Abstract

We show the presence of the Goos–Hänchen effect when a monochromatic beam illuminates a photonic crystal inside a photonic bandgap.

© 2003 Optical Society of America

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References

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  1. F. Goos H. and Hänchen, Ann. Phys. (Leipzig) 6, 333 (1947).
    [CrossRef]
  2. K. Artmann, Ann. Phys. (Leipzig) 12, 87 (1948).
    [CrossRef]
  3. R. Renard, J. Opt. Soc. Am. 54, 1190 (1964).
  4. B. Horowitz and T. Tamir, J. Opt. Soc. Am. 61, 586 (1971).
  5. J. Hugonin and R. Petit, J. Opt. (Paris) 8, 73 (1977).
    [CrossRef]
  6. J. J. Cowan and B. Anicin, J. Opt. Soc. Am. 67, 1307 (1977).
  7. J. F. Bretenaker, A. Le Floch, and L. Dutriaux, Phys. Rev. Lett. 68, 931 (1992).
    [CrossRef] [PubMed]
  8. A. Haibel, G. Nimtz, and A. A. Stahlhofen, Phys. Rev. E 63, 047601 (2001).
    [CrossRef]
  9. J. D. Joannopoulos, R. Meade, and J. Winn, Photonic Crystals (Princeton U. Press, Princeton, N.J., 1995).
  10. These data are available at http://home.earthlink.net/~jpdowling/pbgbib.html.
  11. D. Felbacq, B. Guizal, and F. Zolla, Opt. Commun. 152, 119 (1998).
    [CrossRef]
  12. D. Felbacq, B. Guizal, and F. Zolla, arXiv.org e-Print archive, physics/0104074, April 23, 2001, http://arXiv.org/abs/physics/0104074.
  13. D. Felbacq, B. Guizal, and F. Zolla, J. Opt. A Pure Appl. Opt. 2, L30 (2000).
  14. L. Wu, M. Mazilu, T. Karle, and T. F. Krauss, IEEE J. Quantum Electron. 38, 915 (2002).
    [CrossRef]

2002 (1)

L. Wu, M. Mazilu, T. Karle, and T. F. Krauss, IEEE J. Quantum Electron. 38, 915 (2002).
[CrossRef]

2001 (1)

A. Haibel, G. Nimtz, and A. A. Stahlhofen, Phys. Rev. E 63, 047601 (2001).
[CrossRef]

2000 (1)

D. Felbacq, B. Guizal, and F. Zolla, J. Opt. A Pure Appl. Opt. 2, L30 (2000).

1998 (1)

D. Felbacq, B. Guizal, and F. Zolla, Opt. Commun. 152, 119 (1998).
[CrossRef]

1992 (1)

J. F. Bretenaker, A. Le Floch, and L. Dutriaux, Phys. Rev. Lett. 68, 931 (1992).
[CrossRef] [PubMed]

1977 (2)

J. Hugonin and R. Petit, J. Opt. (Paris) 8, 73 (1977).
[CrossRef]

J. J. Cowan and B. Anicin, J. Opt. Soc. Am. 67, 1307 (1977).

1971 (1)

1964 (1)

1948 (1)

K. Artmann, Ann. Phys. (Leipzig) 12, 87 (1948).
[CrossRef]

1947 (1)

F. Goos H. and Hänchen, Ann. Phys. (Leipzig) 6, 333 (1947).
[CrossRef]

Anicin, B.

Artmann, K.

K. Artmann, Ann. Phys. (Leipzig) 12, 87 (1948).
[CrossRef]

Bretenaker, J. F.

J. F. Bretenaker, A. Le Floch, and L. Dutriaux, Phys. Rev. Lett. 68, 931 (1992).
[CrossRef] [PubMed]

Cowan, J. J.

Dutriaux, L.

