Abstract

Goos–Hänchen (GH) shift of a transverse-magnetic (TM) wave reflected from a semi-infinite anisotropic metamaterial consisting of aligned metallic nanowires in a dielectric matrix is investigated. Based on Bruggeman effective medium theory, we obtain the conditions for realizing the negative refraction, which are dependent on both the incident wavelength and the volume fraction of metallic inclusions. Then, we investigate the GH shifts from the composite metamaterial with positive and negative refractions with the stationary-phase method. Numerical results show that the enhancement of GH shift can be achieved near the pseudo-Brewster angle for small volume fractions and at the close-to-grazing incidence for large volume fractions. We further find that for positively refractive metamaterials with weak absorption, one can realize the transition from negative GH shift to the positive one by adjusting the incident wavelength. However, for negatively refractive composite metamaterials, the reversal of the GH shifts may take place by the adjustment of the volume fraction instead of the incident wavelength. In order to demonstrate the validity of the stationary-phase approach, numerical simulations are performed for a Gaussian-shaped beam. In the end, by using COMSOL simulation, a comprehensive understanding is given and the above analysis is confirmed.

© 2012 Optical Society of America

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  1. F. Goos and H. Hänchen, “Ein neuer und fundamentaler Versuch zur Totalreflexion,” Ann. Phys. 436, 333–346 (1947).
    [CrossRef]
  2. F. Goos and H. Hänchen, “Neumessung des Strahlversetzungseffektes bei Totalreflexion,” Ann. Phys. 440, 251–252 (1949).
    [CrossRef]
  3. K. Artmann, “Berechnung der Seitenversetzung des totalreflektierten Strahles,” Ann. Phys. 437, 87–102 (1948).
    [CrossRef]
  4. T. Tamir and H. L. Bertoni, “Lateral displacement of optical Beams at multilayered and periodic structures,” J. Opt. Soc. Am. 61, 1397–1413 (1971).
    [CrossRef]
  5. M. Miri, A. Naqavi, A. Khavasi, K. Mehrany, S. Khorasani, and B. Rashidian, “Geometrical approach in physical understanding of the Goos–Hänchen shift in one- and two-dimensional periodic structures,” Opt. Lett. 33, 2940–2942 (2008).
    [CrossRef]
  6. L. G. Wang and S. Y. Zhu, “Giant lateral shift of a light beam at the defect mode in one-dimensional photonic crystals,” Opt. Lett. 31, 101–103 (2006).
    [CrossRef]
  7. P. Hou, Y. Y. Chen, X. Chen, J. L. Shi, and Q. Wang, “Giant bistable shifts for one-dimensional nonlinear photonic crystals,” Phys. Rev. A 75, 045802 (2007).
    [CrossRef]
  8. F. Lima, T. Dumelow, E. L. Albuquerque, and J. A. P. da Costa, “Power flow associated with the Goos–Hänchen shift of a normally incident electromagnetic beam reflected off an antiferromagnet,” Phys. Rev. B 79, 155124 (2009).
    [CrossRef]
  9. H. M. Lai, S. W. Chan, and W. H. Wong, “Nonspecular effects on reflection from absorbing media at and around Brewster’s dip,” J. Opt. Soc. Am. A 23, 3208–3216 (2006).
    [CrossRef]
  10. J. B. Götte, A. Aiello, and J. P. Woerdman, “Loss-induced transition of the Goos–Hänchen effect for metals and dielectrics,” Opt. Express 16, 3961–3969 (2008).
    [CrossRef]
  11. B. Zhao and L. Gao, “Temperature-dependent Goos–Hänchen shift on the interface of metal/dielectric composites,” Opt. Express 17, 21433–21441 (2009).
    [CrossRef]
  12. P. R. Berman, “Goos–Hänchen shift in negatively refractive media,” Phys. Rev. E 66, 0676031 (2002).
  13. J. A. Kong, B. I. 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]
  14. A. Lakhtakia, “On planewave remittances and Goos–Hänchen shifts of planar slabs with negative real permittivity and permeability,” Electromagnetics 23, 71–75 (2003).
    [CrossRef]
  15. N. H. Shen, J. Chen, Q. Y. Wu, T. Lan, Y. X. Fan, and H. T. Wang, “Large lateral shift near pseudo-Brewster angle on reflection from a weakly absorbing double negative medium,” Opt. Express 14, 10574–10579 (2006).
    [CrossRef]
  16. D. R. Smith and D. Schuring, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett. 90, 077405 (2003).
    [CrossRef]
  17. C. W. Qiu, L. W. Li, and T. S. Yeo, “Scattering by rotationally symmetric anisotropic spheres: potential formulation and parametric studies,” Phys. Rev. E 75, 026609 (2007).
    [CrossRef]
  18. H. X. Da, C. Xu, Z. Y. Li, and G. Kraftmakher, “Beam shifting of an anisotropic negative refractive medium,” Phys. Rev. E 71, 066612 (2005).
    [CrossRef]
  19. F. M. Kong, B. I. Wu, H. Huang, J. T. Huangfu, S. Xi, and J. A. Kong, “Lateral displacement of an electromagnetic beam reflected from a grounded indefinite uniaxial slab,” Prog. Electromagn. Res. 82, 351–366 (2008).
    [CrossRef]
  20. Y. Wang, K. Yu, X. Zha, J. Xu, and J. Yan, “Reflection and transmission of Gaussian beam from a uniaxial crystal slab,” Europhys. Lett. 75, 569–575 (2006).
    [CrossRef]
  21. Z. P. Wang, C. Wang, and Z. H. Zhang, “Goos–Hänchen shift of the uniaxially anisotropic left-handed material film with an arbitrary angle between the optical axis and the interface,” Opt. Commun. 281, 3019–3024 (2008).
    [CrossRef]
  22. Q. Cheng and T. J. Cui, “Lateral shifts of optical beams on the interface of anisotropic metamaterial,” J. Appl. Phys. 99, 066114 (2006).
    [CrossRef]
  23. Y. Xiang, X. Dai, and S. Wen, “Negative and positive Goos–Hänchen shifts of a light beam transmitted from an indefinite medium slab,” Appl. Phys. A 87, 285–290 (2007).
    [CrossRef]
  24. M. Cheng, R. Chen, and S. Feng, “Lateral shifts of an optical beam in an anisotropic metamaterial slab,” Eur. Phys. J. D 50, 81–85 (2008).
    [CrossRef]
  25. W. T. Lu and S. Sridhar, “Superlens imaging theory for anisotropic nanostructured metamaterials with broadband all-angle negative refraction,” Phys. Rev. B 77, 233101 (2008).
    [CrossRef]
  26. L. Menon, W. T. Lu, A. L. Friedman, S. P. Bennett, D. Heiman, and S. Sridhar, “Negative index metamaterials based on metal-dielectric nanocomposites for imaging applications,” Appl. Phys. Lett. 93, 123117 (2008).
    [CrossRef]
  27. L. H. Shi and L. Gao, “Subwavelength imaging from a multilayered structure containing interleaved nonspherical metal-dielectric composites,” Phys. Rev. B 77, 195121 (2008).
    [CrossRef]
  28. J. Yao, Z. W. Liu, Y. M. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321, 930 (2008).
    [CrossRef]
  29. A. L. Pokrovsky and A. L. Efros, “Nonlocal electrodynamics of two-dimensional wire mesh photonic crystals,” Phys. Rev. B 65, 045110 (2002).
    [CrossRef]
  30. M. G. Silveirinha, “Nonlocal homogenization model for a periodic array of ε-negative rods,” Phys. Rev. E 73, 046612 (2006).
    [CrossRef]
  31. H. Y. Xie, P. T. Leung, and D. P. Tsai, “Molecular decay rates and emission frequencies in the vicinity of an anisotropic metamaterial,” Solid State Commun. 149, 625–629 (2009).
    [CrossRef]
  32. 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]
  33. Y. Gao, J. P. Huang, Y. M. Liu, L. Gao, K. W. Yu, and X. Zhang, “Optical negative refraction in ferrofluids with magnetocontrollability,” Phys. Rev. Lett. 104, 034501 (2010).
    [CrossRef]

