Abstract

Total internal reflection of a pulsed light beam upon an interface between two dielectric media is investigated by means of a rigorous plane-wave expansion method, and a simple analytical expression of the reflected pulsed beam is obtained on the condition of Gaussian-shaped pulsed beam illumination. It is shown that, because of the frequency-dependent Goos–Hänchen shift, the reflected pulsed beam undergoes position-dependent distortions including carrier frequency shift, phase shift, pulse duration, and chirp, which are of theoretical importance for designing optical devices used for total internal reflection of ultrashort pulses.

© 2010 Optical Society of America

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References

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  1. F. Goos and H. Hänchen, “Ein neuer und fundamentaler Versuch zur Totalreflexion,” Ann. Phys. (Leipzig) 436, 333–346 (1947).
    [CrossRef]
  2. K. Artmann, “Berechnung der Seitenversetzung des totalreflektierten Strahles,” Ann. Phys. (Leipzig) 437, 87–102 (1948).
    [CrossRef]
  3. R. H. Renard, “Total reflection: A new evaluation of the Goos–Hänchen shift,” J. Opt. Soc. Am. 54, 1190–1197 (1964).
    [CrossRef]
  4. A. M. Steinberg and R. Y. Chiao, “Tunneling delay times in one and two dimensions,” Phys. Rev. A 49, 3283–3295 (1994).
    [CrossRef] [PubMed]
  5. H. M. Lai, C. W. Kwok, Y. W. Loo, and B. Y. Xu, “Energy-flux pattern in the Goos–Hänchen effect,” Phys. Rev. E 62, 7330–7339 (2000).
    [CrossRef]
  6. C.-F. Li, “Negative lateral shift of a light beam transmitted through a dielectric slab and interaction of boundary effects,” Phys. Rev. Lett. 91, 133903 (2003).
    [CrossRef] [PubMed]
  7. L.-Q. Wang, L.-G. Wang, S.-Y. Zhu, and M. S. Zubairy, “The influence of spatial coherence on the Goos–Hänchen shift at total internal reflection,” J. Phys. B 41, 055401 (2008).
    [CrossRef]
  8. M. Merano, A. Aiello, G. W. Hooft, M. P. Exter, E. R. Eliel, and J. P. Woerdman, “Observation of Goos–Hänchen shifts in metallic reflection,” Opt. Express 15, 15928–15943 (2007).
    [CrossRef] [PubMed]
  9. H. G. L. Schwefel, W. Köhler, Z. H. Lu, J. Fan, and L. J. Wang, “Direct experimental observation of the single reflection optical Goos–Hänchen shift,” Opt. Lett. 33, 794–796 (2008).
    [CrossRef] [PubMed]
  10. D. Chauvat, O. Emile, F. Bretenaker, and A. Le Floch, “Direct measurement of the Wigner delay associated with the Goos–Hänchen effect,” Phys. Rev. Lett. 84, 71–74 (2000).
    [CrossRef] [PubMed]
  11. 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]
  12. L.-G. Wang, H. Chen, N.-H. Liu, and S.-Y. Zhu, “Negative and positive lateral shift of a light beam reflected from a grounded slab,” Opt. Lett. 31, 1124–1126 (2006).
    [CrossRef] [PubMed]
  13. Y. Yan, X. Chen, and C.-F. Li, “Large and negative lateral displacement in an active dielectric slab configuration,” Phys. Lett. A 361, 178–181 (2007).
    [CrossRef]
  14. P. T. Leung, C. W. Chen, and H.-P. Chiang, “Large negative Goos–Hänchen shift at metal surfaces,” Opt. Commun. 276, 206–208 (2007).
    [CrossRef]
  15. T. Sakata, H. Togo, and F. Shimokawa, “Reflection-type 2×2 optical waveguide switch using the Goos–Hänchen shift effect,” Appl. Phys. Lett. 76, 2841–2844 (2000).
    [CrossRef]
  16. T. Yu, H. Li, Z. Cao, Y. Wang, Q. Shen, and Y. He, “Oscillating wave displacement sensor using the enhanced Goos–Hänchen effect in a symmetrical metal-cladding optical waveguide,” Opt. Lett. 33, 1001–1003 (2008).
    [CrossRef] [PubMed]
  17. X. Liu, Q. Yang, P. Zhu, Z. Qiao, and T. Li, “The influence of Goos–Hänchen shift on total reflection of ultrashort light pulses,” J. Opt. 12, 035214 (2010).
    [CrossRef]
  18. B. R. Horowitz and T. Tamir, “Lateral displacement of a light beam at a dielectric interface,” J. Opt. Soc. Am. 61, 586–594 (1971).
    [CrossRef]
  19. K. J. Resch, J. S. Lundeen, and A. M. Steinberg, “Total reflection cannot occur with a negative delay time,” IEEE J. Quantum Electron. 37, 794–799 (2001).
    [CrossRef]
  20. X. Liu, Z. Cao, P. Zhu, and Q. Shen, “Solution to causality paradox upon total reflection in optical planar waveguide,” Phys. Rev. E 73, 016615 (2006).
    [CrossRef]
  21. X. Liu, Z. Cao, P. Zhu, and Q. Shen, “Time delay associated with total reflection of a plane wave upon plasma mirror,” Opt. Express 14, 3588–3593 (2006).
    [CrossRef] [PubMed]
  22. C.-F. Li, “Comment on “Photonic tunneling time in frustrated total internal reflection”,” Phys. Rev. A 65, 066101 (2002).
    [CrossRef]
  23. J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena (Academic, 1996), Chap. 1.
  24. M. Bass, Handbook of Optics Volume II: Devices, Measurements, and Properties (McGraw-Hill, 1995), Chap. 33, p. 67.

