Abstract

We investigate the dependence of the Goos–Hänchen shift on the penetration depth of light beam. Experiments reveal that the deeper the penetration depth, the larger the Goos–Hänchen shift becomes. Through a tuning of 14 pm in wavelength, a lateral displacement as large as 1.5 mm is observed on the surface of symmetric metal-cladding optical waveguides with different thicknesses of the guiding layer experimentally. It is proved that the lateral shift is not only closely dependent on the well excitation condition of the guided modes, but also on the penetration depth of the light beam.

© 2010 Optical Society of America

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    [CrossRef]
  2. F. Goos and H. Hänchen, “Neumessung des Strahlversetzungseffektes bei Totalreflexion,” Ann. Phys. (Leipzig) 440, 251–252 (1949).
    [CrossRef]
  3. C. F. Li and Q. Wang, “Prediction of simultaneously large and opposite generalized Goos–Hänchen shifts for TE and TM light beams in an asymmetric double-prism configuration,” Phys. Rev. E 69, 055601 (2004).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  13. H. Li, Z. Cao, H. Lu, and Q. Shen, “Free-space coupling of a light beam into a symmetrical metal-cladding optical waveguide,” Appl. Phys. Lett. 83, 2757–2759 (2003).
    [CrossRef]
  14. L. Chen, Z. Cao, F. Ou, H. Li, Q. Shen, and H. Qiao, “Observation of large positive and negative lateral shifts of a reflected beam from symmetrical metal-cladding waveguides,” Opt. Lett. 32, 1432–1434 (2007).
    [CrossRef] [PubMed]
  15. X. Liu, Z. Cao, P. Zhu, Q. Shen, and X. Liu, “Large positive and negative lateral optical beam shift in prism-waveguide coupling system,” Phys. Rev. E 73, 056617 (2006).
    [CrossRef]
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    [CrossRef] [PubMed]
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2008 (2)

M. Cheng, Y. Zhou, Y. Li, and X. Li, “Large positive and negative generalized Goos–Hänchen shifts from a double negative metamaterial slab backed by a metal,” J. Opt. Soc. Am. B 25, 773–776 (2008).
[CrossRef]

Z. Luo, X. Liu, W. Shen, H. Xue, and P. Gu, “Large positive and negative lateral beam displacement in a guided-mode resonant filter,” J. Opt. A, Pure Appl. Opt. 10, 115008 (2008).
[CrossRef]

2007 (1)

2006 (2)

X. Liu, Z. Cao, P. Zhu, Q. Shen, and X. Liu, “Large positive and negative lateral optical beam shift in prism-waveguide coupling system,” Phys. Rev. E 73, 056617 (2006).
[CrossRef]

L. G. Wang, H. Chen, and S. Y. Zhu, “Large negative Goos–Hänchen shift from a weakly absorbing dielectric slab,” Opt. Lett. 31, 101–103 (2006).
[CrossRef] [PubMed]

2004 (2)

X. Yin, L. Hesselink, Z. Liu, N. Fang, and X. Zhang, “Large positive and negative lateral optical beam displacements due to surface plasmon resonance,” Appl. Phys. Lett. 85, 372–374 (2004).
[CrossRef]

C. F. Li and Q. Wang, “Prediction of simultaneously large and opposite generalized Goos–Hänchen shifts for TE and TM light beams in an asymmetric double-prism configuration,” Phys. Rev. E 69, 055601 (2004).
[CrossRef]

2003 (1)

H. Li, Z. Cao, H. Lu, and Q. Shen, “Free-space coupling of a light beam into a symmetrical metal-cladding optical waveguide,” Appl. Phys. Lett. 83, 2757–2759 (2003).
[CrossRef]

2002 (2)

1998 (1)

1993 (1)

A. M. Steinberg and R. Y. Chiao, “Measurement of the single-photon tunneling time,” Phys. Rev. Lett. 71, 708–711 (1993).
[CrossRef] [PubMed]

1986 (1)

1971 (1)

1949 (1)

F. Goos and H. Hänchen, “Neumessung des Strahlversetzungseffektes bei Totalreflexion,” Ann. Phys. (Leipzig) 440, 251–252 (1949).
[CrossRef]

1948 (1)

K. Artmann, “Berechnung der Seitenversetzung des totalreflektierten Strahles,” Ann. Phys. (Leipzig) 2, 87–102 (1948).

1947 (1)

F. Goos and H. Hänchen, “Ein neuer und fundamentaler Versuch zur Totalreflexion,” Ann. Phys. (Leipzig) 436, 333–346 (1947).
[CrossRef]

Artmann, K.

