 313 (1999).
[Crossref]

1996 (1)

1992 (1)

V. S. Liberman and B. Y. Zel’dovich, “Spin-orbit interaction of a photon in an inhomogeneous medium,” Phys. Rev. A 46, 5199 (1992).
[Crossref] [PubMed]

1988 (1)

V. G. Fedoseyev, “Conservation laws and transverse motion of energy on reflection and transmission of electromagnetic waves,” J. Phys. A: Math. Gen 21, 2045 (1988).
[Crossref]

1987 (1)

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

1986 (1)

1978 (1)

1972 (2)

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 (1972).
[Crossref]

K. W. Chiu and J. J. Quinn, “On the Goos-Hänchen Effect: A Simple Example of a Time Delay Scattering Process,” Am. J. Phys. 40, 1847 (1972)
[Crossref]

1965 (1)

H. Schilling, “Die Strahlversetzung bei der Reflexion linear oder elliptisch polarisierter ebener Wellen an der Trennebene zwischen absorbierenden Medien,” Ann. Phys. (Berlin) 16, 122 (1965).
[Crossref]

1955 (1)

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

1948 (1)

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

1947 (1)

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

’t Hooft, G. W.

Aiello, A.

M. Ornigotti, A. Aiello, and C. Conti, “Goos-Hänchen and Imbert-Fedorov shifts for paraxial X-Waves,” Opt. Lett. 40, 558 (2015).
[Crossref] [PubMed]

M. Ornigotti and A. Aiello, “Goos-Hänchen and Imbert-Fedorov for bounded wave packets of light,” J. Opt. 15, 014004 (2013).
[Crossref]

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

M. Merano, N. Hermosa, J.P. Woerdman, and A. Aiello, “How orbital angular momentum affects beam shifts in optical reflection,” Phys. Rev. A 82, 023817 (2010).
[Crossref]

A. Aiello and J. P. Woerdman, “Goos-Hänchen and Imbert-Fedorov shifts of a non diffracting Bessel beam,” Opt. Lett 36, 543 (2010).
[Crossref]

M. Merano, A. Aiello, and J. P. Woerdman, “Duality between spatial and angular shift in optical reflection,” Phys. Rev. A 80, 061801 (2009).
[Crossref]

A. Aiello and J. P. Woerdman, “Role of beam propagation in Goos-Hänchen and Imbert-Fedorov shifts,” Opt. Lett. 33, 1437 (2008).
[Crossref] [PubMed]

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

A. Aiello and J. P. Woerdman, “Theory of angular Goos-Hänchen shift near brewster incidence,” arXiv:0903.3730v2 [physics.optics].

Artmann, K.

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

Bahloulia, H.

A. Jellala, I. Redouanic, Y. Zahidic, and H. Bahloulia, “Goos-Hänchen like shifts in graphene double barriers,” Physica E 58, 30 (2014).
[Crossref]

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]

Bliokh, K. Y.

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

K. Y. 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]

Bliokh, Y. P.

K. Y. 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]

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]

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th edition (Cambridge University Press, 2003).

Calogeracos, A.

A. Calogeracos and N. Dombey, “History and physics of the Klein paradox,” Contemp. Phys. 40, 313 (1999).
[Crossref]

CastroNeto, A. H.

A. H. CastroNeto, 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]

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 (2007).
[Crossref]

Chen, X. D.

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 (2007).
[Crossref]

Chiu, K. W.

K. W. Chiu and J. J. Quinn, “On the Goos-Hänchen Effect: A Simple Example of a Time Delay Scattering Process,” Am. J. Phys. 40, 1847 (1972)
[Crossref]

Conti, C.

Dai, Y.

T. Zhan, X. Shi, Y. Dai, X. Liu, and J. Zi, “Transfer matrix method for optics in graphene layers,” J. Phys.: Conden. Matt. 25, 215301 (2013).

Della Valle, G.

S. Longhi, G. Della Valle, and K. Staliunas, “Goos-Hänchen shift in complex crystals,” Phys. Rev. A 84, 042119 (2011).
[Crossref]

Dombey, N.

A. Calogeracos and N. Dombey, “History and physics of the Klein paradox,” Contemp. Phys. 40, 313 (1999).
[Crossref]

Dubonos, S. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438, 197 (2005).
[Crossref] [PubMed]

Dutta Gupta, S.

D. Golla and S. Dutta Gupta, “Goos-Hänchen shift for higher order Hermite-Gaussian beams,” arXiv:1011.3968v1.

Eliel, E. R.

Fedorov, F. I.

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

Fedoseyev, V. G.