2010 (1)

Y. Gao, J. P. Huang, Y. M. Liu, L. Gao, K. W. Yu, and X. Zhang, “Optical negative refraction in ferrofluids with magnetocontrollability,” Phys. Rev. Lett. 104, 034501 (2010).
[CrossRef]

2009 (3)

F. Lima, T. Dumelow, E. L. Albuquerque, and J. A. P. da Costa, “Power flow associated with the Goos–Hänchen shift of a normally incident electromagnetic beam reflected off an antiferromagnet,” Phys. Rev. B 79, 155124 (2009).
[CrossRef]

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

H. Y. Xie, P. T. Leung, and D. P. Tsai, “Molecular decay rates and emission frequencies in the vicinity of an anisotropic metamaterial,” Solid State Commun. 149, 625–629 (2009).
[CrossRef]

2008 (9)

M. Cheng, R. Chen, and S. Feng, “Lateral shifts of an optical beam in an anisotropic metamaterial slab,” Eur. Phys. J. D 50, 81–85 (2008).
[CrossRef]

W. T. Lu and S. Sridhar, “Superlens imaging theory for anisotropic nanostructured metamaterials with broadband all-angle negative refraction,” Phys. Rev. B 77, 233101 (2008).
[CrossRef]

L. Menon, W. T. Lu, A. L. Friedman, S. P. Bennett, D. Heiman, and S. Sridhar, “Negative index metamaterials based on metal-dielectric nanocomposites for imaging applications,” Appl. Phys. Lett. 93, 123117 (2008).
[CrossRef]

L. H. Shi and L. Gao, “Subwavelength imaging from a multilayered structure containing interleaved nonspherical metal-dielectric composites,” Phys. Rev. B 77, 195121 (2008).
[CrossRef]

J. Yao, Z. W. Liu, Y. M. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321, 930 (2008).
[CrossRef]

F. M. Kong, B. I. Wu, H. Huang, J. T. Huangfu, S. Xi, and J. A. Kong, “Lateral displacement of an electromagnetic beam reflected from a grounded indefinite uniaxial slab,” Prog. Electromagn. Res. 82, 351–366 (2008).
[CrossRef]

