Abstract

It is found that the generalized Goos–Hänchen (GGH) shift of a light beam reflecting from a double negative metamaterial slab backed by a metal can be large positive as well as negative. We give an analytical expression for the GGH shift from which the necessary condition for the GGH shift to be positive or negative can be obtained. Numerical results validate the conclusions. A Gaussian-shaped beam was analyzed in the paraxial approximation and it was proven that there is no angular shift in this case. Finally we discuss the lossy effect of the metamaterial slab on the GGH shift.

© 2008 Optical Society of America

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  1. F. Goos and H. Hanchen, “Ein neuer und fundamentaler versuch zur totalreflektion,” Ann. Phys. 1, 333-346 (1947) (in German).
    [CrossRef]
  2. F. Goos and H. Hänchen, “Neumessung des strahlversetzungseffektes bei totalreflexion,” Ann. Phys. 3, 251-252 (1949) (in German).
    [CrossRef]
  3. K. Artmann, “Berechnung der Seitenversetzung des totalreflektierten strahles,” Ann. Phys. 1, 87-102 (1948) (in German).
    [CrossRef]
  4. R. H. Renard, “Total reflection: a new evaluation of the Goos-Hänchen shift,” J. Opt. Soc. Am. 54, 1190-1192 (1964).
    [CrossRef]
  5. B. R. Horowitz and T. Tamir, “Lateral displacement of a light beam at a dielectric interface,” J. Opt. Soc. Am. 61, 586-594 (1971).
    [CrossRef]
  6. J. J. Cowan and B. Anicin, “Longitudinal and transverse displacements of a bounded microwave beam at total internal reflection,” J. Opt. Soc. Am. 67, 1307-1311 (1977).
    [CrossRef]
  7. F. Bretenaker, A. Le Floch, and L. Dutriaux, “Direct measurement of the optical Goos-Hänchen effect in lasers,” Phys. Rev. Lett. 68, 931-933 (1992).
    [CrossRef] [PubMed]
  8. E. Pfleghaar, A. Marseille, and A. Weis, “Quantitative investigation of the effect of resonant absorbers on the Goos-Hänchen shift,” Phys. Rev. Lett. 70, 2281-2284 (1993).
    [CrossRef] [PubMed]
  9. B. M. Jost, A.-A. R. Al-Rashed, and B. E. A. Saleh, “Observation of the Goos-Hänchen effect in a phase-conjugate mirror,” Phys. Rev. Lett. 81, 2233-2235 (1998).
    [CrossRef]
  10. A. Haibel, G. Nimtz, and A. A. Stahlhofen, “The double-prism frustrated total reflection: revisited,” Phys. Rev. E 63, 047601-047603 (2001).
    [CrossRef]
  11. H. K. V. Lotsch, “Beam displacement at total reflection: the Goos-Hánchen effect, I,” Optik (Stuttgart) 32, 116-137 (1970).
  12. H. K. V. Lotsch, “Beam displacement at total reflection: the Goos-Hanchen effect, II,” Optik (Stuttgart) 32, 189-204 (1970).
  13. H. K. V. Lotsch, “Beam displacement at total reflection: the Goos-Hanchen effect, IV,” Optik (Stuttgart) 32, 553-560 (1971).
  14. W. J. Wild and C. L. Giles, “Goos-Hänchen shifts from absorbing media,” Phys. Rev. A 25, 2099-2101 (1982).
    [CrossRef]
  15. D. Felbacq, A. Moreau, and R. Smaâli, “Goos-Hänchen effect in the gaps of photonic crystals,” Opt. Lett. 28, 1633-1635 (2003).
    [CrossRef] [PubMed]
  16. C. F. Li, “Negative lateral shift of a light beam transmitted through a dielectric slab and interaction of boundary effects,” Phys. Rev. Lett. 91, 133903-133906 (2003).
    [CrossRef] [PubMed]
  17. H. M. Lai and S. W. Chan, “Large and negative Goos-Hänchen shift near the Brewster dip on reflection from weakly absorbing media,” Opt. Lett. 27, 680-682 (2002).
    [CrossRef]
  18. V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of epsi and μ,” Sov. Phys. Usp. 10, 509-514 (1968).
    [CrossRef]
  19. C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, “Experimental verification and simulation of negative index of refraction using Snell's law,” Phys. Rev. Lett. 90, 107401-107404 (2003).
    [CrossRef] [PubMed]
  20. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 79-81 (2001).
    [CrossRef]
  21. D. R. Smith and N. Kroll, “Negative refractive index in left-handed materials,” Phys. Rev. Lett. 85, 2933-2936 (2000).
    [CrossRef] [PubMed]
  22. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966-3969 (2000).
    [CrossRef] [PubMed]
  23. E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, “Electromagnetic waves: negative refraction by photonic crystals,” Nature 423, 604-605 (2003).
    [CrossRef] [PubMed]
  24. A. Lakhtakia, “Positive and negative Goos-Hänchen shifts and negative phase-velocity mediums (alias left-handed materials),” AEU, Int. J. Electron. Commun. 58, 229-231 (2004).
    [CrossRef]
  25. A. Lakhtakia, “On planewave remittances and Goos-Hänchen shifts of planar slabs with negative real permittivity and permeability,” Electromagnetics 23, 71-75 (2003).
    [CrossRef]
  26. D.-K. Qing and G. Chen, “Goos-Hänchen shifts at the interfaces between left- and right-handed media,” Opt. Lett. 29, 872-875 (2004).
    [CrossRef] [PubMed]
  27. P. R. Berman, “Goos-Hänchen shift in negatively refractive media,” Phys. Rev. E 66, 0676031-0676033 (2002).
    [CrossRef]
  28. X. Chen and C.-F. Li, “Lateral shift of the transmitted light beam through a left-handed slab,” Phys. Rev. E 69, 0666171-0666176 (2004).
    [CrossRef]
  29. L.-G. Wang and S.-Y. Zhu, “Large negative lateral shifts from the Kretschmann-Raether configuration with left-handed materials,” Appl. Phys. Lett. 87, 2211021-2211022 (2005).
  30. J. A. Kong, B.-L. Wu, and Y. Zhang, “Lateral displacement of a Gaussian beam reflected from a grounded slab with negative permittivity and permeability,” Appl. Phys. Lett. 80, 2084-2086 (2002).
    [CrossRef]
  31. I. V. Shadrivov, A. A. Zharov, and Y. S. Kivshar, “Giant Goos-Hänchen effect at the reflection from left-handed metamaterials,” Appl. Phys. Lett. 83, 2713-2715 (2003).
    [CrossRef]
  32. L.-G. Wang and S.-Y. Zhu, “Large positive and negative Goos-Hänchen shifts from a weakly absorbing left-handed slab,” J. Appl. Phys. 98, 0435221-0435224 (2005).
  33. C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, “Experimental verification and simulation of negative index of refraction using Snell's law,” Phys. Rev. Lett. 90, 107401-107404 (2003).
    [CrossRef] [PubMed]