2010 (1)

X. Liu, Q. Yang, P. Zhu, Z. Qiao, and T. Li, “The influence of Goos–Hänchen shift on total reflection of ultrashort light pulses,” J. Opt. 12, 035214 (2010).
[CrossRef]

2008 (3)

2007 (3)

M. Merano, A. Aiello, G. W. Hooft, M. P. Exter, E. R. Eliel, and J. P. Woerdman, “Observation of Goos–Hänchen shifts in metallic reflection,” Opt. Express 15, 15928–15943 (2007).
[CrossRef] [PubMed]

Y. Yan, X. Chen, and C.-F. Li, “Large and negative lateral displacement in an active dielectric slab configuration,” Phys. Lett. A 361, 178–181 (2007).
[CrossRef]

P. T. Leung, C. W. Chen, and H.-P. Chiang, “Large negative Goos–Hänchen shift at metal surfaces,” Opt. Commun. 276, 206–208 (2007).
[CrossRef]

2006 (4)

X. Liu, Z. Cao, P. Zhu, and Q. Shen, “Solution to causality paradox upon total reflection in optical planar waveguide,” Phys. Rev. E 73, 016615 (2006).
[CrossRef]

L.-G. Wang, H. Chen, N.-H. Liu, and S.-Y. Zhu, “Negative and positive lateral shift of a light beam reflected from a grounded slab,” Opt. Lett. 31, 1124–1126 (2006).
[CrossRef] [PubMed]

X. Liu, Z. Cao, P. Zhu, and Q. Shen, “Time delay associated with total reflection of a plane wave upon plasma mirror,” Opt. Express 14, 3588–3593 (2006).
[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]

2003 (1)

C.-F. Li, “Negative lateral shift of a light beam transmitted through a dielectric slab and interaction of boundary effects,” Phys. Rev. Lett. 91, 133903 (2003).
[CrossRef] [PubMed]

2002 (1)

C.-F. Li, “Comment on “Photonic tunneling time in frustrated total internal reflection”,” Phys. Rev. A 65, 066101 (2002).
[CrossRef]

2001 (1)

K. J. Resch, J. S. Lundeen, and A. M. Steinberg, “Total reflection cannot occur with a negative delay time,” IEEE J. Quantum Electron. 37, 794–799 (2001).
[CrossRef]

2000 (3)