Z. P. Wang, C. Wang, and Z. H. Zhang, “Goos–Hänchen shift of the uniaxially anisotropic left-handed material film with an arbitrary angle between the optical axis and the interface,” Opt. Commun. 281, 3019–3024 (2008).
[CrossRef]

J. B. Götte, A. Aiello, and J. P. Woerdman, “Loss-induced transition of the Goos–Hänchen effect for metals and dielectrics,” Opt. Express 16, 3961–3969 (2008).
[CrossRef]

M. Miri, A. Naqavi, A. Khavasi, K. Mehrany, S. Khorasani, and B. Rashidian, “Geometrical approach in physical understanding of the Goos–Hänchen shift in one- and two-dimensional periodic structures,” Opt. Lett. 33, 2940–2942 (2008).
[CrossRef]

2007 (3)

P. Hou, Y. Y. Chen, X. Chen, J. L. Shi, and Q. Wang, “Giant bistable shifts for one-dimensional nonlinear photonic crystals,” Phys. Rev. A 75, 045802 (2007).
[CrossRef]

Y. Xiang, X. Dai, and S. Wen, “Negative and positive Goos–Hänchen shifts of a light beam transmitted from an indefinite medium slab,” Appl. Phys. A 87, 285–290 (2007).
[CrossRef]

C. W. Qiu, L. W. Li, and T. S. Yeo, “Scattering by rotationally symmetric anisotropic spheres: potential formulation and parametric studies,” Phys. Rev. E 75, 026609 (2007).
[CrossRef]

2006 (6)

Y. Wang, K. Yu, X. Zha, J. Xu, and J. Yan, “Reflection and transmission of Gaussian beam from a uniaxial crystal slab,” Europhys. Lett. 75, 569–575 (2006).
[CrossRef]

Q. Cheng and T. J. Cui, “Lateral shifts of optical beams on the interface of anisotropic metamaterial,” J. Appl. Phys. 99, 066114 (2006).
[CrossRef]

M. G. Silveirinha, “Nonlocal homogenization model for a periodic array of ε-negative rods,” Phys. Rev. E 73, 046612 (2006).
[CrossRef]

L. G. Wang and S. Y. Zhu, “Giant lateral shift of a light beam at the defect mode in one-dimensional photonic crystals,” Opt. Lett. 31, 101–103 (2006).
[CrossRef]

N. H. Shen, J. Chen, Q. Y. Wu, T. Lan, Y. X. Fan, and H. T. Wang, “Large lateral shift near pseudo-Brewster angle on reflection from a weakly absorbing double negative medium,” Opt. Express 14, 10574–10579 (2006).
[CrossRef]

H. M. Lai, S. W. Chan, and W. H. Wong, “Nonspecular effects on reflection from absorbing media at and around Brewster’s dip,” J. Opt. Soc. Am. A 23, 3208–3216 (2006).
[CrossRef]

2005 (1)

H. X. Da, C. Xu, Z. Y. Li, and G. Kraftmakher, “Beam shifting of an anisotropic negative refractive medium,” Phys. Rev. E 71, 066612 (2005).
[CrossRef]

2003 (2)

D. R. Smith and D. Schuring, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett. 90, 077405 (2003).
[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]

2002 (4)

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]

P. R. Berman, “Goos–Hänchen shift in negatively refractive media,” Phys. Rev. E 66, 0676031 (2002).

J. A. Kong, B. I. 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]

A. L. Pokrovsky and A. L. Efros, “Nonlocal electrodynamics of two-dimensional wire mesh photonic crystals,” Phys. Rev. B 65, 045110 (2002).
[CrossRef]

1971 (1)

1949 (1)

F. Goos and H. Hänchen, “Neumessung des Strahlversetzungseffektes bei Totalreflexion,” Ann. Phys. 440, 251–252 (1949).
[CrossRef]

1948 (1)

K. Artmann, “Berechnung der Seitenversetzung des totalreflektierten Strahles,” Ann. Phys. 437, 87–102 (1948).
[CrossRef]

1947 (1)

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

Aiello, A.

Albuquerque, E. L.

F. Lima, T. Dumelow, E. L. Albuquerque, and J. A. P. da Costa, “Power flow associated with the Goos–Hänchen shift of a normally incident electromagnetic beam reflected off an antiferromagnet,” Phys. Rev. B 79, 155124 (2009).
[CrossRef]

Artmann, K.

K. Artmann, “Berechnung der Seitenversetzung des totalreflektierten Strahles,” Ann. Phys. 437, 87–102 (1948).
[CrossRef]

Bartal, G.

J. Yao, Z. W. Liu, Y. M. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321, 930 (2008).
[CrossRef]

Bennett, S. P.

L. Menon, W. T. Lu, A. L. Friedman, S. P. Bennett, D. Heiman, and S. Sridhar, “Negative index metamaterials based on metal-dielectric nanocomposites for imaging applications,” Appl. Phys. Lett. 93, 123117 (2008).
[CrossRef]

Berman, P. R.

P. R. Berman, “Goos–Hänchen shift in negatively refractive media,” Phys. Rev. E 66, 0676031 (2002).

Bertoni, H. L.

Chan, S. W.

Chen, J.

Chen, R.