2005 (2)

L.-G. Wang and S.-Y. Zhu, “Large negative lateral shifts from the Kretschmann-Raether configuration with left-handed materials,” Appl. Phys. Lett. 87, 2211021-2211022 (2005).

L.-G. Wang and S.-Y. Zhu, “Large positive and negative Goos-Hänchen shifts from a weakly absorbing left-handed slab,” J. Appl. Phys. 98, 0435221-0435224 (2005).

2004 (3)

X. Chen and C.-F. Li, “Lateral shift of the transmitted light beam through a left-handed slab,” Phys. Rev. E 69, 0666171-0666176 (2004).
[CrossRef]

D.-K. Qing and G. Chen, “Goos-Hänchen shifts at the interfaces between left- and right-handed media,” Opt. Lett. 29, 872-875 (2004).
[CrossRef] [PubMed]

A. Lakhtakia, “Positive and negative Goos-Hänchen shifts and negative phase-velocity mediums (alias left-handed materials),” AEU, Int. J. Electron. Commun. 58, 229-231 (2004).
[CrossRef]

2003 (7)

A. Lakhtakia, “On planewave remittances and Goos-Hänchen shifts of planar slabs with negative real permittivity and permeability,” Electromagnetics 23, 71-75 (2003).
[CrossRef]

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, “Experimental verification and simulation of negative index of refraction using Snell's law,” Phys. Rev. Lett. 90, 107401-107404 (2003).
[CrossRef] [PubMed]

