Abstract

It is theoretically shown that the negative Goos–Hänchen shifts near resonance, Re[kzd]=mπ, can be an order of magnitude larger than the wavelength for both TE- and TM-polarized beams reflected from a weakly absorbing dielectric slab if the absorption of the slab is sufficiently weak, which is different from the case for a lossless dielectric slab [Phys. Rev. Lett. 91, 133903 (2003) ].

© 2005 Optical Society of America

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  1. F. Goos and H. Hanchen, Ann. Phys. 1, 333 (1947).
    [CrossRef]
  2. F. Goos and H. Hanchen, Ann. Phys. 5, 251 (1949).
    [CrossRef]
  3. K. Artmann, Ann. Phys. 2, 87 (1948).
    [CrossRef]
  4. W. J. Wild and C. L. Giles, Phys. Rev. A 25, 2099 (1982).
    [CrossRef]
  5. R. H. Renard, J. Opt. Soc. Am. 54, 1190 (1964).
    [CrossRef]
  6. B. R. Horowitz and T. Tamir, J. Opt. Soc. Am. 61, 586 (1971).
    [CrossRef]
  7. D. Felbacq, A. Moreau, and R. Smaâli, Opt. Lett. 28, 1633 (2003).
    [CrossRef] [PubMed]
  8. C. F. Li, Phys. Rev. Lett. 91, 133903 (2003).
    [CrossRef]
  9. H. M. Lai and S. W. Chan, Opt. Lett. 27, 680 (2002).
    [CrossRef]
  10. J. J. Cowan and B. Anicin, J. Opt. Soc. Am. 67, 1307 (1977).
    [CrossRef]
  11. F. Bretenaker, A. Le Floch, and L. Dutriaux, Phys. Rev. Lett. 68, 931 (1992).
    [CrossRef] [PubMed]
  12. E. Pfleghaar, A. Marseille, and A. Weis, Phys. Rev. Lett. 70, 2281 (1993).
    [CrossRef] [PubMed]
  13. R. Schlesser and A. Weis, Opt. Lett. 17, 1015 (1992).
    [CrossRef] [PubMed]
  14. B. M. Jost, A.-A. R. Al-Rashed, and B. E.A. Saleh, Phys. Rev. Lett. 81, 2233 (1998).
    [CrossRef]
  15. A. Haibel, G. Nimtz, and A. A. Stahlhofen, Phys. Rev. E 63, 047601 (2001).
    [CrossRef]
  16. C. Bonnet, D. Chauvat, O. Emile, F. Bretenaker, and A. Le Floch, Opt. Lett. 26, 666 (2001).
    [CrossRef]
  17. N. F. Declercq, J. Degrieck, R. Briers, and O. Leroy, Appl. Phys. Lett. 82, 2533 (2003).
    [CrossRef]
  18. T. Tamir and H. L. Bertoni, J. Opt. Soc. Am. 61, 1937 (1971).
    [CrossRef]
  19. H. M. Lai, C. W. Kwok, Y. W. Loo, and B. Y. Xu, Phys. Rev. E 62, 7330 (2000).
    [CrossRef]
  20. P. R. Berman, Phys. Rev. E 66, 067603 (2002).
    [CrossRef]
  21. A. Lakhtakia, Electromagnetics 23, 71 (2003).
    [CrossRef]
  22. D.-K. Qing and G. Chen, Opt. Lett. 29, 872 (2004).
    [CrossRef] [PubMed]
  23. J. A. Kong, B.-L. Wu, and Y. Zhang, Appl. Phys. Lett. 80, 2084 (2002).
    [CrossRef]
  24. I. V. Shadrivov, A. A Zharov, and Y. S. Kivshar, Appl. Phys. Lett. 83, 2713 (2003).
    [CrossRef]
  25. X. Chen and C.-F. Li, Phys. Rev. E 69, 066617 (2004).
    [CrossRef]
  26. L.-G. Wang, N.-H. Liu, Q. Lin, and S.-Y. ZhuPhys. Rev. E 70, 016601 (2004).
    [CrossRef]
  27. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).
    [CrossRef]
  28. A. M. Steinberg and R. Y. Chiao, Phys. Rev. A 49, 3283 (1994).
    [CrossRef] [PubMed]

2004 (3)

D.-K. Qing and G. Chen, Opt. Lett. 29, 872 (2004).
[CrossRef] [PubMed]

X. Chen and C.-F. Li, Phys. Rev. E 69, 066617 (2004).
[CrossRef]

L.-G. Wang, N.-H. Liu, Q. Lin, and S.-Y. ZhuPhys. Rev. E 70, 016601 (2004).
[CrossRef]