M. Cheng, R. Chen, and S. Feng, “Lateral shifts of an optical beam in an anisotropic metamaterial slab,” Eur. Phys. J. D 50, 81–85 (2008).
[CrossRef]

Chen, X.

P. Hou, Y. Y. Chen, X. Chen, J. L. Shi, and Q. Wang, “Giant bistable shifts for one-dimensional nonlinear photonic crystals,” Phys. Rev. A 75, 045802 (2007).
[CrossRef]

Chen, Y. Y.

P. Hou, Y. Y. Chen, X. Chen, J. L. Shi, and Q. Wang, “Giant bistable shifts for one-dimensional nonlinear photonic crystals,” Phys. Rev. A 75, 045802 (2007).
[CrossRef]

Cheng, M.

M. Cheng, R. Chen, and S. Feng, “Lateral shifts of an optical beam in an anisotropic metamaterial slab,” Eur. Phys. J. D 50, 81–85 (2008).
[CrossRef]

Cheng, Q.

Q. Cheng and T. J. Cui, “Lateral shifts of optical beams on the interface of anisotropic metamaterial,” J. Appl. Phys. 99, 066114 (2006).
[CrossRef]

Cui, T. J.

Q. Cheng and T. J. Cui, “Lateral shifts of optical beams on the interface of anisotropic metamaterial,” J. Appl. Phys. 99, 066114 (2006).
[CrossRef]

Da, H. X.

H. X. Da, C. Xu, Z. Y. Li, and G. Kraftmakher, “Beam shifting of an anisotropic negative refractive medium,” Phys. Rev. E 71, 066612 (2005).
[CrossRef]

da Costa, J. A. P.

F. Lima, T. Dumelow, E. L. Albuquerque, and J. A. P. da Costa, “Power flow associated with the Goos–Hänchen shift of a normally incident electromagnetic beam reflected off an antiferromagnet,” Phys. Rev. B 79, 155124 (2009).
[CrossRef]

Dai, X.

Y. Xiang, X. Dai, and S. Wen, “Negative and positive Goos–Hänchen shifts of a light beam transmitted from an indefinite medium slab,” Appl. Phys. A 87, 285–290 (2007).
[CrossRef]

Dumelow, T.

F. Lima, T. Dumelow, E. L. Albuquerque, and J. A. P. da Costa, “Power flow associated with the Goos–Hänchen shift of a normally incident electromagnetic beam reflected off an antiferromagnet,” Phys. Rev. B 79, 155124 (2009).
[CrossRef]

Efros, A. L.

A. L. Pokrovsky and A. L. Efros, “Nonlocal electrodynamics of two-dimensional wire mesh photonic crystals,” Phys. Rev. B 65, 045110 (2002).
[CrossRef]

Fan, Y. X.

Feng, S.

M. Cheng, R. Chen, and S. Feng, “Lateral shifts of an optical beam in an anisotropic metamaterial slab,” Eur. Phys. J. D 50, 81–85 (2008).
[CrossRef]

Friedman, A. L.

L. Menon, W. T. Lu, A. L. Friedman, S. P. Bennett, D. Heiman, and S. Sridhar, “Negative index metamaterials based on metal-dielectric nanocomposites for imaging applications,” Appl. Phys. Lett. 93, 123117 (2008).
[CrossRef]

Gao, L.

Y. Gao, J. P. Huang, Y. M. Liu, L. Gao, K. W. Yu, and X. Zhang, “Optical negative refraction in ferrofluids with magnetocontrollability,” Phys. Rev. Lett. 104, 034501 (2010).
[CrossRef]

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

L. H. Shi and L. Gao, “Subwavelength imaging from a multilayered structure containing interleaved nonspherical metal-dielectric composites,” Phys. Rev. B 77, 195121 (2008).
[CrossRef]

Gao, Y.

Y. Gao, J. P. Huang, Y. M. Liu, L. Gao, K. W. Yu, and X. Zhang, “Optical negative refraction in ferrofluids with magnetocontrollability,” Phys. Rev. Lett. 104, 034501 (2010).
[CrossRef]

Goos, F.

F. Goos and H. Hänchen, “Neumessung des Strahlversetzungseffektes bei Totalreflexion,” Ann. Phys. 440, 251–252 (1949).
[CrossRef]

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

Götte, J. B.

Hänchen, H.

F. Goos and H. Hänchen, “Neumessung des Strahlversetzungseffektes bei Totalreflexion,” Ann. Phys. 440, 251–252 (1949).
[CrossRef]

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

Heiman, D.

L. Menon, W. T. Lu, A. L. Friedman, S. P. Bennett, D. Heiman, and S. Sridhar, “Negative index metamaterials based on metal-dielectric nanocomposites for imaging applications,” Appl. Phys. Lett. 93, 123117 (2008).
[CrossRef]

Hou, P.

P. Hou, Y. Y. Chen, X. Chen, J. L. Shi, and Q. Wang, “Giant bistable shifts for one-dimensional nonlinear photonic crystals,” Phys. Rev. A 75, 045802 (2007).
[CrossRef]

Huang, H.

F. M. Kong, B. I. Wu, H. Huang, J. T. Huangfu, S. Xi, and J. A. Kong, “Lateral displacement of an electromagnetic beam reflected from a grounded indefinite uniaxial slab,” Prog. Electromagn. Res. 82, 351–366 (2008).
[CrossRef]

Huang, J. P.