V. G. Fedoseyev, “Conservation laws and transverse motion of energy on reflection and transmission of electromagnetic waves,” J. Phys. A: Math. Gen 21, 2045 (1988).
[Crossref]

Firsov, A. A.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438, 197 (2005).
[Crossref] [PubMed]

Geim, A. K.

A. H. CastroNeto, 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]

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]

T. Stauber, N. M. R. Peres, and A. K. Geim, “Optical conductivity of graphene in the visible region of the spectrum,” Phys. Rev. B 78, 085432 (2008).
[Crossref]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438, 197 (2005).
[Crossref] [PubMed]

Gilles, H.

Girard, S.

Golla, D.

D. Golla and S. Dutta Gupta, “Goos-Hänchen shift for higher order Hermite-Gaussian beams,” arXiv:1011.3968v1.

Goos, F.

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

Grigorenko, A. N.

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]

Grigorieva, I. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438, 197 (2005).
[Crossref] [PubMed]

Guinea, F.

A. H. CastroNeto, 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]

Hänchen, H.

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

He, J.

He, S.

Hermosa, N.

M. Merano, N. Hermosa, J.P. Woerdman, and A. Aiello, “How orbital angular momentum affects beam shifts in optical reflection,” Phys. Rev. A 82, 023817 (2010).
[Crossref]

Hosten, O.

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

Imbert, C.

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 (1972).
[Crossref]

Itzykson, C.

C. Itzykson and J. B. Zuber, Quantum Field Theory (Dover, 2006).

Janil, M. B. A.

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

Jellala, A.

A. Jellala, I. Redouanic, Y. Zahidic, and H. Bahloulia, “Goos-Hänchen like shifts in graphene double barriers,” Physica E 58, 30 (2014).
[Crossref]

Jiang, D.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438, 197 (2005).
[Crossref] [PubMed]

Katsnelson, M. I.

M. I. Katsnelson, “Zitterbewegung, chirality, and minimal conductivity in graphene,” Eur. Phys. J. B. 51, 157 (2006).
[Crossref]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438, 197 (2005).
[Crossref] [PubMed]

M. I. Katsnelson, Graphene: Carbon in Two Dimensions (Cambridge University Press, 2012).
[Crossref]

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, 201 (2005).
[Crossref] [PubMed]

Kivshar, Yu S.

I. V. Shadrivov, A. A. Zharov, and Yu S. Kivshar, “Giant Goos-Hänchen effect at the reflection from left-handed metamaterials,” Appl. Whys. Let. 83, 2713 (2003).
[Crossref]

Kozaki, S.

Kwiat, P.

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

Landry, G. D.

Leung, P. T.

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

Li, X.

Liberman, V. S.

V. S. Liberman and B. Y. Zel’dovich, “Spin-orbit interaction of a photon in an inhomogeneous medium,” Phys. Rev. A 46, 5199 (1992).
[Crossref] [PubMed]

Liu, X.

T. Zhan, X. Shi, Y. Dai, X. Liu, and J. Zi, “Transfer matrix method for optics in graphene layers,” J. Phys.: Conden. Matt. 25, 215301 (2013).

Liu, Z. B.

Longhi, S.

S. Longhi, G. Della Valle, and K. Staliunas, “Goos-Hänchen shift in complex crystals,” Phys. Rev. A 84, 042119 (2011).
[Crossref]

Maldonado, T. A.

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics, (Cambridge University Press, New York, 1995).
[Crossref]

Martinez, J. C.

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

Merano, M.

M. Merano, N. Hermosa, J.P. Woerdman, and A. Aiello, “How orbital angular momentum affects beam shifts in optical reflection,” Phys. Rev. A 82, 023817 (2010).
[Crossref]

M. Merano, A. Aiello, and J. P. Woerdman, “Duality between spatial and angular shift in optical reflection,” Phys. Rev. A 80, 061801 (2009).
[Crossref]

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

Morozov, S. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438, 197 (2005).
[Crossref] [PubMed]

Nair, R. R.

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]

Novoselov, K. S.

A. H. CastroNeto, 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]

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]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438, 197 (2005).
[Crossref] [PubMed]

Ornigotti, M.

M. Ornigotti, A. Aiello, and C. Conti, “Goos-Hänchen and Imbert-Fedorov shifts for paraxial X-Waves,” Opt. Lett. 40, 558 (2015).
[Crossref] [PubMed]

M. Ornigotti and A. Aiello, “Goos-Hänchen and Imbert-Fedorov for bounded wave packets of light,” J. Opt. 15, 014004 (2013).
[Crossref]

Peres, N. M. R.