T. Sakata, H. Togo, and F. Shimokawa, “Reflection-type 2×2 optical waveguide switch using the Goos–Hänchen shift effect,” Appl. Phys. Lett. 76, 2841–2844 (2000).
[CrossRef]

D. Chauvat, O. Emile, F. Bretenaker, and A. Le Floch, “Direct measurement of the Wigner delay associated with the Goos–Hänchen effect,” Phys. Rev. Lett. 84, 71–74 (2000).
[CrossRef] [PubMed]

H. M. Lai, C. W. Kwok, Y. W. Loo, and B. Y. Xu, “Energy-flux pattern in the Goos–Hänchen effect,” Phys. Rev. E 62, 7330–7339 (2000).
[CrossRef]

1994 (1)

A. M. Steinberg and R. Y. Chiao, “Tunneling delay times in one and two dimensions,” Phys. Rev. A 49, 3283–3295 (1994).
[CrossRef] [PubMed]

1971 (1)

1964 (1)

1948 (1)

K. Artmann, “Berechnung der Seitenversetzung des totalreflektierten Strahles,” Ann. Phys. (Leipzig) 437, 87–102 (1948).
[CrossRef]

1947 (1)

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

Aiello, A.

Artmann, K.

K. Artmann, “Berechnung der Seitenversetzung des totalreflektierten Strahles,” Ann. Phys. (Leipzig) 437, 87–102 (1948).
[CrossRef]

Bass, M.

M. Bass, Handbook of Optics Volume II: Devices, Measurements, and Properties (McGraw-Hill, 1995), Chap. 33, p. 67.

Bretenaker, F.

D. Chauvat, O. Emile, F. Bretenaker, and A. Le Floch, “Direct measurement of the Wigner delay associated with the Goos–Hänchen effect,” Phys. Rev. Lett. 84, 71–74 (2000).
[CrossRef] [PubMed]

Cao, Z.

T. Yu, H. Li, Z. Cao, Y. Wang, Q. Shen, and Y. He, “Oscillating wave displacement sensor using the enhanced Goos–Hänchen effect in a symmetrical metal-cladding optical waveguide,” Opt. Lett. 33, 1001–1003 (2008).
[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]

X. Liu, Z. Cao, P. Zhu, and Q. Shen, “Solution to causality paradox upon total reflection in optical planar waveguide,” Phys. Rev. E 73, 016615 (2006).
[CrossRef]

X. Liu, Z. Cao, P. Zhu, and Q. Shen, “Time delay associated with total reflection of a plane wave upon plasma mirror,” Opt. Express 14, 3588–3593 (2006).
[CrossRef] [PubMed]

Chauvat, D.

D. Chauvat, O. Emile, F. Bretenaker, and A. Le Floch, “Direct measurement of the Wigner delay associated with the Goos–Hänchen effect,” Phys. Rev. Lett. 84, 71–74 (2000).
[CrossRef] [PubMed]

Chen, C. W.

P. T. Leung, C. W. Chen, and H.-P. Chiang, “Large negative Goos–Hänchen shift at metal surfaces,” Opt. Commun. 276, 206–208 (2007).
[CrossRef]

Chen, H.

Chen, X.

Y. Yan, X. Chen, and C.-F. Li, “Large and negative lateral displacement in an active dielectric slab configuration,” Phys. Lett. A 361, 178–181 (2007).
[CrossRef]

Chiang, H. -P.

P. T. Leung, C. W. Chen, and H.-P. Chiang, “Large negative Goos–Hänchen shift at metal surfaces,” Opt. Commun. 276, 206–208 (2007).
[CrossRef]

Chiao, R. Y.

A. M. Steinberg and R. Y. Chiao, “Tunneling delay times in one and two dimensions,” Phys. Rev. A 49, 3283–3295 (1994).
[CrossRef] [PubMed]

Diels, J. -C.

J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena (Academic, 1996), Chap. 1.

Eliel, E. R.

Emile, O.

D. Chauvat, O. Emile, F. Bretenaker, and A. Le Floch, “Direct measurement of the Wigner delay associated with the Goos–Hänchen effect,” Phys. Rev. Lett. 84, 71–74 (2000).
[CrossRef] [PubMed]

Exter, M. P.

