Abstract

We consider the lateral shift (LS) of a light beam reflecting from a dielectric slab backed by a metal. It is found that the LS of the reflected beam can be negative while the intensity of reflected beam is almost equal to the incident one under a certain condition. The explanation for the negativity of the LS is given in terms of the interference of the reflected waves from the two interfaces. It is also shown that the LS can be enhanced or suppressed under some other conditions. The numerical calculation on the LS for a realistic Gaussian-shaped beam confirms our theoretical prediction.

© 2006 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  18. P. R. Berman, Phys. Rev. E 66, 067603 (2002).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  23. R. P. Riesz and R. Simon, J. Opt. Soc. Am. A 2, 1809 (1985).
    [CrossRef]
  24. L. G. Wang, H. Chen, and S. Y. Zhu, Opt. Lett. 30, 2936 (2005).
    [CrossRef] [PubMed]
  25. F. Wang and A. Lakhtakia, Opt. Commun. 235, 107 (2004).
    [CrossRef]

2005

L. G. Wang and S. Y. Zhu, Appl. Phys. Lett. 87, 221102 (2005).
[CrossRef]

L. G. Wang, H. Chen, and S. Y. Zhu, Opt. Lett. 30, 2936 (2005).
[CrossRef] [PubMed]

2004

F. Wang and A. Lakhtakia, Opt. Commun. 235, 107 (2004).
[CrossRef]

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

2003

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

A. Lakhtakia, Electromagnetics 23, 71 (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] [PubMed]

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

2002

2001

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

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

1998

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

1993

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

1992

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

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

1985

1982

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

1977

1971

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]

1949

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

1947

F. Goos and H. Hänchen, 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.

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.

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, H.

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. Hänchen, 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]

Hänchen, H.

F. Goos and H. Hänchen, 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]

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.

F. Wang and A. Lakhtakia, Opt. Commun. 235, 107 (2004).
[CrossRef]

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] [PubMed]

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.

Riesz, R. P.

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]

Simon, R.

Smaâli, R.

Stahlhofen, A. A.

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

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, F.

F. Wang and A. Lakhtakia, Opt. Commun. 235, 107 (2004).
[CrossRef]

Wang, L. G.

L. G. Wang, H. Chen, and S. Y. Zhu, Opt. Lett. 30, 2936 (2005).
[CrossRef] [PubMed]

L. G. Wang and S. Y. Zhu, Appl. Phys. Lett. 87, 221102 (2005).
[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]

Xu, B. Y.

H. M. Lai, C. W. Kwok, Y. W. Loo, and B. Y. Xu, Phys. Rev. E 62, 7330 (2000).
[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 and S. Y. Zhu, Appl. Phys. Lett. 87, 221102 (2005).
[CrossRef]

L. G. Wang, H. Chen, and S. Y. Zhu, Opt. Lett. 30, 2936 (2005).
[CrossRef] [PubMed]

Ann. Phys.

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

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

Appl. Phys. Lett.

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

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

L. G. Wang and S. Y. Zhu, Appl. Phys. Lett. 87, 221102 (2005).
[CrossRef]

Electromagnetics

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

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Commun.

F. Wang and A. Lakhtakia, Opt. Commun. 235, 107 (2004).
[CrossRef]

Opt. Lett.

Phys. Rev. A

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

Phys. Rev. E

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

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

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]

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Figures (4)

Fig. 1
Fig. 1

Sketch of a dielectric slab backed by a metal. The dotted and dashed lines are, respectively, the paths of reflection from the first and second interfaces predicted by geometrical optics. Ray 1, negative LS; ray 2, positive LS.

Fig. 2
Fig. 2

Dependence of the LS Δ on the thickness d (re scaled by k z 1 d ) for the slab with ϵ 1 = 3.0 (solid curve) and ϵ 1 = 9.0 (dashed curve) at wavelength λ with θ = 80 ° .

Fig. 3
Fig. 3

Dependence of the LS Δ on the thickness d (rescaled by k z 1 d π ) with ϵ 1 = 3.0 and θ = 85 ° under the conditions (a) k z 1 d ( ϵ 1 1 ) ( 2 cos 2 θ ) and (b) k z 1 d ( ϵ 1 1 ) ( 2 cos 2 θ ) . The first and second terms and the exact result of Eq. (4) are denoted by dashed, short-dashed, and solid curves, respectively.

Fig. 4
Fig. 4

Numerical (dots) and analytical results (thin curves) of the LS for the slab system ( ϵ 1 = 4.0 and ϵ 2 = 50 + 0.5 i ) for different thicknesses: (a) d = λ , (b) d = 6 λ . The thick curve in (b) denotes the shift Δ ¯ from geometrical optics. Left inset, the shapes of the incident (dashed curve) and reflected (solid curve) beams at θ = 85 ° ; right inset, the shift near large angles.

Equations (4)

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r ( θ ) = [ ( k z 0 k z 1 ) ( k z 1 + k z 2 ) + ( k z 0 + k z 1 ) ( k z 1 k z 2 ) exp ( 2 i k z 1 d ) ] [ ( k z 0 + k z 1 ) ( k z 1 + k z 2 ) + ( k z 0 k z 1 ) ( k z 1 k z 2 ) exp ( 2 i k z 1 d ) ] ,
Δ = 2 d tan θ cos 2 θ + ( ϵ 1 1 ) [ sin ( 2 k z 1 d ) 2 k z 1 d ] cos 2 θ + ( ϵ 1 1 ) cos 2 [ k z 1 d ] .
cos 2 θ + ( ϵ 1 1 ) sin ( 2 k z 1 d ) 2 k z 1 d < 0
Δ = 2 d sin θ cos θ cos 2 θ + ( ϵ 1 1 ) cos 2 ( k z 1 d ) + ( ϵ 1 1 ) tan θ k z 1 sin ( 2 k z 1 d ) cos 2 θ + ( ϵ 1 1 ) cos 2 ( k z 1 d ) .

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