2003 (5)

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

I. V. Shadrivov, A. A Zharov, and Y. S. Kivshar, Appl. Phys. Lett. 83, 2713 (2003).
[CrossRef]

N. F. Declercq, J. Degrieck, R. Briers, and O. Leroy, Appl. Phys. Lett. 82, 2533 (2003).
[CrossRef]

D. Felbacq, A. Moreau, and R. Smaâli, Opt. Lett. 28, 1633 (2003).
[CrossRef] [PubMed]

C. F. Li, Phys. Rev. Lett. 91, 133903 (2003).
[CrossRef]

2002 (3)

H. M. Lai and S. W. Chan, Opt. Lett. 27, 680 (2002).
[CrossRef]

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

J. A. Kong, B.-L. Wu, and Y. Zhang, Appl. Phys. Lett. 80, 2084 (2002).
[CrossRef]

2001 (2)

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

C. Bonnet, D. Chauvat, O. Emile, F. Bretenaker, and A. Le Floch, Opt. Lett. 26, 666 (2001).
[CrossRef]

2000 (1)

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

1998 (1)

B. M. Jost, A.-A. R. Al-Rashed, and B. E.A. Saleh, Phys. Rev. Lett. 81, 2233 (1998).
[CrossRef]

1994 (1)

A. M. Steinberg and R. Y. Chiao, Phys. Rev. A 49, 3283 (1994).
[CrossRef] [PubMed]

1993 (1)

E. Pfleghaar, A. Marseille, and A. Weis, Phys. Rev. Lett. 70, 2281 (1993).
[CrossRef] [PubMed]

1992 (2)

R. Schlesser and A. Weis, Opt. Lett. 17, 1015 (1992).
[CrossRef] [PubMed]

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

1982 (1)

W. J. Wild and C. L. Giles, Phys. Rev. A 25, 2099 (1982).
[CrossRef]

1977 (1)

1971 (2)

B. R. Horowitz and T. Tamir, J. Opt. Soc. Am. 61, 586 (1971).
[CrossRef]

T. Tamir and H. L. Bertoni, J. Opt. Soc. Am. 61, 1937 (1971).
[CrossRef]

1964 (1)

1949 (1)

F. Goos and H. Hanchen, Ann. Phys. 5, 251 (1949).
[CrossRef]

1948 (1)

K. Artmann, Ann. Phys. 2, 87 (1948).
[CrossRef]

1947 (1)

F. Goos and H. Hanchen, Ann. Phys. 1, 333 (1947).
[CrossRef]

Al-Rashed, A.-A. R.

B. M. Jost, A.-A. R. Al-Rashed, and B. E.A. Saleh, Phys. Rev. Lett. 81, 2233 (1998).
[CrossRef]

Anicin, B.

Artmann, K.

K. Artmann, Ann. Phys. 2, 87 (1948).
[CrossRef]

Berman, P. R.

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

Bertoni, H. L.

T. Tamir and H. L. Bertoni, J. Opt. Soc. Am. 61, 1937 (1971).
[CrossRef]

Bonnet, C.

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).
[CrossRef]

Bretenaker, F.

Briers, R.

N. F. Declercq, J. Degrieck, R. Briers, and O. Leroy, Appl. Phys. Lett. 82, 2533 (2003).
[CrossRef]

Chan, S. W.

Chauvat, D.

Chen, G.

Chen, X.

X. Chen and C.-F. Li, Phys. Rev. E 69, 066617 (2004).
[CrossRef]

Chiao, R. Y.

A. M. Steinberg and R. Y. Chiao, Phys. Rev. A 49, 3283 (1994).
[CrossRef] [PubMed]

Cowan, J. J.

Declercq, N. F.

N. F. Declercq, J. Degrieck, R. Briers, and O. Leroy, Appl. Phys. Lett. 82, 2533 (2003).
[CrossRef]

Degrieck, J.

N. F. Declercq, J. Degrieck, R. Briers, and O. Leroy, Appl. Phys. Lett. 82, 2533 (2003).
[CrossRef]

Dutriaux, L.

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

Emile, O.

Felbacq, D.

Giles, C. L.

W. J. Wild and C. L. Giles, Phys. Rev. A 25, 2099 (1982).
[CrossRef]

Goos, F.

F. Goos and H. Hanchen, Ann. Phys. 5, 251 (1949).
[CrossRef]

F. Goos and H. Hanchen, Ann. Phys. 1, 333 (1947).
[CrossRef]

Haibel, A.