D. Felbacq, A. Moreau, and R. Smaâli, “Goos-Hänchen effect in the gaps of photonic crystals,” Opt. Lett. 28, 1633-1635 (2003).
[CrossRef] [PubMed]

I. V. Shadrivov, A. A. Zharov, and Y. S. Kivshar, “Giant Goos-Hänchen effect at the reflection from left-handed metamaterials,” Appl. Phys. Lett. 83, 2713-2715 (2003).
[CrossRef]

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, “Experimental verification and simulation of negative index of refraction using Snell's law,” Phys. Rev. Lett. 90, 107401-107404 (2003).
[CrossRef] [PubMed]

C. F. Li, “Negative lateral shift of a light beam transmitted through a dielectric slab and interaction of boundary effects,” Phys. Rev. Lett. 91, 133903-133906 (2003).
[CrossRef] [PubMed]

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, “Electromagnetic waves: negative refraction by photonic crystals,” Nature 423, 604-605 (2003).
[CrossRef] [PubMed]

2002 (3)

P. R. Berman, “Goos-Hänchen shift in negatively refractive media,” Phys. Rev. E 66, 0676031-0676033 (2002).
[CrossRef]

J. A. Kong, B.-L. Wu, and Y. Zhang, “Lateral displacement of a Gaussian beam reflected from a grounded slab with negative permittivity and permeability,” Appl. Phys. Lett. 80, 2084-2086 (2002).
[CrossRef]

H. M. Lai and S. W. Chan, “Large and negative Goos-Hänchen shift near the Brewster dip on reflection from weakly absorbing media,” Opt. Lett. 27, 680-682 (2002).
[CrossRef]

2001 (2)

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 79-81 (2001).
[CrossRef]

A. Haibel, G. Nimtz, and A. A. Stahlhofen, “The double-prism frustrated total reflection: revisited,” Phys. Rev. E 63, 047601-047603 (2001).
[CrossRef]

2000 (2)

D. R. Smith and N. Kroll, “Negative refractive index in left-handed materials,” Phys. Rev. Lett. 85, 2933-2936 (2000).
[CrossRef] [PubMed]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

1998 (1)

B. M. Jost, A.-A. R. Al-Rashed, and B. E. A. Saleh, “Observation of the Goos-Hänchen effect in a phase-conjugate mirror,” Phys. Rev. Lett. 81, 2233-2235 (1998).
[CrossRef]

1993 (1)

E. Pfleghaar, A. Marseille, and A. Weis, “Quantitative investigation of the effect of resonant absorbers on the Goos-Hänchen shift,” Phys. Rev. Lett. 70, 2281-2284 (1993).
[CrossRef] [PubMed]

1992 (1)

F. Bretenaker, A. Le Floch, and L. Dutriaux, “Direct measurement of the optical Goos-Hänchen effect in lasers,” Phys. Rev. Lett. 68, 931-933 (1992).
[CrossRef] [PubMed]

1982 (1)

W. J. Wild and C. L. Giles, “Goos-Hänchen shifts from absorbing media,” Phys. Rev. A 25, 2099-2101 (1982).
[CrossRef]

1977 (1)

1971 (2)

B. R. Horowitz and T. Tamir, “Lateral displacement of a light beam at a dielectric interface,” J. Opt. Soc. Am. 61, 586-594 (1971).
[CrossRef]

H. K. V. Lotsch, “Beam displacement at total reflection: the Goos-Hanchen effect, IV,” Optik (Stuttgart) 32, 553-560 (1971).

1970 (2)

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

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

1968 (1)

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of epsi and μ,” Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

1964 (1)

1949 (1)

F. Goos and H. Hänchen, “Neumessung des strahlversetzungseffektes bei totalreflexion,” Ann. Phys. 3, 251-252 (1949) (in German).
[CrossRef]

1948 (1)

K. Artmann, “Berechnung der Seitenversetzung des totalreflektierten strahles,” Ann. Phys. 1, 87-102 (1948) (in German).
[CrossRef]

1947 (1)

F. Goos and H. Hanchen, “Ein neuer und fundamentaler versuch zur totalreflektion,” Ann. Phys. 1, 333-346 (1947) (in German).
[CrossRef]

Al-Rashed, A.-A. R.