A. H. CastroNeto, 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]

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]

T. Stauber, N. M. R. Peres, and A. K. Geim, “Optical conductivity of graphene in the visible region of the spectrum,” Phys. Rev. B 78, 085432 (2008).
[Crossref]

Pillon, F.

Player, M. A.

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

Quinn, J. J.

K. W. Chiu and J. J. Quinn, “On the Goos-Hänchen Effect: A Simple Example of a Time Delay Scattering Process,” Am. J. Phys. 40, 1847 (1972)
[Crossref]

Redouanic, I.

A. Jellala, I. Redouanic, Y. Zahidic, and H. Bahloulia, “Goos-Hänchen like shifts in graphene double barriers,” Physica E 58, 30 (2014).
[Crossref]

Sakurai, H.

Schilling, H.

H. Schilling, “Die Strahlversetzung bei der Reflexion linear oder elliptisch polarisierter ebener Wellen an der Trennebene zwischen absorbierenden Medien,” Ann. Phys. (Berlin) 16, 122 (1965).
[Crossref]

Shadrivov, I. V.

I. V. Shadrivov, A. A. Zharov, and Yu S. Kivshar, “Giant Goos-Hänchen effect at the reflection from left-handed metamaterials,” Appl. Whys. Let. 83, 2713 (2003).
[Crossref]

Shi, X.

T. Zhan, X. Shi, Y. Dai, X. Liu, and J. Zi, “Transfer matrix method for optics in graphene layers,” J. Phys.: Conden. Matt. 25, 215301 (2013).

Staliunas, K.

S. Longhi, G. Della Valle, and K. Staliunas, “Goos-Hänchen shift in complex crystals,” Phys. Rev. A 84, 042119 (2011).
[Crossref]

Stauber, T.

T. Stauber, N. M. R. Peres, and A. K. Geim, “Optical conductivity of graphene in the visible region of the spectrum,” Phys. Rev. B 78, 085432 (2008).
[Crossref]

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]

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, 201 (2005).
[Crossref] [PubMed]

Tamir, T.

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, 201 (2005).
[Crossref] [PubMed]

Tian, J. G.

von Exter, M. P.

Wang, P.

Woerdman, J. P.

A. Aiello and J. P. Woerdman, “Goos-Hänchen and Imbert-Fedorov shifts of a non diffracting Bessel beam,” Opt. Lett 36, 543 (2010).
[Crossref]

M. Merano, A. Aiello, and J. P. Woerdman, “Duality between spatial and angular shift in optical reflection,” Phys. Rev. A 80, 061801 (2009).
[Crossref]

A. Aiello and J. P. Woerdman, “Role of beam propagation in Goos-Hänchen and Imbert-Fedorov shifts,” Opt. Lett. 33, 1437 (2008).
[Crossref] [PubMed]

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

A. Aiello and J. P. Woerdman, “Theory of angular Goos-Hänchen shift near brewster incidence,” arXiv:0903.3730v2 [physics.optics].

Woerdman, J.P.

M. Merano, N. Hermosa, J.P. Woerdman, and A. Aiello, “How orbital angular momentum affects beam shifts in optical reflection,” Phys. Rev. A 82, 023817 (2010).
[Crossref]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th edition (Cambridge University Press, 2003).

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics, (Cambridge University Press, New York, 1995).
[Crossref]

Xing, F.

Yi, J.

Zahidic, Y.

A. Jellala, I. Redouanic, Y. Zahidic, and H. Bahloulia, “Goos-Hänchen like shifts in graphene double barriers,” Physica E 58, 30 (2014).
[Crossref]

Zel’dovich, B. Y.

V. S. Liberman and B. Y. Zel’dovich, “Spin-orbit interaction of a photon in an inhomogeneous medium,” Phys. Rev. A 46, 5199 (1992).
[Crossref] [PubMed]

Zhan, T.

T. Zhan, X. Shi, Y. Dai, X. Liu, and J. Zi, “Transfer matrix method for optics in graphene layers,” J. Phys.: Conden. Matt. 25, 215301 (2013).

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, 201 (2005).
[Crossref] [PubMed]

Zharov, A. A.

I. V. Shadrivov, A. A. Zharov, and Yu S. Kivshar, “Giant Goos-Hänchen effect at the reflection from left-handed metamaterials,” Appl. Whys. Let. 83, 2713 (2003).
[Crossref]

Zi, J.

T. Zhan, X. Shi, Y. Dai, X. Liu, and J. Zi, “Transfer matrix method for optics in graphene layers,” J. Phys.: Conden. Matt. 25, 215301 (2013).

Zuber, J. B.