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

Hanchen, H.

F. Goos and H. Hanchen, Ann. Phys. 5, 251 (1949).
[CrossRef]

F. Goos and H. Hanchen, Ann. Phys. 1, 333 (1947).
[CrossRef]

Horowitz, B. R.

Jost, B. M.

B. M. Jost, A.-A. R. Al-Rashed, and B. E.A. Saleh, Phys. Rev. Lett. 81, 2233 (1998).
[CrossRef]

Kivshar, Y. S.

I. V. Shadrivov, A. A Zharov, and Y. S. Kivshar, Appl. Phys. Lett. 83, 2713 (2003).
[CrossRef]

Kong, J. A.

J. A. Kong, B.-L. Wu, and Y. Zhang, Appl. Phys. Lett. 80, 2084 (2002).
[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 and S. W. Chan, Opt. Lett. 27, 680 (2002).
[CrossRef]

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

Lakhtakia, A.

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

Le Floch, A.

Leroy, O.

N. F. Declercq, J. Degrieck, R. Briers, and O. Leroy, Appl. Phys. Lett. 82, 2533 (2003).
[CrossRef]

Li, C. F.

C. F. Li, Phys. Rev. Lett. 91, 133903 (2003).
[CrossRef]

Li, C.-F.

X. Chen and C.-F. Li, Phys. Rev. E 69, 066617 (2004).
[CrossRef]

Lin, Q.

L.-G. Wang, N.-H. Liu, Q. Lin, and S.-Y. ZhuPhys. Rev. E 70, 016601 (2004).
[CrossRef]

Liu, N.-H.

L.-G. Wang, N.-H. Liu, Q. Lin, and S.-Y. ZhuPhys. Rev. E 70, 016601 (2004).
[CrossRef]

Loo, Y. W.

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

Marseille, A.

E. Pfleghaar, A. Marseille, and A. Weis, Phys. Rev. Lett. 70, 2281 (1993).
[CrossRef] [PubMed]

Moreau, A.

Nimtz, G.

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

Pfleghaar, E.

E. Pfleghaar, A. Marseille, and A. Weis, Phys. Rev. Lett. 70, 2281 (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, Phys. Rev. Lett. 81, 2233 (1998).
[CrossRef]

Schlesser, R.

Shadrivov, I. V.

I. V. Shadrivov, A. A Zharov, and Y. S. Kivshar, Appl. Phys. Lett. 83, 2713 (2003).
[CrossRef]

Smaâli, R.

Stahlhofen, A. A.

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

Steinberg, A. M.

A. M. Steinberg and R. Y. Chiao, Phys. Rev. A 49, 3283 (1994).
[CrossRef] [PubMed]

Tamir, T.

T. Tamir and H. L. Bertoni, J. Opt. Soc. Am. 61, 1937 (1971).
[CrossRef]

B. R. Horowitz and T. Tamir, J. Opt. Soc. Am. 61, 586 (1971).
[CrossRef]

Wang, L.-G.

L.-G. Wang, N.-H. Liu, Q. Lin, and S.-Y. ZhuPhys. Rev. E 70, 016601 (2004).
[CrossRef]

Weis, A.

E. Pfleghaar, A. Marseille, and A. Weis, Phys. Rev. Lett. 70, 2281 (1993).
[CrossRef] [PubMed]

R. Schlesser and A. Weis, Opt. Lett. 17, 1015 (1992).
[CrossRef] [PubMed]

Wild, W. J.

W. J. Wild and C. L. Giles, Phys. Rev. A 25, 2099 (1982).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).
[CrossRef]

Wu, B.-L.

J. A. Kong, B.-L. Wu, and Y. Zhang, Appl. Phys. Lett. 80, 2084 (2002).
[CrossRef]

Xu, B. Y.

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

Zhang, Y.

J. A. Kong, B.-L. Wu, and Y. Zhang, Appl. Phys. Lett. 80, 2084 (2002).
[CrossRef]

Zharov, A. A

I. V. Shadrivov, A. A Zharov, and Y. S. Kivshar, Appl. Phys. Lett. 83, 2713 (2003).
[CrossRef]

Zhu, S.-Y.