B. M. Jost, A.-A. R. Al-Rashed, and B. E. A. Saleh, “Observation of the Goos-Hänchen effect in a phase-conjugate mirror,” Phys. Rev. Lett. 81, 2233-2235 (1998).
[CrossRef]

Anicin, B.

Artmann, K.

K. Artmann, “Berechnung der Seitenversetzung des totalreflektierten strahles,” Ann. Phys. 1, 87-102 (1948) (in German).
[CrossRef]

Aydin, K.

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, “Electromagnetic waves: negative refraction by photonic crystals,” Nature 423, 604-605 (2003).
[CrossRef] [PubMed]

Berman, P. R.

P. R. Berman, “Goos-Hänchen shift in negatively refractive media,” Phys. Rev. E 66, 0676031-0676033 (2002).
[CrossRef]

Bretenaker, F.

F. Bretenaker, A. Le Floch, and L. Dutriaux, “Direct measurement of the optical Goos-Hänchen effect in lasers,” Phys. Rev. Lett. 68, 931-933 (1992).
[CrossRef] [PubMed]

Chan, S. W.

Chen, G.

Chen, X.

X. Chen and C.-F. Li, “Lateral shift of the transmitted light beam through a left-handed slab,” Phys. Rev. E 69, 0666171-0666176 (2004).
[CrossRef]

Cowan, J. J.

Cubukcu, E.

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, “Electromagnetic waves: negative refraction by photonic crystals,” Nature 423, 604-605 (2003).
[CrossRef] [PubMed]

Dutriaux, L.

F. Bretenaker, A. Le Floch, and L. Dutriaux, “Direct measurement of the optical Goos-Hänchen effect in lasers,” Phys. Rev. Lett. 68, 931-933 (1992).
[CrossRef] [PubMed]

Felbacq, D.

Foteinopoulou, S.

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, “Electromagnetic waves: negative refraction by photonic crystals,” Nature 423, 604-605 (2003).
[CrossRef] [PubMed]

Giles, C. L.

W. J. Wild and C. L. Giles, “Goos-Hänchen shifts from absorbing media,” Phys. Rev. A 25, 2099-2101 (1982).
[CrossRef]

Goos, F.

F. Goos and H. Hänchen, “Neumessung des strahlversetzungseffektes bei totalreflexion,” Ann. Phys. 3, 251-252 (1949) (in German).
[CrossRef]

F. Goos and H. Hanchen, “Ein neuer und fundamentaler versuch zur totalreflektion,” Ann. Phys. 1, 333-346 (1947) (in German).
[CrossRef]

Greegor, R. B.

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, “Experimental verification and simulation of negative index of refraction using Snell's law,” Phys. Rev. Lett. 90, 107401-107404 (2003).
[CrossRef] [PubMed]

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, “Experimental verification and simulation of negative index of refraction using Snell's law,” Phys. Rev. Lett. 90, 107401-107404 (2003).
[CrossRef] [PubMed]

Haibel, A.

A. Haibel, G. Nimtz, and A. A. Stahlhofen, “The double-prism frustrated total reflection: revisited,” Phys. Rev. E 63, 047601-047603 (2001).
[CrossRef]

Hanchen, H.

F. Goos and H. Hanchen, “Ein neuer und fundamentaler versuch zur totalreflektion,” Ann. Phys. 1, 333-346 (1947) (in German).
[CrossRef]

Hänchen, H.

F. Goos and H. Hänchen, “Neumessung des strahlversetzungseffektes bei totalreflexion,” Ann. Phys. 3, 251-252 (1949) (in German).
[CrossRef]

Horowitz, B. R.

Jost, B. M.

B. M. Jost, A.-A. R. Al-Rashed, and B. E. A. Saleh, “Observation of the Goos-Hänchen effect in a phase-conjugate mirror,” Phys. Rev. Lett. 81, 2233-2235 (1998).
[CrossRef]

Kivshar, Y. S.

I. V. Shadrivov, A. A. Zharov, and Y. S. Kivshar, “Giant Goos-Hänchen effect at the reflection from left-handed metamaterials,” Appl. Phys. Lett. 83, 2713-2715 (2003).
[CrossRef]

Koltenbah, B. E. C.

