Abstract

The Goos–Hänchen shift caused by total internal reflection at the interface between two media is analyzed. For two media of the same handedness the Goos–Hänchen phase shift opposes the phase variation associated with propagation through the incident medium. The Goos–Hänchen lateral shift is in the same direction as the horizontal component of the incident energy flux. Conversely, for two media of opposite handedness the Goos–Hänchen phase shift reinforces the phase variation associated with propagation through the incident medium. The lateral shift is in the opposite direction of the horizontal component of the incident energy flux.

© 2004 Optical Society of America

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  1. F. Goos and H. Hänchen, Ann. Phys. (Leipzig) 6, 333 (1947).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  12. A. Lakhtakia, arXiv.org e-Print archive, , May30, 2003, http://arxiv.org/abs/physics/0305133v1 .

2003

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, Phys. Rev. E 67, 057602 (2003).
[CrossRef]

B. Wu, T. M. Grzegorczyk, Y. Zhang, and J. A. Kong, J. Appl. Phys. 93, 9386 (2003).
[CrossRef]

H. Cory and A. Barger, Micro. Opt. Technol. Lett. 38, 392 (2003).
[CrossRef]

A. Lakhtakia, Electromagnetics 23, 71 (2003).
[CrossRef]

2002

N. Engheta, IEEE Antennas Wireless Propag. Lett. 1, 10 (2002).
[CrossRef]

P. R. Berman, Phys. Rev. E 66, 067603 (2002).
[CrossRef]

2001

R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
[CrossRef] [PubMed]

2000

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef] [PubMed]

1986

1966

V. G. Veselago, Sov. Phys. Usp. 10, 509 (1966).
[CrossRef]

1947

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

Barger, A.

H. Cory and A. Barger, Micro. Opt. Technol. Lett. 38, 392 (2003).
[CrossRef]

Berman, P. R.

P. R. Berman, Phys. Rev. E 66, 067603 (2002).
[CrossRef]

Birman, J. L.

Cory, H.

H. Cory and A. Barger, Micro. Opt. Technol. Lett. 38, 392 (2003).
[CrossRef]

Engheta, N.

N. Engheta, IEEE Antennas Wireless Propag. Lett. 1, 10 (2002).
[CrossRef]

Goos, F.

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

Grzegorczyk, T. M.

B. Wu, T. M. Grzegorczyk, Y. Zhang, and J. A. Kong, J. Appl. Phys. 93, 9386 (2003).
[CrossRef]

Hänchen, H.

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

Kivshar, Y. S.

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, Phys. Rev. E 67, 057602 (2003).
[CrossRef]

Kong, J. A.

B. Wu, T. M. Grzegorczyk, Y. Zhang, and J. A. Kong, J. Appl. Phys. 93, 9386 (2003).
[CrossRef]

Lakhtakia, A.

A. Lakhtakia, Electromagnetics 23, 71 (2003).
[CrossRef]

A. Lakhtakia, arXiv.org e-Print archive, , May30, 2003, http://arxiv.org/abs/physics/0305133v1 .

Pendry, J. B.

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef] [PubMed]

Puri, A.

Schultz, S.

R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
[CrossRef] [PubMed]

Shadrivov, I. V.

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, Phys. Rev. E 67, 057602 (2003).
[CrossRef]

Shelby, R. A.

R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
[CrossRef] [PubMed]

Smith, D. R.

R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
[CrossRef] [PubMed]

Sukhorukov, A. A.

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, Phys. Rev. E 67, 057602 (2003).
[CrossRef]

Veselago, V. G.

V. G. Veselago, Sov. Phys. Usp. 10, 509 (1966).
[CrossRef]

Wu, B.

B. Wu, T. M. Grzegorczyk, Y. Zhang, and J. A. Kong, J. Appl. Phys. 93, 9386 (2003).
[CrossRef]

Zhang, Y.

B. Wu, T. M. Grzegorczyk, Y. Zhang, and J. A. Kong, J. Appl. Phys. 93, 9386 (2003).
[CrossRef]

Ann. Phys. (Leipzig)

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

Electromagnetics

A. Lakhtakia, Electromagnetics 23, 71 (2003).
[CrossRef]

IEEE Antennas Wireless Propag. Lett.

N. Engheta, IEEE Antennas Wireless Propag. Lett. 1, 10 (2002).
[CrossRef]

J. Appl. Phys.

B. Wu, T. M. Grzegorczyk, Y. Zhang, and J. A. Kong, J. Appl. Phys. 93, 9386 (2003).
[CrossRef]

J. Opt. Soc. Am. A

Micro. Opt. Technol. Lett.

H. Cory and A. Barger, Micro. Opt. Technol. Lett. 38, 392 (2003).
[CrossRef]

Phys. Rev. E

P. R. Berman, Phys. Rev. E 66, 067603 (2002).
[CrossRef]

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, Phys. Rev. E 67, 057602 (2003).
[CrossRef]

Phys. Rev. Lett.

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef] [PubMed]

Science

R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
[CrossRef] [PubMed]

Sov. Phys. Usp.

V. G. Veselago, Sov. Phys. Usp. 10, 509 (1966).
[CrossRef]

Other

A. Lakhtakia, arXiv.org e-Print archive, , May30, 2003, http://arxiv.org/abs/physics/0305133v1 .

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Figures (2)

Fig. 1
Fig. 1

Typical system with two semi-infinite media with incident waves from (a) a left-handed and (b) a right-handed medium. Thin solid arrows indicate the phase propagation directions, and thick empty arrows indicate the energy flux directions.

Fig. 2
Fig. 2

Schematic representation of the Goos–Hänchen shift at the interface between (a) left- and right-handed, (b) left- and left-handed, (c) right- and right-handed, and (d) right- and left-handed media. Thin solid arrows indicate phase propagation directions, thick empty arrows indicate energy flux directions, and thick solid arrows indicate Goos–Hänchen lateral shift directions.

Equations (8)

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

Eix,y,t=Ez0 expikx1x+ky1y-ωt,
E1x,y,t=Ez0 exp-iωtexpikx1x+ky1y+A expikx2x+ky2y,
E2x,y,t=BEz0 expikx3x+ky3y-ωt,
1+A=B,
kx1+Akx2/μ1=Bkx3/μ2.
A=μ2Kx1+iμ1Kx3/μ2Kx1-iμ2Kx3expiδ,
Y=μ1μ2Ky1Ky12-ε2μ2ω2ε1μ1ω2-Ky12.
A=μ2Kx1-iμ1Kx3/μ2Kx1+iμ1Kx3expiδ,

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