Fan, J.

Goos, F.

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

Hänchen, H.

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

He, Y.

Hooft, G. W.

Horowitz, B. R.

Köhler, W.

Kwok, C. W.

H. M. Lai, C. W. Kwok, Y. W. Loo, and B. Y. Xu, “Energy-flux pattern in the Goos–Hänchen effect,” Phys. Rev. E 62, 7330–7339 (2000).
[CrossRef]

Lai, H. M.

H. M. Lai, C. W. Kwok, Y. W. Loo, and B. Y. Xu, “Energy-flux pattern in the Goos–Hänchen effect,” Phys. Rev. E 62, 7330–7339 (2000).
[CrossRef]

Le Floch, A.

D. Chauvat, O. Emile, F. Bretenaker, and A. Le Floch, “Direct measurement of the Wigner delay associated with the Goos–Hänchen effect,” Phys. Rev. Lett. 84, 71–74 (2000).
[CrossRef] [PubMed]

Leung, P. T.

P. T. Leung, C. W. Chen, and H.-P. Chiang, “Large negative Goos–Hänchen shift at metal surfaces,” Opt. Commun. 276, 206–208 (2007).
[CrossRef]

Li, C. -F.

Y. Yan, X. Chen, and C.-F. Li, “Large and negative lateral displacement in an active dielectric slab configuration,” Phys. Lett. A 361, 178–181 (2007).
[CrossRef]

C.-F. Li, “Negative lateral shift of a light beam transmitted through a dielectric slab and interaction of boundary effects,” Phys. Rev. Lett. 91, 133903 (2003).
[CrossRef] [PubMed]

C.-F. Li, “Comment on “Photonic tunneling time in frustrated total internal reflection”,” Phys. Rev. A 65, 066101 (2002).
[CrossRef]

Li, H.

Li, T.

X. Liu, Q. Yang, P. Zhu, Z. Qiao, and T. Li, “The influence of Goos–Hänchen shift on total reflection of ultrashort light pulses,” J. Opt. 12, 035214 (2010).
[CrossRef]

Liu, N. -H.

Liu, X.

X. Liu, Q. Yang, P. Zhu, Z. Qiao, and T. Li, “The influence of Goos–Hänchen shift on total reflection of ultrashort light pulses,” J. Opt. 12, 035214 (2010).
[CrossRef]

X. Liu, Z. Cao, P. Zhu, and Q. Shen, “Time delay associated with total reflection of a plane wave upon plasma mirror,” Opt. Express 14, 3588–3593 (2006).
[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]

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, and Q. Shen, “Solution to causality paradox upon total reflection in optical planar waveguide,” Phys. Rev. E 73, 016615 (2006).
[CrossRef]

Loo, Y. W.

H. M. Lai, C. W. Kwok, Y. W. Loo, and B. Y. Xu, “Energy-flux pattern in the Goos–Hänchen effect,” Phys. Rev. E 62, 7330–7339 (2000).
[CrossRef]

Lu, Z. H.

Lundeen, J. S.

K. J. Resch, J. S. Lundeen, and A. M. Steinberg, “Total reflection cannot occur with a negative delay time,” IEEE J. Quantum Electron. 37, 794–799 (2001).
[CrossRef]

Merano, M.

Qiao, Z.

X. Liu, Q. Yang, P. Zhu, Z. Qiao, and T. Li, “The influence of Goos–Hänchen shift on total reflection of ultrashort light pulses,” J. Opt. 12, 035214 (2010).
[CrossRef]

Renard, R. H.

Resch, K. J.

K. J. Resch, J. S. Lundeen, and A. M. Steinberg, “Total reflection cannot occur with a negative delay time,” IEEE J. Quantum Electron. 37, 794–799 (2001).
[CrossRef]

Rudolph, W.

J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena (Academic, 1996), Chap. 1.

Sakata, T.

T. Sakata, H. Togo, and F. Shimokawa, “Reflection-type 2×2 optical waveguide switch using the Goos–Hänchen shift effect,” Appl. Phys. Lett. 76, 2841–2844 (2000).
[CrossRef]

Schwefel, H. G. L.