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, “Experimental verification and simulation of negative index of refraction using Snell's law,” Phys. Rev. Lett. 90, 107401-107404 (2003).
[CrossRef] [PubMed]

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, “Experimental verification and simulation of negative index of refraction using Snell's law,” Phys. Rev. Lett. 90, 107401-107404 (2003).
[CrossRef] [PubMed]

Kong, J. A.

J. A. Kong, B.-L. Wu, and Y. Zhang, “Lateral displacement of a Gaussian beam reflected from a grounded slab with negative permittivity and permeability,” Appl. Phys. Lett. 80, 2084-2086 (2002).
[CrossRef]

Kroll, N.

D. R. Smith and N. Kroll, “Negative refractive index in left-handed materials,” Phys. Rev. Lett. 85, 2933-2936 (2000).
[CrossRef] [PubMed]

Lai, H. M.

Lakhtakia, A.

A. Lakhtakia, “Positive and negative Goos-Hänchen shifts and negative phase-velocity mediums (alias left-handed materials),” AEU, Int. J. Electron. Commun. 58, 229-231 (2004).
[CrossRef]

A. Lakhtakia, “On planewave remittances and Goos-Hänchen shifts of planar slabs with negative real permittivity and permeability,” Electromagnetics 23, 71-75 (2003).
[CrossRef]

Le Floch, A.

F. Bretenaker, A. Le Floch, and L. Dutriaux, “Direct measurement of the optical Goos-Hänchen effect in lasers,” Phys. Rev. Lett. 68, 931-933 (1992).
[CrossRef] [PubMed]

Li, C. F.

C. F. Li, “Negative lateral shift of a light beam transmitted through a dielectric slab and interaction of boundary effects,” Phys. Rev. Lett. 91, 133903-133906 (2003).
[CrossRef] [PubMed]

Li, C.-F.

X. Chen and C.-F. Li, “Lateral shift of the transmitted light beam through a left-handed slab,” Phys. Rev. E 69, 0666171-0666176 (2004).
[CrossRef]

Li, K.

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, “Experimental verification and simulation of negative index of refraction using Snell's law,” Phys. Rev. Lett. 90, 107401-107404 (2003).
[CrossRef] [PubMed]

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, “Experimental verification and simulation of negative index of refraction using Snell's law,” Phys. Rev. Lett. 90, 107401-107404 (2003).
[CrossRef] [PubMed]

Lotsch, H. K. V.

H. K. V. Lotsch, “Beam displacement at total reflection: the Goos-Hanchen effect, IV,” Optik (Stuttgart) 32, 553-560 (1971).

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

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

Marseille, A.

E. Pfleghaar, A. Marseille, and A. Weis, “Quantitative investigation of the effect of resonant absorbers on the Goos-Hänchen shift,” Phys. Rev. Lett. 70, 2281-2284 (1993).
[CrossRef] [PubMed]

Moreau, A.

Nimtz, G.

A. Haibel, G. Nimtz, and A. A. Stahlhofen, “The double-prism frustrated total reflection: revisited,” Phys. Rev. E 63, 047601-047603 (2001).
[CrossRef]

Ozbay, E.

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, “Electromagnetic waves: negative refraction by photonic crystals,” Nature 423, 604-605 (2003).
[CrossRef] [PubMed]

Parazzoli, C. G.

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, “Experimental verification and simulation of negative index of refraction using Snell's law,” Phys. Rev. Lett. 90, 107401-107404 (2003).
[CrossRef] [PubMed]

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, “Experimental verification and simulation of negative index of refraction using Snell's law,” Phys. Rev. Lett. 90, 107401-107404 (2003).
[CrossRef] [PubMed]

Pendry, J. B.

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

Pfleghaar, E.

E. Pfleghaar, A. Marseille, and A. Weis, “Quantitative investigation of the effect of resonant absorbers on the Goos-Hänchen shift,” Phys. Rev. Lett. 70, 2281-2284 (1993).
[CrossRef] [PubMed]

Qing, D.-K.

Renard, R. H.

Saleh, B. E. A.