J. F. Bretenaker, A. Le Floch, and L. Dutriaux, Phys. Rev. Lett. 68, 931 (1992).
[CrossRef] [PubMed]

Felbacq, D.

D. Felbacq, B. Guizal, and F. Zolla, J. Opt. A Pure Appl. Opt. 2, L30 (2000).

D. Felbacq, B. Guizal, and F. Zolla, Opt. Commun. 152, 119 (1998).
[CrossRef]

D. Felbacq, B. Guizal, and F. Zolla, arXiv.org e-Print archive, physics/0104074, April 23, 2001, http://arXiv.org/abs/physics/0104074.

Goos, F.

F. Goos H. and Hänchen, Ann. Phys. (Leipzig) 6, 333 (1947).
[CrossRef]

Guizal, B.

D. Felbacq, B. Guizal, and F. Zolla, J. Opt. A Pure Appl. Opt. 2, L30 (2000).

D. Felbacq, B. Guizal, and F. Zolla, Opt. Commun. 152, 119 (1998).
[CrossRef]

D. Felbacq, B. Guizal, and F. Zolla, arXiv.org e-Print archive, physics/0104074, April 23, 2001, http://arXiv.org/abs/physics/0104074.

Haibel, A.

A. Haibel, G. Nimtz, and A. A. Stahlhofen, Phys. Rev. E 63, 047601 (2001).
[CrossRef]

Hänchen, H.

F. Goos H. and Hänchen, Ann. Phys. (Leipzig) 6, 333 (1947).
[CrossRef]

Horowitz, B.

Hugonin, J.

J. Hugonin and R. Petit, J. Opt. (Paris) 8, 73 (1977).
[CrossRef]

Joannopoulos, J. D.

J. D. Joannopoulos, R. Meade, and J. Winn, Photonic Crystals (Princeton U. Press, Princeton, N.J., 1995).

Karle, T.

L. Wu, M. Mazilu, T. Karle, and T. F. Krauss, IEEE J. Quantum Electron. 38, 915 (2002).
[CrossRef]

Krauss, T. F.

L. Wu, M. Mazilu, T. Karle, and T. F. Krauss, IEEE J. Quantum Electron. 38, 915 (2002).
[CrossRef]

Le Floch, A.

J. F. Bretenaker, A. Le Floch, and L. Dutriaux, Phys. Rev. Lett. 68, 931 (1992).
[CrossRef] [PubMed]

Mazilu, M.

L. Wu, M. Mazilu, T. Karle, and T. F. Krauss, IEEE J. Quantum Electron. 38, 915 (2002).
[CrossRef]

Meade, R.

J. D. Joannopoulos, R. Meade, and J. Winn, Photonic Crystals (Princeton U. Press, Princeton, N.J., 1995).

Nimtz, G.

A. Haibel, G. Nimtz, and A. A. Stahlhofen, Phys. Rev. E 63, 047601 (2001).
[CrossRef]

Petit, R.

J. Hugonin and R. Petit, J. Opt. (Paris) 8, 73 (1977).
[CrossRef]

Renard, R.

Stahlhofen, A. A.

A. Haibel, G. Nimtz, and A. A. Stahlhofen, Phys. Rev. E 63, 047601 (2001).
[CrossRef]

Tamir, T.

Winn, J.

J. D. Joannopoulos, R. Meade, and J. Winn, Photonic Crystals (Princeton U. Press, Princeton, N.J., 1995).

Wu, L.

L. Wu, M. Mazilu, T. Karle, and T. F. Krauss, IEEE J. Quantum Electron. 38, 915 (2002).
[CrossRef]

Zolla, F.

D. Felbacq, B. Guizal, and F. Zolla, J. Opt. A Pure Appl. Opt. 2, L30 (2000).

D. Felbacq, B. Guizal, and F. Zolla, Opt. Commun. 152, 119 (1998).
[CrossRef]

D. Felbacq, B. Guizal, and F. Zolla, arXiv.org e-Print archive, physics/0104074, April 23, 2001, http://arXiv.org/abs/physics/0104074.