K. Artmann, “Berechnung der Seitenversetzung des totalreflektierten Strahles,” Ann. Phys. (Leipzig) 2, 87–102 (1948).

Bertoni, H. L.

Bryngdahl, O.

Cao, Z.

L. Chen, Z. Cao, F. Ou, H. Li, Q. Shen, and H. Qiao, “Observation of large positive and negative lateral shifts of a reflected beam from symmetrical metal-cladding waveguides,” Opt. Lett. 32, 1432–1434 (2007).
[CrossRef] [PubMed]

X. Liu, Z. Cao, P. Zhu, Q. Shen, and X. Liu, “Large positive and negative lateral optical beam shift in prism-waveguide coupling system,” Phys. Rev. E 73, 056617 (2006).
[CrossRef]

H. Li, Z. Cao, H. Lu, and Q. Shen, “Free-space coupling of a light beam into a symmetrical metal-cladding optical waveguide,” Appl. Phys. Lett. 83, 2757–2759 (2003).
[CrossRef]

Chan, S. W.

Chen, H.

Chen, L.

Cheng, F. C.

Cheng, M.

Chiao, R. Y.

A. M. Steinberg and R. Y. Chiao, “Measurement of the single-photon tunneling time,” Phys. Rev. Lett. 71, 708–711 (1993).
[CrossRef] [PubMed]

Fang, N.

X. Yin, L. Hesselink, Z. Liu, N. Fang, and X. Zhang, “Large positive and negative lateral optical beam displacements due to surface plasmon resonance,” Appl. Phys. Lett. 85, 372–374 (2004).
[CrossRef]

Gilles, H.

Girard, S.

Goos, F.

F. Goos and H. Hänchen, “Neumessung des Strahlversetzungseffektes bei Totalreflexion,” Ann. Phys. (Leipzig) 440, 251–252 (1949).
[CrossRef]

F. Goos and H. Hänchen, “Ein neuer und fundamentaler Versuch zur Totalreflexion,” Ann. Phys. (Leipzig) 436, 333–346 (1947).
[CrossRef]

Gu, P.

Z. Luo, X. Liu, W. Shen, H. Xue, and P. Gu, “Large positive and negative lateral beam displacement in a guided-mode resonant filter,” J. Opt. A, Pure Appl. Opt. 10, 115008 (2008).
[CrossRef]

Hamel, J.

Hänchen, H.

F. Goos and H. Hänchen, “Neumessung des Strahlversetzungseffektes bei Totalreflexion,” Ann. Phys. (Leipzig) 440, 251–252 (1949).
[CrossRef]

F. Goos and H. Hänchen, “Ein neuer und fundamentaler Versuch zur Totalreflexion,” Ann. Phys. (Leipzig) 436, 333–346 (1947).
[CrossRef]

Hesselink, L.

X. Yin, L. Hesselink, Z. Liu, N. Fang, and X. Zhang, “Large positive and negative lateral optical beam displacements due to surface plasmon resonance,” Appl. Phys. Lett. 85, 372–374 (2004).
[CrossRef]

Lai, H. M.

Li, C. F.

C. F. Li and Q. Wang, “Prediction of simultaneously large and opposite generalized Goos–Hänchen shifts for TE and TM light beams in an asymmetric double-prism configuration,” Phys. Rev. E 69, 055601 (2004).
[CrossRef]

Li, H.