B. M. Jost, A.-A. R. Al-Rashed, and B. E. A. Saleh, “Observation of the Goos-Hänchen effect in a phase-conjugate mirror,” Phys. Rev. Lett. 81, 2233-2235 (1998).
[CrossRef]

Schultz, S.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 79-81 (2001).
[CrossRef]

Shadrivov, I. V.

I. V. Shadrivov, A. A. Zharov, and Y. S. Kivshar, “Giant Goos-Hänchen effect at the reflection from left-handed metamaterials,” Appl. Phys. Lett. 83, 2713-2715 (2003).
[CrossRef]

Shelby, R. A.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 79-81 (2001).
[CrossRef]

Smaâli, R.

Smith, D. R.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 79-81 (2001).
[CrossRef]

D. R. Smith and N. Kroll, “Negative refractive index in left-handed materials,” Phys. Rev. Lett. 85, 2933-2936 (2000).
[CrossRef] [PubMed]

Soukoulis, C. M.

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, “Electromagnetic waves: negative refraction by photonic crystals,” Nature 423, 604-605 (2003).
[CrossRef] [PubMed]

Stahlhofen, A. A.

A. Haibel, G. Nimtz, and A. A. Stahlhofen, “The double-prism frustrated total reflection: revisited,” Phys. Rev. E 63, 047601-047603 (2001).
[CrossRef]

Tamir, T.

Tanielian, M.

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, “Experimental verification and simulation of negative index of refraction using Snell's law,” Phys. Rev. Lett. 90, 107401-107404 (2003).
[CrossRef] [PubMed]

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, “Experimental verification and simulation of negative index of refraction using Snell's law,” Phys. Rev. Lett. 90, 107401-107404 (2003).
[CrossRef] [PubMed]

Veselago, V. G.

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of epsi and μ,” Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Wang, L.-G.

L.-G. Wang and S.-Y. Zhu, “Large negative lateral shifts from the Kretschmann-Raether configuration with left-handed materials,” Appl. Phys. Lett. 87, 2211021-2211022 (2005).

L.-G. Wang and S.-Y. Zhu, “Large positive and negative Goos-Hänchen shifts from a weakly absorbing left-handed slab,” J. Appl. Phys. 98, 0435221-0435224 (2005).

Weis, A.

E. Pfleghaar, A. Marseille, and A. Weis, “Quantitative investigation of the effect of resonant absorbers on the Goos-Hänchen shift,” Phys. Rev. Lett. 70, 2281-2284 (1993).
[CrossRef] [PubMed]

Wild, W. J.

W. J. Wild and C. L. Giles, “Goos-Hänchen shifts from absorbing media,” Phys. Rev. A 25, 2099-2101 (1982).
[CrossRef]

Wu, B.-L.

J. A. Kong, B.-L. Wu, and Y. Zhang, “Lateral displacement of a Gaussian beam reflected from a grounded slab with negative permittivity and permeability,” Appl. Phys. Lett. 80, 2084-2086 (2002).
[CrossRef]

Zhang, Y.

J. A. Kong, B.-L. Wu, and Y. Zhang, “Lateral displacement of a Gaussian beam reflected from a grounded slab with negative permittivity and permeability,” Appl. Phys. Lett. 80, 2084-2086 (2002).
[CrossRef]

Zharov, A. A.

I. V. Shadrivov, A. A. Zharov, and Y. S. Kivshar, “Giant Goos-Hänchen effect at the reflection from left-handed metamaterials,” Appl. Phys. Lett. 83, 2713-2715 (2003).
[CrossRef]

Zhu, S.-Y.

L.-G. Wang and S.-Y. Zhu, “Large positive and negative Goos-Hänchen shifts from a weakly absorbing left-handed slab,” J. Appl. Phys. 98, 0435221-0435224 (2005).

L.-G. Wang and S.-Y. Zhu, “Large negative lateral shifts from the Kretschmann-Raether configuration with left-handed materials,” Appl. Phys. Lett. 87, 2211021-2211022 (2005).

