Abstract

Using Yasumoto and Õishi’s energy flux method, a generalized analytical formulation for analyzing the Goos–Hänchen (GH) shift in frustrated total internal reflection is provided, from which the GH shift given by Artman’s stationary phase method is shown to equal the GH calculated by Renard’s conventional energy flux method plus a self-interference shift. The self-interference shift, originating from the interference between the incident and reflected beams, sheds light on the asymptotic behavior of the GH shift in such optical tunneling process in term of energy flux.

© 2012 Optical Society of America

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References

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  1. F. Goos and H. Hänchen, Ann. Phys. 436, 333 (1947).
    [CrossRef]
  2. F. Goos and H. Hänchen, Ann. Phys. 5, 251 (1949).
  3. C. W. Hsue and T. Tamir, J. Opt. Soc. Am. A 2, 978 (1985).
  4. A. K. Ghatak, M. R. Shenoy, I. C. Goyal, and K. Thyagarajan, Opt. Commun. 56, 313 (1986).
  5. A. Haibel, G. Nimtz, and A. A. Stahlhofen, Phys. Rev. E 63, 047601 (2001).
    [CrossRef]
  6. X. Chen, C. F. Li, R. R. Wei, and Y. Zhang, Phys. Rev. A 80, 015803 (2009).
  7. M. Qu and Z.-X. Huang, Opt. Commun. 284, 2604 (2011).
    [CrossRef]
  8. X. Yin, L. Hesselink, Z. Liu, N. Fang, and X. Zhang, Appl. Phys. Lett. 85, 372 (2004).
    [CrossRef]
  9. F. Pillon, H. Gilles, S. Girard, M. Laroche, R. Kaiser, and A. Gazibegovic, J. Opt. Soc. Am. B 22, 1290 (2005).
    [CrossRef]
  10. K. V. Artmann, Ann. Phys. 2, 87 (1948).
  11. R. H. Renard, J. Opt. Soc. Am. 54, 1190 (1964).
    [CrossRef]
  12. H. M. Lai, C. W. Kwok, Y. W. Loo, and B. Y. Xu, Phys. Rev. E 62, 7330 (2000).
    [CrossRef]
  13. K. Yasumoto and Y. Oishi, J. Appl. Phys. 54, 2170 (1983).
    [CrossRef]
  14. V. G. Fedoseyev, J. Opt. Soc. Am. A 3, 826 (1986).
    [CrossRef]
  15. S. R. Seshadri, J. Opt. Soc. Am. A 5, 583 (1988).
    [CrossRef]
  16. H. G. Winful and C. Zhang, Phys. Rev. A 79, 023826 (2009).
    [CrossRef]
  17. H. G. Winful, Phys. Rev. Lett. 91, 260401 (2003).
    [CrossRef]
  18. G. Isić, V. Milanvić, J. Radivanović, Z. Ikonić, D. Indjin, and P. Harrison, Phys. Rev. A 77, 033821 (1986).
    [CrossRef]

2011 (1)

M. Qu and Z.-X. Huang, Opt. Commun. 284, 2604 (2011).
[CrossRef]

2009 (2)

X. Chen, C. F. Li, R. R. Wei, and Y. Zhang, Phys. Rev. A 80, 015803 (2009).

H. G. Winful and C. Zhang, Phys. Rev. A 79, 023826 (2009).
[CrossRef]

2005 (1)

2004 (1)

X. Yin, L. Hesselink, Z. Liu, N. Fang, and X. Zhang, Appl. Phys. Lett. 85, 372 (2004).
[CrossRef]

2003 (1)

H. G. Winful, Phys. Rev. Lett. 91, 260401 (2003).
[CrossRef]

2001 (1)

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

2000 (1)

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

1988 (1)

1986 (3)

G. Isić, V. Milanvić, J. Radivanović, Z. Ikonić, D. Indjin, and P. Harrison, Phys. Rev. A 77, 033821 (1986).
[CrossRef]

V. G. Fedoseyev, J. Opt. Soc. Am. A 3, 826 (1986).
[CrossRef]

A. K. Ghatak, M. R. Shenoy, I. C. Goyal, and K. Thyagarajan, Opt. Commun. 56, 313 (1986).

1985 (1)

1983 (1)

K. Yasumoto and Y. Oishi, J. Appl. Phys. 54, 2170 (1983).
[CrossRef]

1964 (1)

1949 (1)

F. Goos and H. Hänchen, Ann. Phys. 5, 251 (1949).

1948 (1)

K. V. Artmann, Ann. Phys. 2, 87 (1948).

1947 (1)

F. Goos and H. Hänchen, Ann. Phys. 436, 333 (1947).
[CrossRef]

Artmann, K. V.