L.-G. Wang, N.-H. Liu, Q. Lin, and S.-Y. ZhuPhys. Rev. E 70, 016601 (2004).
[CrossRef]

Ann. Phys. (3)

F. Goos and H. Hanchen, Ann. Phys. 1, 333 (1947).
[CrossRef]

F. Goos and H. Hanchen, Ann. Phys. 5, 251 (1949).
[CrossRef]

K. Artmann, Ann. Phys. 2, 87 (1948).
[CrossRef]

Appl. Phys. Lett. (3)

N. F. Declercq, J. Degrieck, R. Briers, and O. Leroy, Appl. Phys. Lett. 82, 2533 (2003).
[CrossRef]

J. A. Kong, B.-L. Wu, and Y. Zhang, Appl. Phys. Lett. 80, 2084 (2002).
[CrossRef]

I. V. Shadrivov, A. A Zharov, and Y. S. Kivshar, Appl. Phys. Lett. 83, 2713 (2003).
[CrossRef]

Electromagnetics (1)

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

J. Opt. Soc. Am. (4)

Opt. Lett. (5)

Phys. Rev. A (2)

W. J. Wild and C. L. Giles, Phys. Rev. A 25, 2099 (1982).
[CrossRef]

A. M. Steinberg and R. Y. Chiao, Phys. Rev. A 49, 3283 (1994).
[CrossRef] [PubMed]

Phys. Rev. E (5)

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

X. Chen and C.-F. Li, Phys. Rev. E 69, 066617 (2004).
[CrossRef]

L.-G. Wang, N.-H. Liu, Q. Lin, and S.-Y. ZhuPhys. Rev. E 70, 016601 (2004).
[CrossRef]

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

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

Phys. Rev. Lett. (4)

C. F. Li, Phys. Rev. Lett. 91, 133903 (2003).
[CrossRef]

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

E. Pfleghaar, A. Marseille, and A. Weis, Phys. Rev. Lett. 70, 2281 (1993).
[CrossRef] [PubMed]

B. M. Jost, A.-A. R. Al-Rashed, and B. E.A. Saleh, Phys. Rev. Lett. 81, 2233 (1998).
[CrossRef]

Other (1)

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Weakly absorbing dielectric slab. The incident, reflected, and transmitted beams are identified by their respective beam axes. Dashed line, path expected from geometrical optics.

Fig. 2
Fig. 2

Dependence of Δ r on θ with d = 1.8 λ and ϵ r = 2.0 ; (a) and (b), TE polarization; (c) and (d) TM polarization. Solid curves, ϵ i = 0.02 ; dashed curves, ϵ i = 0.05 ; dotted curves, lossless slab ( ϵ i = 0 ) . The upper plots of (b) and (d) are the values of r , and the lower plots of (b) and (d) are the relative phases ϕ r .

Fig. 3
Fig. 3

(a) Dependence of the lateral shifts on the slab thickness for the reflected (solid curve) and transmitted (dashed curve) beams from the slab with ϵ r = 2.0 , ϵ i = 0.05 , and θ = 30 ° . (b) Δ r near one of the resonant conditions for different absorptive cases: solid curve, ϵ i = 0.1 ; dashed curve, ϵ i = 0.05 ; dotted curve ϵ i = 0.01 . Other parameters are the same as in Fig. 3(a).

Equations (8)

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[ cos ( k z d ) i 1 q sin ( k z d ) i q sin ( k z d ) cos ( k z d ) ] ,
r ( d , θ ) = i 2 ( cos θ q q cos θ ) sin ( k z d ) cos ( k z d ) i 2 ( cos θ q + q cos θ ) sin ( k z d ) ,
t ( d , θ ) = 1 cos ( k z d ) i 2 ( cos θ q + q cos θ ) sin ( k z d ) .
Δ r , t = λ 2 π d ϕ r , t d θ ,
d ϕ r ( d , θ ) d θ = i [ 1 r ( d , θ ) d r ( d , θ ) d θ 1 r ( d , θ ) d r ( d , θ ) d θ ] ,
d r ( d , θ ) d θ = 1 r ( d , θ ) { Re [ r ( d , θ ) ] d Re [ r ( d , θ ) ] d θ + Im [ r ( d , θ ) ] d Im [ r ( d , θ ) ] d θ } .
Δ r = λ 2 π d ϕ r d θ = λ 2 π 1 r ( d , θ ) 2 { Re [ r ( d , θ ) ] d Im [ r ( d , θ ) ] d θ Im [ r ( d , θ ) ] d Re [ r ( d , θ ) ] d θ } .
Δ t = λ 2 π d ϕ t d θ = λ 2 π 1 t ( d , θ ) 2 { Re [ t ( d , θ ) ] d Im [ t ( d , θ ) ] d θ Im [ t ( d , θ ) ] d Re [ t ( d , θ ) ] d θ } .

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