Y. Gao, J. P. Huang, Y. M. Liu, L. Gao, K. W. Yu, and X. Zhang, “Optical negative refraction in ferrofluids with magnetocontrollability,” Phys. Rev. Lett. 104, 034501 (2010).
[CrossRef]

Huangfu, J. T.

F. M. Kong, B. I. Wu, H. Huang, J. T. Huangfu, S. Xi, and J. A. Kong, “Lateral displacement of an electromagnetic beam reflected from a grounded indefinite uniaxial slab,” Prog. Electromagn. Res. 82, 351–366 (2008).
[CrossRef]

Khavasi, A.

Khorasani, S.

Kong, F. M.

F. M. Kong, B. I. Wu, H. Huang, J. T. Huangfu, S. Xi, and J. A. Kong, “Lateral displacement of an electromagnetic beam reflected from a grounded indefinite uniaxial slab,” Prog. Electromagn. Res. 82, 351–366 (2008).
[CrossRef]

Kong, J. A.

F. M. Kong, B. I. Wu, H. Huang, J. T. Huangfu, S. Xi, and J. A. Kong, “Lateral displacement of an electromagnetic beam reflected from a grounded indefinite uniaxial slab,” Prog. Electromagn. Res. 82, 351–366 (2008).
[CrossRef]

J. A. Kong, B. I. 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]

Kraftmakher, G.

H. X. Da, C. Xu, Z. Y. Li, and G. Kraftmakher, “Beam shifting of an anisotropic negative refractive medium,” Phys. Rev. E 71, 066612 (2005).
[CrossRef]

Lai, H. M.

Lakhtakia, A.

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

Lan, T.

Leung, P. T.

H. Y. Xie, P. T. Leung, and D. P. Tsai, “Molecular decay rates and emission frequencies in the vicinity of an anisotropic metamaterial,” Solid State Commun. 149, 625–629 (2009).
[CrossRef]

Li, L. W.

C. W. Qiu, L. W. Li, and T. S. Yeo, “Scattering by rotationally symmetric anisotropic spheres: potential formulation and parametric studies,” Phys. Rev. E 75, 026609 (2007).
[CrossRef]

Li, Z. Y.

H. X. Da, C. Xu, Z. Y. Li, and G. Kraftmakher, “Beam shifting of an anisotropic negative refractive medium,” Phys. Rev. E 71, 066612 (2005).
[CrossRef]

Lima, F.

F. Lima, T. Dumelow, E. L. Albuquerque, and J. A. P. da Costa, “Power flow associated with the Goos–Hänchen shift of a normally incident electromagnetic beam reflected off an antiferromagnet,” Phys. Rev. B 79, 155124 (2009).
[CrossRef]

Liu, Y. M.

Y. Gao, J. P. Huang, Y. M. Liu, L. Gao, K. W. Yu, and X. Zhang, “Optical negative refraction in ferrofluids with magnetocontrollability,” Phys. Rev. Lett. 104, 034501 (2010).
[CrossRef]

J. Yao, Z. W. Liu, Y. M. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321, 930 (2008).
[CrossRef]

Liu, Z. W.

J. Yao, Z. W. Liu, Y. M. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321, 930 (2008).
[CrossRef]

Lu, W. T.

W. T. Lu and S. Sridhar, “Superlens imaging theory for anisotropic nanostructured metamaterials with broadband all-angle negative refraction,” Phys. Rev. B 77, 233101 (2008).
[CrossRef]

L. Menon, W. T. Lu, A. L. Friedman, S. P. Bennett, D. Heiman, and S. Sridhar, “Negative index metamaterials based on metal-dielectric nanocomposites for imaging applications,” Appl. Phys. Lett. 93, 123117 (2008).
[CrossRef]

Mehrany, K.

Menon, L.

L. Menon, W. T. Lu, A. L. Friedman, S. P. Bennett, D. Heiman, and S. Sridhar, “Negative index metamaterials based on metal-dielectric nanocomposites for imaging applications,” Appl. Phys. Lett. 93, 123117 (2008).
[CrossRef]

Miri, M.

Naqavi, A.

Pokrovsky, A. L.

A. L. Pokrovsky and A. L. Efros, “Nonlocal electrodynamics of two-dimensional wire mesh photonic crystals,” Phys. Rev. B 65, 045110 (2002).
[CrossRef]

Qiu, C. W.

C. W. Qiu, L. W. Li, and T. S. Yeo, “Scattering by rotationally symmetric anisotropic spheres: potential formulation and parametric studies,” Phys. Rev. E 75, 026609 (2007).
[CrossRef]

Rashidian, B.

Schuring, D.

D. R. Smith and D. Schuring, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett. 90, 077405 (2003).
[CrossRef]

Shen, N. H.

Shi, J. L.

P. Hou, Y. Y. Chen, X. Chen, J. L. Shi, and Q. Wang, “Giant bistable shifts for one-dimensional nonlinear photonic crystals,” Phys. Rev. A 75, 045802 (2007).
[CrossRef]

Shi, L. H.