K. V. Artmann, Ann. Phys. 2, 87 (1948).

Chen, X.

X. Chen, C. F. Li, R. R. Wei, and Y. Zhang, Phys. Rev. A 80, 015803 (2009).

Fang, N.

X. Yin, L. Hesselink, Z. Liu, N. Fang, and X. Zhang, Appl. Phys. Lett. 85, 372 (2004).
[CrossRef]

Fedoseyev, V. G.

Gazibegovic, A.

Ghatak, A. K.

A. K. Ghatak, M. R. Shenoy, I. C. Goyal, and K. Thyagarajan, Opt. Commun. 56, 313 (1986).

Gilles, H.

Girard, S.

Goos, F.

F. Goos and H. Hänchen, Ann. Phys. 5, 251 (1949).

F. Goos and H. Hänchen, Ann. Phys. 436, 333 (1947).
[CrossRef]

Goyal, I. C.

A. K. Ghatak, M. R. Shenoy, I. C. Goyal, and K. Thyagarajan, Opt. Commun. 56, 313 (1986).

Haibel, A.

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

Hänchen, H.

F. Goos and H. Hänchen, Ann. Phys. 5, 251 (1949).

F. Goos and H. Hänchen, Ann. Phys. 436, 333 (1947).
[CrossRef]

Harrison, P.

G. Isić, V. Milanvić, J. Radivanović, Z. Ikonić, D. Indjin, and P. Harrison, Phys. Rev. A 77, 033821 (1986).
[CrossRef]

Hesselink, L.

X. Yin, L. Hesselink, Z. Liu, N. Fang, and X. Zhang, Appl. Phys. Lett. 85, 372 (2004).
[CrossRef]

Hsue, C. W.

Huang, Z.-X.

M. Qu and Z.-X. Huang, Opt. Commun. 284, 2604 (2011).
[CrossRef]

Ikonic, Z.

G. Isić, V. Milanvić, J. Radivanović, Z. Ikonić, D. Indjin, and P. Harrison, Phys. Rev. A 77, 033821 (1986).
[CrossRef]

Indjin, D.

G. Isić, V. Milanvić, J. Radivanović, Z. Ikonić, D. Indjin, and P. Harrison, Phys. Rev. A 77, 033821 (1986).
[CrossRef]

Isic, G.

G. Isić, V. Milanvić, J. Radivanović, Z. Ikonić, D. Indjin, and P. Harrison, Phys. Rev. A 77, 033821 (1986).
[CrossRef]

Kaiser, R.

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]

Laroche, M.

Li, C. F.

X. Chen, C. F. Li, R. R. Wei, and Y. Zhang, Phys. Rev. A 80, 015803 (2009).

Liu, Z.

X. Yin, L. Hesselink, Z. Liu, N. Fang, and X. Zhang, Appl. Phys. Lett. 85, 372 (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]

Milanvic, V.

G. Isić, V. Milanvić, J. Radivanović, Z. Ikonić, D. Indjin, and P. Harrison, Phys. Rev. A 77, 033821 (1986).
[CrossRef]

Nimtz, G.

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

Oishi, Y.

K. Yasumoto and Y. Oishi, J. Appl. Phys. 54, 2170 (1983).
[CrossRef]

Pillon, F.

Qu, M.

M. Qu and Z.-X. Huang, Opt. Commun. 284, 2604 (2011).
[CrossRef]

Radivanovic, J.

G. Isić, V. Milanvić, J. Radivanović, Z. Ikonić, D. Indjin, and P. Harrison, Phys. Rev. A 77, 033821 (1986).
[CrossRef]

Renard, R. H.

Seshadri, S. R.

Shenoy, M. R.

A. K. Ghatak, M. R. Shenoy, I. C. Goyal, and K. Thyagarajan, Opt. Commun. 56, 313 (1986).

Stahlhofen, A. A.

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

Tamir, T.

Thyagarajan, K.

A. K. Ghatak, M. R. Shenoy, I. C. Goyal, and K. Thyagarajan, Opt. Commun. 56, 313 (1986).

Wei, R. R.

X. Chen, C. F. Li, R. R. Wei, and Y. Zhang, Phys. Rev. A 80, 015803 (2009).

Winful, H. G.