Shen, Q.

T. Yu, H. Li, Z. Cao, Y. Wang, Q. Shen, and Y. He, “Oscillating wave displacement sensor using the enhanced Goos–Hänchen effect in a symmetrical metal-cladding optical waveguide,” Opt. Lett. 33, 1001–1003 (2008).
[CrossRef] [PubMed]

X. Liu, Z. Cao, P. Zhu, and Q. Shen, “Solution to causality paradox upon total reflection in optical planar waveguide,” Phys. Rev. E 73, 016615 (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]

X. Liu, Z. Cao, P. Zhu, and Q. Shen, “Time delay associated with total reflection of a plane wave upon plasma mirror,” Opt. Express 14, 3588–3593 (2006).
[CrossRef] [PubMed]

Shimokawa, F.

T. Sakata, H. Togo, and F. Shimokawa, “Reflection-type 2×2 optical waveguide switch using the Goos–Hänchen shift effect,” Appl. Phys. Lett. 76, 2841–2844 (2000).
[CrossRef]

Steinberg, A. M.

K. J. Resch, J. S. Lundeen, and A. M. Steinberg, “Total reflection cannot occur with a negative delay time,” IEEE J. Quantum Electron. 37, 794–799 (2001).
[CrossRef]

A. M. Steinberg and R. Y. Chiao, “Tunneling delay times in one and two dimensions,” Phys. Rev. A 49, 3283–3295 (1994).
[CrossRef] [PubMed]

Tamir, T.

Togo, H.

T. Sakata, H. Togo, and F. Shimokawa, “Reflection-type 2×2 optical waveguide switch using the Goos–Hänchen shift effect,” Appl. Phys. Lett. 76, 2841–2844 (2000).
[CrossRef]

Wang, L. -G.

L.-Q. Wang, L.-G. Wang, S.-Y. Zhu, and M. S. Zubairy, “The influence of spatial coherence on the Goos–Hänchen shift at total internal reflection,” J. Phys. B 41, 055401 (2008).
[CrossRef]

L.-G. Wang, H. Chen, N.-H. Liu, and S.-Y. Zhu, “Negative and positive lateral shift of a light beam reflected from a grounded slab,” Opt. Lett. 31, 1124–1126 (2006).
[CrossRef] [PubMed]

Wang, L. J.

Wang, L. -Q.

L.-Q. Wang, L.-G. Wang, S.-Y. Zhu, and M. S. Zubairy, “The influence of spatial coherence on the Goos–Hänchen shift at total internal reflection,” J. Phys. B 41, 055401 (2008).
[CrossRef]

Wang, Y.

Woerdman, J. P.

Xu, B. Y.

H. M. Lai, C. W. Kwok, Y. W. Loo, and B. Y. Xu, “Energy-flux pattern in the Goos–Hänchen effect,” Phys. Rev. E 62, 7330–7339 (2000).
[CrossRef]

Yan, Y.

Y. Yan, X. Chen, and C.-F. Li, “Large and negative lateral displacement in an active dielectric slab configuration,” Phys. Lett. A 361, 178–181 (2007).
[CrossRef]

Yang, Q.

X. Liu, Q. Yang, P. Zhu, Z. Qiao, and T. Li, “The influence of Goos–Hänchen shift on total reflection of ultrashort light pulses,” J. Opt. 12, 035214 (2010).
[CrossRef]

Yu, T.

Zhu, P.

X. Liu, Q. Yang, P. Zhu, Z. Qiao, and T. Li, “The influence of Goos–Hänchen shift on total reflection of ultrashort light pulses,” J. Opt. 12, 035214 (2010).
[CrossRef]

X. Liu, Z. Cao, P. Zhu, and Q. Shen, “Time delay associated with total reflection of a plane wave upon plasma mirror,” Opt. Express 14, 3588–3593 (2006).
[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]

X. Liu, Z. Cao, P. Zhu, and Q. Shen, “Solution to causality paradox upon total reflection in optical planar waveguide,” Phys. Rev. E 73, 016615 (2006).
[CrossRef]

Zhu, S. -Y.