C. Itzykson and J. B. Zuber, Quantum Field Theory (Dover, 2006).

Am. J. Phys. (1)

K. W. Chiu and J. J. Quinn, “On the Goos-Hänchen Effect: A Simple Example of a Time Delay Scattering Process,” Am. J. Phys. 40, 1847 (1972)
[Crossref]

Ann. Phys. (2)

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

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

Ann. Phys. (Berlin) (1)

H. Schilling, “Die Strahlversetzung bei der Reflexion linear oder elliptisch polarisierter ebener Wellen an der Trennebene zwischen absorbierenden Medien,” Ann. Phys. (Berlin) 16, 122 (1965).
[Crossref]

Appl. Opt. (2)

Appl. Whys. Let. (1)

I. V. Shadrivov, A. A. Zharov, and Yu S. Kivshar, “Giant Goos-Hänchen effect at the reflection from left-handed metamaterials,” Appl. Whys. Let. 83, 2713 (2003).
[Crossref]

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Eur. Phys. J. B. (1)

M. I. Katsnelson, “Zitterbewegung, chirality, and minimal conductivity in graphene,” Eur. Phys. J. B. 51, 157 (2006).
[Crossref]

Europhys. Lett. (1)

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

J. Opt. (2)

M. Ornigotti and A. Aiello, “Goos-Hänchen and Imbert-Fedorov for bounded wave packets of light,” J. Opt. 15, 014004 (2013).
[Crossref]

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

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

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

V. G. Fedoseyev, “Conservation laws and transverse motion of energy on reflection and transmission of electromagnetic waves,” J. Phys. A: Math. Gen 21, 2045 (1988).
[Crossref]

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

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

J. Phys.: Conden. Matt. (1)

T. Zhan, X. Shi, Y. Dai, X. Liu, and J. Zi, “Transfer matrix method for optics in graphene layers,” J. Phys.: Conden. Matt. 25, 215301 (2013).

Nature (2)

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438, 197 (2005).
[Crossref] [PubMed]

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, 201 (2005).
[Crossref] [PubMed]

Opt. Commun. (1)

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

Opt. Express (2)

Opt. Lett (1)

A. Aiello and J. P. Woerdman, “Goos-Hänchen and Imbert-Fedorov shifts of a non diffracting Bessel beam,” Opt. Lett 36, 543 (2010).
[Crossref]

Opt. Lett. (3)

Phys. Rev. A (4)

V. S. Liberman and B. Y. Zel’dovich, “Spin-orbit interaction of a photon in an inhomogeneous medium,” Phys. Rev. A 46, 5199 (1992).
[Crossref] [PubMed]

S. Longhi, G. Della Valle, and K. Staliunas, “Goos-Hänchen shift in complex crystals,” Phys. Rev. A 84, 042119 (2011).
[Crossref]

M. Merano, N. Hermosa, J.P. Woerdman, and A. Aiello, “How orbital angular momentum affects beam shifts in optical reflection,” Phys. Rev. A 82, 023817 (2010).
[Crossref]

M. Merano, A. Aiello, and J. P. Woerdman, “Duality between spatial and angular shift in optical reflection,” Phys. Rev. A 80, 061801 (2009).
[Crossref]

Phys. Rev. B (1)

T. Stauber, N. M. R. Peres, and A. K. Geim, “Optical conductivity of graphene in the visible region of the spectrum,” Phys. Rev. B 78, 085432 (2008).
[Crossref]

Phys. Rev. D (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 (1972).
[Crossref]

Phys. Rev. Lett. (1)

K. Y. 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]

Physica E (1)

A. Jellala, I. Redouanic, Y. Zahidic, and H. Bahloulia, “Goos-Hänchen like shifts in graphene double barriers,” Physica E 58, 30 (2014).
[Crossref]

Rev. Mod. Phys. (1)

A. H. CastroNeto, 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]

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]

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

Other (7)

C. Itzykson and J. B. Zuber, Quantum Field Theory (Dover, 2006).

M. I. Katsnelson, Graphene: Carbon in Two Dimensions (Cambridge University Press, 2012).
[Crossref]

D. Golla and S. Dutta Gupta, “Goos-Hänchen shift for higher order Hermite-Gaussian beams,” arXiv:1011.3968v1.

Digital Library of Mathematical Functions, http://dlmf.nist.gov , National Institute of Standard and Technology (2010).

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics, (Cambridge University Press, New York, 1995).
[Crossref]

A. Aiello and J. P. Woerdman, “Theory of angular Goos-Hänchen shift near brewster incidence,” arXiv:0903.3730v2 [physics.optics].