L. H. Shi and L. Gao, “Subwavelength imaging from a multilayered structure containing interleaved nonspherical metal-dielectric composites,” Phys. Rev. B 77, 195121 (2008).
[CrossRef]

Silveirinha, M. G.

M. G. Silveirinha, “Nonlocal homogenization model for a periodic array of ε-negative rods,” Phys. Rev. E 73, 046612 (2006).
[CrossRef]

Smith, D. R.

D. R. Smith and D. Schuring, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett. 90, 077405 (2003).
[CrossRef]

Sridhar, S.

W. T. Lu and S. Sridhar, “Superlens imaging theory for anisotropic nanostructured metamaterials with broadband all-angle negative refraction,” Phys. Rev. B 77, 233101 (2008).
[CrossRef]

L. Menon, W. T. Lu, A. L. Friedman, S. P. Bennett, D. Heiman, and S. Sridhar, “Negative index metamaterials based on metal-dielectric nanocomposites for imaging applications,” Appl. Phys. Lett. 93, 123117 (2008).
[CrossRef]

Stacy, A. M.

J. Yao, Z. W. Liu, Y. M. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321, 930 (2008).
[CrossRef]

Sun, C.

J. Yao, Z. W. Liu, Y. M. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321, 930 (2008).
[CrossRef]

Tamir, T.

Tsai, D. P.

H. Y. Xie, P. T. Leung, and D. P. Tsai, “Molecular decay rates and emission frequencies in the vicinity of an anisotropic metamaterial,” Solid State Commun. 149, 625–629 (2009).
[CrossRef]

Wang, C.

Z. P. Wang, C. Wang, and Z. H. Zhang, “Goos–Hänchen shift of the uniaxially anisotropic left-handed material film with an arbitrary angle between the optical axis and the interface,” Opt. Commun. 281, 3019–3024 (2008).
[CrossRef]

Wang, H. T.

Wang, L. G.

Wang, Q.

P. Hou, Y. Y. Chen, X. Chen, J. L. Shi, and Q. Wang, “Giant bistable shifts for one-dimensional nonlinear photonic crystals,” Phys. Rev. A 75, 045802 (2007).
[CrossRef]

Wang, Y.

J. Yao, Z. W. Liu, Y. M. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321, 930 (2008).
[CrossRef]

Y. Wang, K. Yu, X. Zha, J. Xu, and J. Yan, “Reflection and transmission of Gaussian beam from a uniaxial crystal slab,” Europhys. Lett. 75, 569–575 (2006).
[CrossRef]

Wang, Z. P.

Z. P. Wang, C. Wang, and Z. H. Zhang, “Goos–Hänchen shift of the uniaxially anisotropic left-handed material film with an arbitrary angle between the optical axis and the interface,” Opt. Commun. 281, 3019–3024 (2008).
[CrossRef]

Wen, S.

Y. Xiang, X. Dai, and S. Wen, “Negative and positive Goos–Hänchen shifts of a light beam transmitted from an indefinite medium slab,” Appl. Phys. A 87, 285–290 (2007).
[CrossRef]

Woerdman, J. P.

Wong, W. H.

Wu, B. I.

F. M. Kong, B. I. Wu, H. Huang, J. T. Huangfu, S. Xi, and J. A. Kong, “Lateral displacement of an electromagnetic beam reflected from a grounded indefinite uniaxial slab,” Prog. Electromagn. Res. 82, 351–366 (2008).
[CrossRef]

J. A. Kong, B. I. 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]

Wu, Q. Y.

Xi, S.

F. M. Kong, B. I. Wu, H. Huang, J. T. Huangfu, S. Xi, and J. A. Kong, “Lateral displacement of an electromagnetic beam reflected from a grounded indefinite uniaxial slab,” Prog. Electromagn. Res. 82, 351–366 (2008).
[CrossRef]

Xiang, Y.

Y. Xiang, X. Dai, and S. Wen, “Negative and positive Goos–Hänchen shifts of a light beam transmitted from an indefinite medium slab,” Appl. Phys. A 87, 285–290 (2007).
[CrossRef]

Xie, H. Y.

H. Y. Xie, P. T. Leung, and D. P. Tsai, “Molecular decay rates and emission frequencies in the vicinity of an anisotropic metamaterial,” Solid State Commun. 149, 625–629 (2009).
[CrossRef]

Xu, C.

H. X. Da, C. Xu, Z. Y. Li, and G. Kraftmakher, “Beam shifting of an anisotropic negative refractive medium,” Phys. Rev. E 71, 066612 (2005).
[CrossRef]

Xu, J.

Y. Wang, K. Yu, X. Zha, J. Xu, and J. Yan, “Reflection and transmission of Gaussian beam from a uniaxial crystal slab,” Europhys. Lett. 75, 569–575 (2006).
[CrossRef]

Yan, J.

Y. Wang, K. Yu, X. Zha, J. Xu, and J. Yan, “Reflection and transmission of Gaussian beam from a uniaxial crystal slab,” Europhys. Lett. 75, 569–575 (2006).
[CrossRef]

Yao, J.

J. Yao, Z. W. Liu, Y. M. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321, 930 (2008).
[CrossRef]

Yeo, T. S.