Ann. Phys. (Leipzig) (2)

F. Goos H. and Hänchen, Ann. Phys. (Leipzig) 6, 333 (1947).
[CrossRef]

K. Artmann, Ann. Phys. (Leipzig) 12, 87 (1948).
[CrossRef]

IEEE J. Quantum Electron. (1)

L. Wu, M. Mazilu, T. Karle, and T. F. Krauss, IEEE J. Quantum Electron. 38, 915 (2002).
[CrossRef]

J. Opt. (Paris) (1)

J. Hugonin and R. Petit, J. Opt. (Paris) 8, 73 (1977).
[CrossRef]

J. Opt. A Pure Appl. Opt. (1)

D. Felbacq, B. Guizal, and F. Zolla, J. Opt. A Pure Appl. Opt. 2, L30 (2000).

J. Opt. Soc. Am. (3)

Opt. Commun. (1)

D. Felbacq, B. Guizal, and F. Zolla, Opt. Commun. 152, 119 (1998).
[CrossRef]

Phys. Rev. E (1)

A. Haibel, G. Nimtz, and A. A. Stahlhofen, Phys. Rev. E 63, 047601 (2001).
[CrossRef]

Phys. Rev. Lett. (1)

J. F. Bretenaker, A. Le Floch, and L. Dutriaux, Phys. Rev. Lett. 68, 931 (1992).
[CrossRef] [PubMed]

Other (3)

J. D. Joannopoulos, R. Meade, and J. Winn, Photonic Crystals (Princeton U. Press, Princeton, N.J., 1995).

These data are available at http://home.earthlink.net/~jpdowling/pbgbib.html.

D. Felbacq, B. Guizal, and F. Zolla, arXiv.org e-Print archive, physics/0104074, April 23, 2001, http://arXiv.org/abs/physics/0104074.

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Figures (3)

Fig. 1
Fig. 1

One period of the photonic crystal consists in two layers of height d and of permittivity ε1=11.56 and ε2=1. The Goos–Hänchen shift is the distance between the centers of the incident and reflected beams.

Fig. 2
Fig. 2

Goos–Hänchen shift for a Gaussian beam of waist 10λ under a 50° angle of incidence for a wavelength λ/d4.5,18 (the height of a layer being of size 1). The dashed–dotted curve represents g so that the gaps, characterized by g=1, can be easily identified by the reader. The dashed curve represents the derivative of the phase of g, which can barely be distinguished from the shift for a Gaussian beam (solid curve).

Fig. 3
Fig. 3

Goos–Hänchen shift (normalized by λ=10) for a Gaussian beam for an angle of incidence θ0,70. The dashed-dotted curve represents g.

Equations (13)

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uix,y=Aα,Wexp iax+k02-α2ydα,
Aα,W=W2πexp-W24α-α02,
ux,y=expik0x sin θ-y cos θ+rk0,θexpik0x sin θ+y cos θ, fory0 ux,y=tk0,θexpik0x sin θ-y+hcos θ, fory-h
T1+riβ01-r=t1iβ0,
rk0,θ=μ-1fμ2-g-1f, tk0,θ=μ1-g-1fμ2-g-1f,
gk0,θ=iβ0v1-v2iβ0v1+v2, fk0,θ=iβ0w1-w2iβ0w1+w2.
rk0,θ=g+g-fm=1+μ2mgmf-m,
tk0θ=1-gf-1m=0+μ2mgmf-m.
udx,y=Ak0 sin θ,Wgk0,θ×expik0x sin θ+y cos θcos θdθ.
gk0,θ=expiϕk0,θ.
Gr=xudx,02dxudx,02dx.
Gr=-A2θ,k0Wαϕαcos θdθA2θ,k0Wcos θdθ.
Gr-k0 cos θ-1ϕθ.

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