M. Born and E. Wolf, Principles of Optics, 7th edition (Cambridge University Press, 2003).

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Figures (5)

Fig. 1
Fig. 1 (a) Schematic representation of the considered surface. The graphene layer (green) is characterized by its surface conductivity σ(Ω), whose explicit expression is given by Eq. (1). The dielectric substrate (green) is characterized by the refractive index n. (b) Geometry of beam reflection at the interface. The single graphene layer is located on the surface at z = 0. The different Cartesian coordinate systems K,Ki,Kr are shown.
Fig. 2
Fig. 2 Modulus (left column) and phase (right column) of the reflection coefficients rλ = Rλ exp(λ) for p-polarization (top row) and s-polarization (bottom row). In all graphs, the solid black line corresponds to the case of the graphene-coated surface, while the green dashed curve corresponds to the case without graphene coating. The refractive index of the bulk medium is chosen to be n = 1.5.
Fig. 3
Fig. 3 Spatial IF shift ΔIF for (a) circular polarization and (b) 45° linear polarization for a graphene coated surface. The spatial IF shifts are nonzero even for linear polarization. Spatial GH shift ΔGH for (c) p- polarization and (d) s-polarization for a graphene-coated surface. Since ∂ϕλ/∂θ ≠ 0, in both cases ΔGH ≠ 0. In particular, since ϕp varies very rapidly with θ in the vicinity of the Brewster angle, the corresponding spatial shift for p-polarization [Panel (c)] is giant in modulus, and negative due to the fact that ϕp varies from 0 to −π [See Fig. 2(b)].
Fig. 4
Fig. 4 Modulus (left column) and phase (right column) of the reflection coefficients rλ = Rλ exp(λ) for p-polarization (top row) and s-polarization (bottom row) for the case with TIR. In all graphs, the solid black line corresponds to the case of the graphene-coated surface, while the green dashed curve corresponds to the case without graphene coating. The refractive index of the dielectric medium is chosen to be n = 1.5.
Fig. 5
Fig. 5 Spatial IF shift ΔIF for (a) circular polarization and (b) 45° linear polarization for a graphene coated surface for the case with TIR. Spatial GH shift ΔGH for (c) p- polarization and (d) s-polarization for a graphene-coated surface for the case with TIR.

Equations (17)

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σ ( Ω ) σ 0 = Θ ( Ω 2 ) + i [ 1 π Ω 1 π ln | Ω + 2 Ω 2 | ] ,
E i ( r ) = l = 1 2 d 2 K e ^ λ ( U , V , θ ) A λ ( U , V , θ ) e i k i r i ,
A ( U , V ) = e w 0 2 ( U 2 + V 2 ) ,
E i ( r r ) = λ = 1 2 d 2 K e ^ λ ( U , V , π θ ) A ˜ λ ( U , V , θ ) e i k r r r ,
r s ( θ ) = cos θ n 2 sin 2 θ σ ( Ω ) cos θ + n 2 sin 2 θ + σ ( Ω ) ,
r p ( θ ) = n 2 cos θ n 2 sin 2 θ [ 1 σ ( Ω ) cos θ ] n 2 cos θ + n 2 sin 2 θ [ 1 + σ ( Ω ) cos θ ] ,
R = + R | E r | 2 d X r d Y r + | E r | 2 d X r d Y r = X r X ^ r + Y r y ^ r ,
k 0 Δ GH = X r | z = 0 , Θ GH = X r z ,
k 0 Δ IF = Y r | z = 0 , Θ IF = Y r z .
k 0 Δ GH = w p ϕ p θ + w s ϕ s θ ,
k 0 Δ IF = cot θ [ w p a s 2 + w s a p 2 a p a s sin η + 2 w p w s sin ( η ϕ p + ϕ s ) ] ,
Θ GH = ( w p ln R p θ + w s ln R s θ ) ,
Θ IF = w p a s 2 w s a p 1 a p a s cos η cot θ ,
r s ( θ ) = n cos θ 1 n 2 sin 2 θ n σ ( Ω ) n cos θ + 1 n 2 sin 2 θ + n σ ( Ω ) ,
r p ( θ ) = cos θ n 1 n 2 sin 2 θ [ 1 σ ( Ω ) cos θ ] n cos θ + n 1 n 2 sin 2 θ [ 1 + σ ( Ω ) cos θ ] ,
k 0 Δ GH = w p ϕ p θ + w s ϕ s θ ,
k 0 Δ IF = 4 a p a s a p 2 + a s 2 cot θ sin ( η ϕ p ϕ s 2 ) cos ( ϕ p ϕ s 2 ) ,

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