Abstract

Negative group delay times upon total reflection from frustrated Gires–Tournois interferometers seem to violate causality. Contrary to what has been recently argued in the literature, I show with the example of total light reflection upon an ideal nonabsorbing plasma that adding the time associated with the Goos–Hänchen shift does not solve the paradox, which remains open.

© 2005 Optical Society of America

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References

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  1. P. Tournois, IEEE J. Quantum Electron. 33, 519 (1997).
    [CrossRef]
  2. K. J. Resch, J. S. Lundeen, and A. M. Steinberg, IEEE J. Quantum Electron. 37, 794 (2001).
    [CrossRef]
  3. J. S. Lundeen, K. J. Resch, L. Wawrezinieck, and A. M. Steinberg, poster presented at the 2000 Annual Meeting of the Division of Atomic, Molecular and Optical Physics of the American Physical Society (DAMOS 2000), Storrs, Conn., June 14–17, 2000.
  4. H. M. Lai, C. W. Kwok, Y. W. Loo, and B. Y. Xu, Phys. Rev. E 62, 7330 (2000).
    [CrossRef]

2001

K. J. Resch, J. S. Lundeen, and A. M. Steinberg, IEEE J. Quantum Electron. 37, 794 (2001).
[CrossRef]

2000

H. M. Lai, C. W. Kwok, Y. W. Loo, and B. Y. Xu, Phys. Rev. E 62, 7330 (2000).
[CrossRef]

1997

P. Tournois, IEEE J. Quantum Electron. 33, 519 (1997).
[CrossRef]

Kwok, C. W.

H. M. Lai, C. W. Kwok, Y. W. Loo, and B. Y. Xu, Phys. Rev. E 62, 7330 (2000).
[CrossRef]

Lai, H. M.

H. M. Lai, C. W. Kwok, Y. W. Loo, and B. Y. Xu, Phys. Rev. E 62, 7330 (2000).
[CrossRef]

Loo, Y. W.

H. M. Lai, C. W. Kwok, Y. W. Loo, and B. Y. Xu, Phys. Rev. E 62, 7330 (2000).
[CrossRef]

Lundeen, J. S.

K. J. Resch, J. S. Lundeen, and A. M. Steinberg, IEEE J. Quantum Electron. 37, 794 (2001).
[CrossRef]

J. S. Lundeen, K. J. Resch, L. Wawrezinieck, and A. M. Steinberg, poster presented at the 2000 Annual Meeting of the Division of Atomic, Molecular and Optical Physics of the American Physical Society (DAMOS 2000), Storrs, Conn., June 14–17, 2000.

Resch, K. J.

K. J. Resch, J. S. Lundeen, and A. M. Steinberg, IEEE J. Quantum Electron. 37, 794 (2001).
[CrossRef]

J. S. Lundeen, K. J. Resch, L. Wawrezinieck, and A. M. Steinberg, poster presented at the 2000 Annual Meeting of the Division of Atomic, Molecular and Optical Physics of the American Physical Society (DAMOS 2000), Storrs, Conn., June 14–17, 2000.

Steinberg, A. M.

K. J. Resch, J. S. Lundeen, and A. M. Steinberg, IEEE J. Quantum Electron. 37, 794 (2001).
[CrossRef]

J. S. Lundeen, K. J. Resch, L. Wawrezinieck, and A. M. Steinberg, poster presented at the 2000 Annual Meeting of the Division of Atomic, Molecular and Optical Physics of the American Physical Society (DAMOS 2000), Storrs, Conn., June 14–17, 2000.

Tournois, P.

P. Tournois, IEEE J. Quantum Electron. 33, 519 (1997).
[CrossRef]

Wawrezinieck, L.

J. S. Lundeen, K. J. Resch, L. Wawrezinieck, and A. M. Steinberg, poster presented at the 2000 Annual Meeting of the Division of Atomic, Molecular and Optical Physics of the American Physical Society (DAMOS 2000), Storrs, Conn., June 14–17, 2000.

Xu, B. Y.

H. M. Lai, C. W. Kwok, Y. W. Loo, and B. Y. Xu, Phys. Rev. E 62, 7330 (2000).
[CrossRef]

IEEE J. Quantum Electron.

P. Tournois, IEEE J. Quantum Electron. 33, 519 (1997).
[CrossRef]

K. J. Resch, J. S. Lundeen, and A. M. Steinberg, IEEE J. Quantum Electron. 37, 794 (2001).
[CrossRef]

Phys. Rev. E

H. M. Lai, C. W. Kwok, Y. W. Loo, and B. Y. Xu, Phys. Rev. E 62, 7330 (2000).
[CrossRef]

Other

J. S. Lundeen, K. J. Resch, L. Wawrezinieck, and A. M. Steinberg, poster presented at the 2000 Annual Meeting of the Division of Atomic, Molecular and Optical Physics of the American Physical Society (DAMOS 2000), Storrs, Conn., June 14–17, 2000.

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Figures (5)

Fig. 1
Fig. 1

Low-index layer dielectric F-GTI: Goos–Hänchen and group delay times versus thickness layer for the s and p waves and for a given frequency.

Fig. 2
Fig. 2

Total reflection on a plasma mirror: group delay time, Goos–Hänchen time, and their sum versus frequency for total reflection on a plasma mirror.

Fig. 3
Fig. 3

F-GTI on a plasma mirror: Goos–Hänchen and group delay times versus frequency for n = 1.45 , θ = 60 ° , and α = 3 .

Fig. 4
Fig. 4

F-GTI on a plasma mirror: group delay time versus frequency for different values of α.

Fig. 5
Fig. 5

F-GTI on a plasma mirror: group delay time versus α for different values of frequencies.

Equations (12)

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tan φ 2 = tan Ψ 12 2 tanh [ ω d c ( n 1 2 sin 2 θ n 2 2 ) 1 2 + γ ] ,
tan ( Ψ 12 ) S 2 = ( n 1 2 sin 2 θ n 2 2 ) 1 2 n 1 cos θ ,
tanh γ S = ( n 1 2 sin 2 θ n 3 2 ) 1 2 ( n 1 2 sin 2 θ n 2 2 ) 1 2 ,
tan ( Ψ 12 ) P 2 = ( n 1 n 2 ) 2 tan ( Ψ 12 ) S 2 ,
tanh γ P = ( n 2 n 3 ) 2 tanh γ S ,
tan ( φ p 2 ) = u ( 1 u 2 cos 2 θ ) 1 2 ( 1 u 2 ) cos θ ,
ω p ( t g ) p = δ φ p δ u = 2 cos θ ( 1 u 2 cos 2 θ ) 1 2 ( 1 u 2 cos 2 θ ) ( cos 2 θ u 2 cos 2 θ ) ,
ω p ( t GH ) p = tan θ u ( δ φ p δ θ ) = 2 tan θ sin θ ( 1 u 2 cos 2 θ ) 1 2 ( 1 u 2 ) ( cos 2 θ u 2 cos 2 θ ) ,
u 2 < tan 2 θ 1 tan 2 θ cos 2 θ .
tan φ p 2 = n ( n 2 sin 2 θ 1 ) 1 2 cos θ tanh ε [ α u ( n 2 sin 2 θ 1 ) 1 2 δ p ] ,
tanh ε ( δ p ) = u [ 1 + ( n 2 sin 2 θ 1 ) u 2 ] 1 2 ( 1 u 2 ) ( n 2 sin 2 θ 1 ) 1 2 ,
u 0 = ( n 2 sin 2 θ 1 ) 1 2 ( 2 n 2 sin 2 θ 1 ) 1 2 .

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