C. W. Qiu, L. W. Li, and T. S. Yeo, “Scattering by rotationally symmetric anisotropic spheres: potential formulation and parametric studies,” Phys. Rev. E 75, 026609 (2007).
[CrossRef]

Yu, K.

Y. Wang, K. Yu, X. Zha, J. Xu, and J. Yan, “Reflection and transmission of Gaussian beam from a uniaxial crystal slab,” Europhys. Lett. 75, 569–575 (2006).
[CrossRef]

Yu, K. W.

Y. Gao, J. P. Huang, Y. M. Liu, L. Gao, K. W. Yu, and X. Zhang, “Optical negative refraction in ferrofluids with magnetocontrollability,” Phys. Rev. Lett. 104, 034501 (2010).
[CrossRef]

Zha, X.

Y. Wang, K. Yu, X. Zha, J. Xu, and J. Yan, “Reflection and transmission of Gaussian beam from a uniaxial crystal slab,” Europhys. Lett. 75, 569–575 (2006).
[CrossRef]

Zhang, X.

Y. Gao, J. P. Huang, Y. M. Liu, L. Gao, K. W. Yu, and X. Zhang, “Optical negative refraction in ferrofluids with magnetocontrollability,” Phys. Rev. Lett. 104, 034501 (2010).
[CrossRef]

J. Yao, Z. W. Liu, Y. M. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321, 930 (2008).
[CrossRef]

Zhang, Y.

J. A. Kong, B. I. 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, Z. H.

Z. P. Wang, C. Wang, and Z. H. Zhang, “Goos–Hänchen shift of the uniaxially anisotropic left-handed material film with an arbitrary angle between the optical axis and the interface,” Opt. Commun. 281, 3019–3024 (2008).
[CrossRef]

Zhao, B.

Zhu, S. Y.

Ann. Phys. (3)

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

F. Goos and H. Hänchen, “Neumessung des Strahlversetzungseffektes bei Totalreflexion,” Ann. Phys. 440, 251–252 (1949).
[CrossRef]

K. Artmann, “Berechnung der Seitenversetzung des totalreflektierten Strahles,” Ann. Phys. 437, 87–102 (1948).
[CrossRef]

Appl. Phys. A (1)

Y. Xiang, X. Dai, and S. Wen, “Negative and positive Goos–Hänchen shifts of a light beam transmitted from an indefinite medium slab,” Appl. Phys. A 87, 285–290 (2007).
[CrossRef]

Appl. Phys. Lett. (2)

L. Menon, W. T. Lu, A. L. Friedman, S. P. Bennett, D. Heiman, and S. Sridhar, “Negative index metamaterials based on metal-dielectric nanocomposites for imaging applications,” Appl. Phys. Lett. 93, 123117 (2008).
[CrossRef]

J. A. Kong, B. I. 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]

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]

Eur. Phys. J. D (1)

M. Cheng, R. Chen, and S. Feng, “Lateral shifts of an optical beam in an anisotropic metamaterial slab,” Eur. Phys. J. D 50, 81–85 (2008).
[CrossRef]

Europhys. Lett. (1)

Y. Wang, K. Yu, X. Zha, J. Xu, and J. Yan, “Reflection and transmission of Gaussian beam from a uniaxial crystal slab,” Europhys. Lett. 75, 569–575 (2006).
[CrossRef]

J. Appl. Phys. (1)

Q. Cheng and T. J. Cui, “Lateral shifts of optical beams on the interface of anisotropic metamaterial,” J. Appl. Phys. 99, 066114 (2006).
[CrossRef]

J. Opt. Soc. Am. (1)

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

Opt. Commun. (1)

Z. P. Wang, C. Wang, and Z. H. Zhang, “Goos–Hänchen shift of the uniaxially anisotropic left-handed material film with an arbitrary angle between the optical axis and the interface,” Opt. Commun. 281, 3019–3024 (2008).
[CrossRef]

Opt. Express (3)

Opt. Lett. (3)

Phys. Rev. A (1)

P. Hou, Y. Y. Chen, X. Chen, J. L. Shi, and Q. Wang, “Giant bistable shifts for one-dimensional nonlinear photonic crystals,” Phys. Rev. A 75, 045802 (2007).
[CrossRef]

Phys. Rev. B (4)

F. Lima, T. Dumelow, E. L. Albuquerque, and J. A. P. da Costa, “Power flow associated with the Goos–Hänchen shift of a normally incident electromagnetic beam reflected off an antiferromagnet,” Phys. Rev. B 79, 155124 (2009).
[CrossRef]

L. H. Shi and L. Gao, “Subwavelength imaging from a multilayered structure containing interleaved nonspherical metal-dielectric composites,” Phys. Rev. B 77, 195121 (2008).
[CrossRef]

A. L. Pokrovsky and A. L. Efros, “Nonlocal electrodynamics of two-dimensional wire mesh photonic crystals,” Phys. Rev. B 65, 045110 (2002).
[CrossRef]

W. T. Lu and S. Sridhar, “Superlens imaging theory for anisotropic nanostructured metamaterials with broadband all-angle negative refraction,” Phys. Rev. B 77, 233101 (2008).
[CrossRef]

Phys. Rev. E (4)