L.-Q. Wang, L.-G. Wang, S.-Y. Zhu, and M. S. Zubairy, “The influence of spatial coherence on the Goos–Hänchen shift at total internal reflection,” J. Phys. B 41, 055401 (2008).
[CrossRef]

L.-G. Wang, H. Chen, N.-H. Liu, and S.-Y. Zhu, “Negative and positive lateral shift of a light beam reflected from a grounded slab,” Opt. Lett. 31, 1124–1126 (2006).
[CrossRef] [PubMed]

Zubairy, M. S.

L.-Q. Wang, L.-G. Wang, S.-Y. Zhu, and M. S. Zubairy, “The influence of spatial coherence on the Goos–Hänchen shift at total internal reflection,” J. Phys. B 41, 055401 (2008).
[CrossRef]

Ann. Phys. (Leipzig) (2)

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

K. Artmann, “Berechnung der Seitenversetzung des totalreflektierten Strahles,” Ann. Phys. (Leipzig) 437, 87–102 (1948).
[CrossRef]

Appl. Phys. Lett. (1)

T. Sakata, H. Togo, and F. Shimokawa, “Reflection-type 2×2 optical waveguide switch using the Goos–Hänchen shift effect,” Appl. Phys. Lett. 76, 2841–2844 (2000).
[CrossRef]

IEEE J. Quantum Electron. (1)

K. J. Resch, J. S. Lundeen, and A. M. Steinberg, “Total reflection cannot occur with a negative delay time,” IEEE J. Quantum Electron. 37, 794–799 (2001).
[CrossRef]

J. Opt. (1)

X. Liu, Q. Yang, P. Zhu, Z. Qiao, and T. Li, “The influence of Goos–Hänchen shift on total reflection of ultrashort light pulses,” J. Opt. 12, 035214 (2010).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Phys. B (1)

L.-Q. Wang, L.-G. Wang, S.-Y. Zhu, and M. S. Zubairy, “The influence of spatial coherence on the Goos–Hänchen shift at total internal reflection,” J. Phys. B 41, 055401 (2008).
[CrossRef]

Opt. Commun. (1)

P. T. Leung, C. W. Chen, and H.-P. Chiang, “Large negative Goos–Hänchen shift at metal surfaces,” Opt. Commun. 276, 206–208 (2007).
[CrossRef]

Opt. Express (2)

Opt. Lett. (3)

Phys. Lett. A (1)

Y. Yan, X. Chen, and C.-F. Li, “Large and negative lateral displacement in an active dielectric slab configuration,” Phys. Lett. A 361, 178–181 (2007).
[CrossRef]

Phys. Rev. A (2)

A. M. Steinberg and R. Y. Chiao, “Tunneling delay times in one and two dimensions,” Phys. Rev. A 49, 3283–3295 (1994).
[CrossRef] [PubMed]

C.-F. Li, “Comment on “Photonic tunneling time in frustrated total internal reflection”,” Phys. Rev. A 65, 066101 (2002).
[CrossRef]

Phys. Rev. E (3)

X. Liu, Z. Cao, P. Zhu, and Q. Shen, “Solution to causality paradox upon total reflection in optical planar waveguide,” Phys. Rev. E 73, 016615 (2006).
[CrossRef]

H. M. Lai, C. W. Kwok, Y. W. Loo, and B. Y. Xu, “Energy-flux pattern in the Goos–Hänchen effect,” Phys. Rev. E 62, 7330–7339 (2000).
[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]

Phys. Rev. Lett. (2)

C.-F. Li, “Negative lateral shift of a light beam transmitted through a dielectric slab and interaction of boundary effects,” Phys. Rev. Lett. 91, 133903 (2003).
[CrossRef] [PubMed]

D. Chauvat, O. Emile, F. Bretenaker, and A. Le Floch, “Direct measurement of the Wigner delay associated with the Goos–Hänchen effect,” Phys. Rev. Lett. 84, 71–74 (2000).
[CrossRef] [PubMed]

Other (2)

J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena (Academic, 1996), Chap. 1.