L. Chen, Z. Cao, F. Ou, H. Li, Q. Shen, and H. Qiao, “Observation of large positive and negative lateral shifts of a reflected beam from symmetrical metal-cladding waveguides,” Opt. Lett. 32, 1432–1434 (2007).
[CrossRef] [PubMed]

H. Li, Z. Cao, H. Lu, and Q. Shen, “Free-space coupling of a light beam into a symmetrical metal-cladding optical waveguide,” Appl. Phys. Lett. 83, 2757–2759 (2003).
[CrossRef]

Li, X.

Li, Y.

Liu, X.

Z. Luo, X. Liu, W. Shen, H. Xue, and P. Gu, “Large positive and negative lateral beam displacement in a guided-mode resonant filter,” J. Opt. A, Pure Appl. Opt. 10, 115008 (2008).
[CrossRef]

X. Liu, Z. Cao, P. Zhu, Q. Shen, and X. Liu, “Large positive and negative lateral optical beam shift in prism-waveguide coupling system,” Phys. Rev. E 73, 056617 (2006).
[CrossRef]

X. Liu, Z. Cao, P. Zhu, Q. Shen, and X. Liu, “Large positive and negative lateral optical beam shift in prism-waveguide coupling system,” Phys. Rev. E 73, 056617 (2006).
[CrossRef]

Liu, Z.

X. Yin, L. Hesselink, Z. Liu, N. Fang, and X. Zhang, “Large positive and negative lateral optical beam displacements due to surface plasmon resonance,” Appl. Phys. Lett. 85, 372–374 (2004).
[CrossRef]

Lu, H.

H. Li, Z. Cao, H. Lu, and Q. Shen, “Free-space coupling of a light beam into a symmetrical metal-cladding optical waveguide,” Appl. Phys. Lett. 83, 2757–2759 (2003).
[CrossRef]

Luo, Z.

Z. Luo, X. Liu, W. Shen, H. Xue, and P. Gu, “Large positive and negative lateral beam displacement in a guided-mode resonant filter,” J. Opt. A, Pure Appl. Opt. 10, 115008 (2008).
[CrossRef]

Ou, F.

Qiao, H.

Schmitz, M.

Schreier, F.

Shen, Q.

L. Chen, Z. Cao, F. Ou, H. Li, Q. Shen, and H. Qiao, “Observation of large positive and negative lateral shifts of a reflected beam from symmetrical metal-cladding waveguides,” Opt. Lett. 32, 1432–1434 (2007).
[CrossRef] [PubMed]

X. Liu, Z. Cao, P. Zhu, Q. Shen, and X. Liu, “Large positive and negative lateral optical beam shift in prism-waveguide coupling system,” Phys. Rev. E 73, 056617 (2006).
[CrossRef]

H. Li, Z. Cao, H. Lu, and Q. Shen, “Free-space coupling of a light beam into a symmetrical metal-cladding optical waveguide,” Appl. Phys. Lett. 83, 2757–2759 (2003).
[CrossRef]

Shen, W.

Z. Luo, X. Liu, W. Shen, H. Xue, and P. Gu, “Large positive and negative lateral beam displacement in a guided-mode resonant filter,” J. Opt. A, Pure Appl. Opt. 10, 115008 (2008).
[CrossRef]

Steinberg, A. M.

A. M. Steinberg and R. Y. Chiao, “Measurement of the single-photon tunneling time,” Phys. Rev. Lett. 71, 708–711 (1993).
[CrossRef] [PubMed]

Tamir, T.

Tang, W. K.

Wang, L. G.

Wang, Q.

C. F. Li and Q. Wang, “Prediction of simultaneously large and opposite generalized Goos–Hänchen shifts for TE and TM light beams in an asymmetric double-prism configuration,” Phys. Rev. E 69, 055601 (2004).
[CrossRef]

Xue, H.

Z. Luo, X. Liu, W. Shen, H. Xue, and P. Gu, “Large positive and negative lateral beam displacement in a guided-mode resonant filter,” J. Opt. A, Pure Appl. Opt. 10, 115008 (2008).
[CrossRef]

Yin, X.