H. G. Winful and C. Zhang, Phys. Rev. A 79, 023826 (2009).
[CrossRef]

H. G. Winful, Phys. Rev. Lett. 91, 260401 (2003).
[CrossRef]

Xu, B. Y.

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

Yasumoto, K.

K. Yasumoto and Y. Oishi, J. Appl. Phys. 54, 2170 (1983).
[CrossRef]

Yin, X.

X. Yin, L. Hesselink, Z. Liu, N. Fang, and X. Zhang, Appl. Phys. Lett. 85, 372 (2004).
[CrossRef]

Zhang, C.

H. G. Winful and C. Zhang, Phys. Rev. A 79, 023826 (2009).
[CrossRef]

Zhang, X.

X. Yin, L. Hesselink, Z. Liu, N. Fang, and X. Zhang, Appl. Phys. Lett. 85, 372 (2004).
[CrossRef]

Zhang, Y.

X. Chen, C. F. Li, R. R. Wei, and Y. Zhang, Phys. Rev. A 80, 015803 (2009).

Ann. Phys. (3)

F. Goos and H. Hänchen, Ann. Phys. 436, 333 (1947).
[CrossRef]

F. Goos and H. Hänchen, Ann. Phys. 5, 251 (1949).

K. V. Artmann, Ann. Phys. 2, 87 (1948).

Appl. Phys. Lett. (1)

X. Yin, L. Hesselink, Z. Liu, N. Fang, and X. Zhang, Appl. Phys. Lett. 85, 372 (2004).
[CrossRef]

J. Appl. Phys. (1)

K. Yasumoto and Y. Oishi, J. Appl. Phys. 54, 2170 (1983).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (3)

J. Opt. Soc. Am. B (1)

Opt. Commun. (2)

M. Qu and Z.-X. Huang, Opt. Commun. 284, 2604 (2011).
[CrossRef]

A. K. Ghatak, M. R. Shenoy, I. C. Goyal, and K. Thyagarajan, Opt. Commun. 56, 313 (1986).

Phys. Rev. A (3)

X. Chen, C. F. Li, R. R. Wei, and Y. Zhang, Phys. Rev. A 80, 015803 (2009).

H. G. Winful and C. Zhang, Phys. Rev. A 79, 023826 (2009).
[CrossRef]

G. Isić, V. Milanvić, J. Radivanović, Z. Ikonić, D. Indjin, and P. Harrison, Phys. Rev. A 77, 033821 (1986).
[CrossRef]

Phys. Rev. E (2)

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

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

Phys. Rev. Lett. (1)

H. G. Winful, Phys. Rev. Lett. 91, 260401 (2003).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

Illustration of the GH shift s in FTIR, where an air gap of width a severs as the barrier. The shadow region represents the interference between the incident and reflection beams in the overlap region.

Fig. 2.
Fig. 2.

GH shift versus the incidence angle θ0, where sp (solid line), se (dashed line), and sir (dotted line). Parameters: λ=32.8mm, n=1.605, a=50mm. Vertical line represents the critical angle θc=38.5°, se=sir at the point θp=56.4°.

Fig. 3.
Fig. 3.

Dependence of the GH shift on the air gap a, where (a) θ0=50° and (b) θ0=80°, sp (solid line), se (dashed line), and sir (dotted line). Other parameters are the same as those in Fig. 2.

Fig. 4.
Fig. 4.

Energy flux density distribution (in arbitrary units) for a Gaussian beam in FTIR, where the beam width w=1.2λ, θ0=50° (a), θ0=80° (b). Other parameters are the same as those in Fig. 2.

Equations (11)

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

sp=akyκf2(sin2δsec2δsinh2κa2κasin2δcos2δ).
θ0>θpsin11+n22n2,
se=PSxr=0aSydxSxr,
Sy=12Re[E×H*]y=kycos2δμω0f2[sinh2κ(xa)cos2δ],
se=akyκf2(sin2δsinh2κa2κasin2δcos2δ).
Sir=12Re[Ei×Hr*+Er×Hi*]y=ky|R|μω0cos(2kxxϕr).
Pir=l0Sirdx=ky|R|2μω0kx[sinϕrsin(2kxl+ϕr)].
Pir=1λx0λxPirdx=ky|R|2μω0kxsinϕr.
sir=PirSix,
sir=akyκf2(sin2δtan2δsinh2κa2κa).
sir=Im(R)kytan2θ0,

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