AEU, Int. J. Electron. Commun. (1)

A. Lakhtakia, “Positive and negative Goos-Hänchen shifts and negative phase-velocity mediums (alias left-handed materials),” AEU, Int. J. Electron. Commun. 58, 229-231 (2004).
[CrossRef]

Ann. Phys. (3)

F. Goos and H. Hanchen, “Ein neuer und fundamentaler versuch zur totalreflektion,” Ann. Phys. 1, 333-346 (1947) (in German).
[CrossRef]

F. Goos and H. Hänchen, “Neumessung des strahlversetzungseffektes bei totalreflexion,” Ann. Phys. 3, 251-252 (1949) (in German).
[CrossRef]

K. Artmann, “Berechnung der Seitenversetzung des totalreflektierten strahles,” Ann. Phys. 1, 87-102 (1948) (in German).
[CrossRef]

Appl. Phys. Lett. (3)

L.-G. Wang and S.-Y. Zhu, “Large negative lateral shifts from the Kretschmann-Raether configuration with left-handed materials,” Appl. Phys. Lett. 87, 2211021-2211022 (2005).

J. A. Kong, B.-L. Wu, and Y. Zhang, “Lateral displacement of a Gaussian beam reflected from a grounded slab with negative permittivity and permeability,” Appl. Phys. Lett. 80, 2084-2086 (2002).
[CrossRef]

I. V. Shadrivov, A. A. Zharov, and Y. S. Kivshar, “Giant Goos-Hänchen effect at the reflection from left-handed metamaterials,” Appl. Phys. Lett. 83, 2713-2715 (2003).
[CrossRef]

Electromagnetics (1)

A. Lakhtakia, “On planewave remittances and Goos-Hänchen shifts of planar slabs with negative real permittivity and permeability,” Electromagnetics 23, 71-75 (2003).
[CrossRef]

J. Appl. Phys. (1)

L.-G. Wang and S.-Y. Zhu, “Large positive and negative Goos-Hänchen shifts from a weakly absorbing left-handed slab,” J. Appl. Phys. 98, 0435221-0435224 (2005).

J. Opt. Soc. Am. (3)

Nature (1)

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, “Electromagnetic waves: negative refraction by photonic crystals,” Nature 423, 604-605 (2003).
[CrossRef] [PubMed]

Opt. Lett. (3)

Optik (Stuttgart) (3)

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

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

H. K. V. Lotsch, “Beam displacement at total reflection: the Goos-Hanchen effect, IV,” Optik (Stuttgart) 32, 553-560 (1971).

Phys. Rev. A (1)

W. J. Wild and C. L. Giles, “Goos-Hänchen shifts from absorbing media,” Phys. Rev. A 25, 2099-2101 (1982).
[CrossRef]

Phys. Rev. E (3)

A. Haibel, G. Nimtz, and A. A. Stahlhofen, “The double-prism frustrated total reflection: revisited,” Phys. Rev. E 63, 047601-047603 (2001).
[CrossRef]

P. R. Berman, “Goos-Hänchen shift in negatively refractive media,” Phys. Rev. E 66, 0676031-0676033 (2002).
[CrossRef]

X. Chen and C.-F. Li, “Lateral shift of the transmitted light beam through a left-handed slab,” Phys. Rev. E 69, 0666171-0666176 (2004).
[CrossRef]

Phys. Rev. Lett. (8)

D. R. Smith and N. Kroll, “Negative refractive index in left-handed materials,” Phys. Rev. Lett. 85, 2933-2936 (2000).
[CrossRef] [PubMed]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

F. Bretenaker, A. Le Floch, and L. Dutriaux, “Direct measurement of the optical Goos-Hänchen effect in lasers,” Phys. Rev. Lett. 68, 931-933 (1992).
[CrossRef] [PubMed]

E. Pfleghaar, A. Marseille, and A. Weis, “Quantitative investigation of the effect of resonant absorbers on the Goos-Hänchen shift,” Phys. Rev. Lett. 70, 2281-2284 (1993).
[CrossRef] [PubMed]

B. M. Jost, A.-A. R. Al-Rashed, and B. E. A. Saleh, “Observation of the Goos-Hänchen effect in a phase-conjugate mirror,” Phys. Rev. Lett. 81, 2233-2235 (1998).
[CrossRef]

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, “Experimental verification and simulation of negative index of refraction using Snell's law,” Phys. Rev. Lett. 90, 107401-107404 (2003).
[CrossRef] [PubMed]

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, “Experimental verification and simulation of negative index of refraction using Snell's law,” Phys. Rev. Lett. 90, 107401-107404 (2003).
[CrossRef] [PubMed]