C. W. Qiu, L. W. Li, and T. S. Yeo, “Scattering by rotationally symmetric anisotropic spheres: potential formulation and parametric studies,” Phys. Rev. E 75, 026609 (2007).
[CrossRef]

H. X. Da, C. Xu, Z. Y. Li, and G. Kraftmakher, “Beam shifting of an anisotropic negative refractive medium,” Phys. Rev. E 71, 066612 (2005).
[CrossRef]

M. G. Silveirinha, “Nonlocal homogenization model for a periodic array of ε-negative rods,” Phys. Rev. E 73, 046612 (2006).
[CrossRef]

P. R. Berman, “Goos–Hänchen shift in negatively refractive media,” Phys. Rev. E 66, 0676031 (2002).

Phys. Rev. Lett. (2)

D. R. Smith and D. Schuring, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett. 90, 077405 (2003).
[CrossRef]

Y. Gao, J. P. Huang, Y. M. Liu, L. Gao, K. W. Yu, and X. Zhang, “Optical negative refraction in ferrofluids with magnetocontrollability,” Phys. Rev. Lett. 104, 034501 (2010).
[CrossRef]

Prog. Electromagn. Res. (1)

F. M. Kong, B. I. Wu, H. Huang, J. T. Huangfu, S. Xi, and J. A. Kong, “Lateral displacement of an electromagnetic beam reflected from a grounded indefinite uniaxial slab,” Prog. Electromagn. Res. 82, 351–366 (2008).
[CrossRef]

Science (1)

J. Yao, Z. W. Liu, Y. M. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321, 930 (2008).
[CrossRef]

Solid State Commun. (1)

H. Y. Xie, P. T. Leung, and D. P. Tsai, “Molecular decay rates and emission frequencies in the vicinity of an anisotropic metamaterial,” Solid State Commun. 149, 625–629 (2009).
[CrossRef]

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Figures (8)

Fig. 1.
Fig. 1.

Schematic diagram of a TM wave incident on the composite metamaterial, containing aligned metallic nanowires in a dielectric matrix.

Fig. 2.
Fig. 2.

Dependence of the elements of the effective permittivity tensor and the group refractive index of medium 2 on the incident wavelength λ and the volume fraction f. (a) Re(εx), (b) Re(εz), and (c) Re(n2g).

Fig. 3.
Fig. 3.

(a) GH shifts Δ/λ; (b) the absorption of the metamaterial |Im(n2g)/Re(n2g)|; (c) the reflection coefficient |r|; and (d) the real part of the group index Re(n2g) as a function of the angle of incidence θi for various f and finite λ=300nm. The composite metamaterials are positively refractive.

Fig. 4.
Fig. 4.

(a) Δ/λ; (b) Re(n2g); (c) |r|, and the reflected phase Φ as a function of θi for fixed f=0.05 and various λ.

Fig. 5.
Fig. 5.

(a) Δ/λ; (b) Re(n2g); and (c) |r| as a function of θi for various λ and f=0.15.

Fig. 6.
Fig. 6.

(a) Δ/λ; (b) Re(n2g); (c) |r|; and (d) |Im(n2g)/Re(n2g)| as a function of θi for different volume fraction f and λ=800nm. The composite metamaterials are always negatively refractive.

Fig. 7.
Fig. 7.

Dependence of the GH shift on the angle of incidence for both theoretical results and simulated data.

Fig. 8.
Fig. 8.

COMSOL simulations of the GH shifts near the pseudo-Brewster angle for a TM wave reflected from the composite metamaterial as λ=800nm. Other parameters are (a) θi=40° and f=0.1, and (b) θi=55° and f=0.2.

Equations (15)

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

ε^=(εx000εy000εz),
εx=εy=12{(12f)(εaεm)±[(12f)(εaεm)]2+4εaεm},εz=fεm+(1f)εa.
kx2+k1z2=k02,andkx2εz+k2z2εx=k02,
S2=(tH0)22ωRe(kxεzex+k2zεxez),
n2p=εx+(1εxεz)sin2θi,
n2g=εzεx1+(εxεz21εz)sin2θi.
r=εxcosθiεxεxεzsin2θiεxcosθi+εxεxεzsin2θi,
Φ(θi)=Im{log[εxcosθiεxεxεzsin2θiεxcosθi+εxεxεzsin2θi]}.
Δ=dΦdkx=1k0ε1cosθid[Im(logr)]dθi=1k0ε1cosθiIm(1rdrdθi).
Δλ=tanθi2πε1·1|εxεxεzsin2θi||εzcos2θi(εx1)sin2θi(εz1)|2·εxiA+εziB|εxεxεzsin2θi|+εxrεxrεzr+εxiεzi|εz|2sin2θi,
A=(|εxεxεzsin2θi|+|εx|2cos2θi)[εzr|εz|2+(εzr1)sin2θi],
B=cos2θi[|εxεxεzsin2θi|(|εx|2εxr)+|εx|2(εxrcos2θi1)+|εx|2|εz|2εzrsin2θi]|εx|2|εz|2sin2θi[εzr|εz|2+(εzr1)sin2θi].
εm=εrωp2ω2+iωγ,
Hi(x,z=0)=A(kx)exp(ikxx)dkx,
Hr(x,z=0)=rA(kx)exp(ikxx)dkx.

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