M. Bass, Handbook of Optics Volume II: Devices, Measurements, and Properties (McGraw-Hill, 1995), Chap. 33, p. 67.

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Figures (1)

Fig. 1
Fig. 1

Geometry of a pulsed beam incident on the interface separating two half-spaces dielectric media.

Equations (19)

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

E B i ( x i , 0 , t ) = exp ( x i 2 W 2 ) exp ( t 2 τ G 2 ) exp ( i ω 0 t ) ,
U B i ( x i , 0 , ω ) = π τ G   exp ( x i 2 W 2 ) exp [ τ G 2 4 ( ω ω 0 ) 2 ]
U in ( x , 0 , ω ) = π τ G   exp ( x 2 d 2 ) exp [ τ G 2 4 ( ω ω 0 ) 2 ] exp ( i k x 0 x ) ,
A in ( k x , ω ) = π d τ G   exp [ d 2 4 ( k x k x 0 ) 2 ] exp [ τ G 2 4 ( ω ω 0 ) 2 ] ,
U out ( x , 0 , ω ) = ( 1 / 2 π ) r ( k x , ω ) A in ( k x , ω ) exp ( i k x x ) d k x ,
φ ( k x , ω ) φ ( k x 0 , ω ) s ( ω ) ( k x k x 0 ) .
U out ( x , 0 , ω ) = π τ G   exp [ ( x s ( ω ) ) 2 d 2 ] exp [ τ G 2 4 ( ω ω 0 ) 2 ] e i φ ( k x 0 , ω ) e i k x 0 x ,
U B r ( x r , 0 , ω ) = π τ G   exp [ ( x r + D 0 D ) 2 W 2 ] exp [ τ G 2 4 ( ω ω 0 ) 2 ] exp [ i φ ( k x 0 , ω ) ] exp ( i k x 0 s 0 ) ,
E B r ( x r , 0 , t ) = ( 1 / 2 π ) U B r ( x r , 0 , ω ) exp ( i ω t ) d ω ,
( x r + D 0 D ) 2 x r 2 + 2 x r D 0 Ω ω 0 + D 0 ( D 0 2 x r ) Ω 2 ω 0 2 ,
φ ( k x 0 , ω ) φ 0 ( k x 0 , ω 0 ) + τ d Ω + α d Ω 2 ,
E B r ( x r , 0 , ω ) = π τ G   exp ( x r 2 W 2 ) exp ( τ G 2 4 Ω 2 2 x r D 0 W 2 ω 0 2 Ω ) exp [ i ( φ 0 + τ d Ω + ω τ 0 ) ] ,
τ G 2 = τ G 2 + 4 D 0 ( D 0 2 x r ) W 2 ω 0 2 i 4 α d .
E B r ( x r , 0 , ω ) = π τ G   exp ( x r 2 W 2 ) exp [ τ G 2 4 ( Ω + β ( x r ) ) 2 ] exp [ i ( φ 0 + τ d Ω + ω τ 0 ) ] ,
β ( x r ) = 4 D 0 x r W 2 ω 0 τ G 2 ,
W = W ( 1 4 D 0 2 W 2 ω 0 2 τ G 2 ) 1 / 2 .
exp [ i ( φ 0 + τ d Ω + ω τ 0 ) ] exp ( i ω t ) = exp [ i ( φ 0 β τ d ) ] exp [ i ( ω 0 β ) ( t τ 0 ) ] exp [ i ( Ω + β ) ( t τ 0 τ d ) ] ,
E B r ( x r , 0 , t ) = τ G τ G exp ( x r 2 W 2 ) exp [ ( t τ 0 τ d ) 2 τ G 2 ] exp [ i ( φ 0 β τ d ) ] exp [ i ( ω 0 β ) ( t τ 0 ) ] .
E B r ( x r , 0 , t ) = τ G τ G exp ( x r 2 W 2 ) exp [ ( t τ 0 ) 2 τ G 2 ] exp [ i φ 0 i ( ω 0 β ) ( t τ 0 ) ] ,

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