C. F. Li, “Negative lateral shift of a light beam transmitted through a dielectric slab and interaction of boundary effects,” Phys. Rev. Lett. 91, 133903-133906 (2003).
[CrossRef] [PubMed]

Science (1)

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 79-81 (2001).
[CrossRef]

Sov. Phys. Usp. (1)

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of epsi and μ,” Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Schematic of a light beam incident on a DNM slab backed by a metal. The thin curves are the paths of reflection from the interfaces of the slab according to geometric optics. The GGH shift of the reflected beam may be negative (ray 4) or positive (ray 2).

Fig. 2
Fig. 2

Dependence of the GGH shift Δ (in units of λ) on the angle θ of incidence, where the thickness of the slab is d = 6 λ and all of the other physical parameters are the same as in Fig. 1.

Fig. 3
Fig. 3

Dependence of the GGH shift Δ (in units of λ) on the thickness d of the slab, where the permittivity and permeability of the slab are ε 1 = 1.89 and μ 1 = 0.58 , respectively, at wavelength λ [33]; the angle of incidence is θ = π 2.1 and d is rescaled by k z 1 d .

Equations (11)

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r ( θ ) = ( β 0 β 1 ) ( β 1 + β 2 ) + ( β 0 + β 1 ) ( β 1 β 2 ) exp ( 2 i k z 1 d ) ( β 0 + β 1 ) ( β 1 + β 2 ) + ( β 0 β 1 ) ( β 1 β 2 ) exp ( 2 i k z 1 d ) ,
r ( θ ) = ( k z 1 2 μ 1 2 k z 0 2 ) + ( μ 1 2 k z 0 2 + k z 1 2 ) cos ( 2 k z 1 d ) + 2 i μ 1 k z 0 k z 1 sin ( 2 k z 1 d ) μ 1 2 k z 0 2 k z 1 2 + ( μ 1 2 k z 0 2 k z 1 2 ) cos ( 2 k z 1 d ) .
φ ( θ ) = arctan [ 2 μ 1 k z 0 k z 1 sin ( 2 k z 1 d ) ( k z 1 2 μ 1 2 k z 0 2 ) + ( μ 1 2 k z 0 2 + k z 1 2 ) cos ( 2 k z 1 d ) ] .
Δ = d φ ( θ ) k x 0 d θ ,
Δ = 2 d μ 1 tan θ [ cos 2 θ + ( n 1 2 1 ) sin ( 2 k z 1 d ) 2 k z 1 d ] cos 2 θ [ cos 2 ( k z 1 d ) + μ 1 2 sin 2 ( k z 1 d ) ] + ( n 1 2 1 ) cos 2 ( k z 1 d ) ,
cos θ < ( n 1 2 1 ) sin ( 2 k z 1 d ) 2 k z 1 d 1 2 cos θ p ,
Δ = 2 d μ 1 sin θ cos θ cos 2 θ [ cos 2 ( k z 1 d ) + μ 1 2 sin 2 ( k z 1 d ) ] + ( n 1 2 1 ) cos 2 ( k z 1 d ) + μ 1 ( n 1 2 1 ) tan θ k z 1 sin ( 2 k z 1 d ) cos 2 θ [ cos 2 ( k z 1 d ) + μ 1 2 sin 2 ( k z 1 d ) ] + ( n 1 2 1 ) cos 2 ( k z 1 d ) .
E in ( z ) z = 0 = exp ( x 2 2 w x 2 + i k x 0 x ) = 1 2 π A ( k x ) exp ( i k x x ) d k x ,
E r ( z ) = 1 2 π r ( θ ) A ( k x ) exp { i [ k z z + k x x ] } d k x ,
r ( θ ) exp [ ln r ( k x 0 ) + 1 r ( k x 0 ) d r d k x 0 ( k x k x 0 ) ] = r ( k x 0 ) exp [ ( 1 r ( k x 0 ) d r d k x 0 + i d φ d k x 0 ) ( k x k x 0 ) ] .
E r ( z ) = r ( k x 0 ) exp [ 1 2 w x 2 ( x + d φ d k x 0 z tan θ ) 2 ] × exp ( i k x 0 x ) .

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