X. Yin, L. Hesselink, Z. Liu, N. Fang, and X. Zhang, “Large positive and negative lateral optical beam displacements due to surface plasmon resonance,” Appl. Phys. Lett. 85, 372–374 (2004).
[CrossRef]

Zhang, X.

X. Yin, L. Hesselink, Z. Liu, N. Fang, and X. Zhang, “Large positive and negative lateral optical beam displacements due to surface plasmon resonance,” Appl. Phys. Lett. 85, 372–374 (2004).
[CrossRef]

Zhou, Y.

Zhu, P.

X. Liu, Z. Cao, P. Zhu, Q. Shen, and X. Liu, “Large positive and negative lateral optical beam shift in prism-waveguide coupling system,” Phys. Rev. E 73, 056617 (2006).
[CrossRef]

Zhu, S. Y.

Ann. Phys. (Leipzig) (3)

F. Goos and H. Hänchen, “Ein neuer und fundamentaler Versuch zur Totalreflexion,” Ann. Phys. (Leipzig) 436, 333–346 (1947).
[CrossRef]

F. Goos and H. Hänchen, “Neumessung des Strahlversetzungseffektes bei Totalreflexion,” Ann. Phys. (Leipzig) 440, 251–252 (1949).
[CrossRef]

K. Artmann, “Berechnung der Seitenversetzung des totalreflektierten Strahles,” Ann. Phys. (Leipzig) 2, 87–102 (1948).

Appl. Phys. Lett. (2)

X. Yin, L. Hesselink, Z. Liu, N. Fang, and X. Zhang, “Large positive and negative lateral optical beam displacements due to surface plasmon resonance,” Appl. Phys. Lett. 85, 372–374 (2004).
[CrossRef]

H. Li, Z. Cao, H. Lu, and Q. Shen, “Free-space coupling of a light beam into a symmetrical metal-cladding optical waveguide,” Appl. Phys. Lett. 83, 2757–2759 (2003).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (1)

Z. Luo, X. Liu, W. Shen, H. Xue, and P. Gu, “Large positive and negative lateral beam displacement in a guided-mode resonant filter,” J. Opt. A, Pure Appl. Opt. 10, 115008 (2008).
[CrossRef]

J. Opt. Soc. Am. (1)

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

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

Opt. Lett. (5)

Phys. Rev. E (2)

X. Liu, Z. Cao, P. Zhu, Q. Shen, and X. Liu, “Large positive and negative lateral optical beam shift in prism-waveguide coupling system,” Phys. Rev. E 73, 056617 (2006).
[CrossRef]

C. F. Li and Q. Wang, “Prediction of simultaneously large and opposite generalized Goos–Hänchen shifts for TE and TM light beams in an asymmetric double-prism configuration,” Phys. Rev. E 69, 055601 (2004).
[CrossRef]

Phys. Rev. Lett. (1)

A. M. Steinberg and R. Y. Chiao, “Measurement of the single-photon tunneling time,” Phys. Rev. Lett. 71, 708–711 (1993).
[CrossRef] [PubMed]

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Figures (5)

Fig. 1
Fig. 1

(a) Field distribution. (b) The structure of the SMCW.

Fig. 2
Fig. 2

Calculated shift as a function of thickness of the guiding layer of the waveguide parameters used: ε 1 = 2.8 , ε 2 = 34 + i 1.17 , θ = 3 ° , h 1 = 33   nm , h 3 = 300   nm , and λ = 860   nm .

Fig. 3
Fig. 3

(a) Calculated phase as a function of incident wavelength with respect to thickness of the guiding layer. (b) Experimental and theoretical GH shifts with various thicknesses of the guiding layer.

Fig. 4
Fig. 4

Experimental setup for shift sensing.

Fig. 5
Fig. 5

Theoretical and experimental reflected beam displacements ( S ) with respect to the light wavelength; the parameters are as follows: ε 1 = 2.8 , ε 2 = 34 + i 1.17 , θ = 1.9 ° , h 1 = 33.1   nm , h 2 = 3.04   mm , and h 3 = 300   nm .

Equations (1)

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Im ( β 0 ) = Im ( Δ β rad ) ,

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