Abstract

We present a solution to the problem of reflection and refraction of a polarized Gaussian beam at the interface between the transparent medium and the moving object based on Minkowski’s constitutive relations. The Goos–Hänchen (GH) and Imbert–Fedorov (IF) effects are discussed in detail when the object moves parallel to the interface. It is shown that the IF shifts of reflection and transmission beams can reach several wavelengths of the incident beam at some certain incident angles and moving velocities of the object. The transitions from the positive IF shift to the negative IF shift have been observed with the increase of the velocity of the moving object. Furthermore, our calculations show that some unusual GH effects can also be caused by the movement of the medium. The physical origins for these phenomena have been analyzed. It is well known that the IF shift is directly related to the spin-Hall effects of light. Thus, these findings can also provide an alternative pathway for controlling the spin-Hall effects of light.

© 2012 Optical Society of America

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  1. F. Goos and H. Hanchen, “Ein neuer und fundamentaler Versuch zur Totalreflexion,” Ann. Phys. 436, 333–346 (1947).
    [CrossRef]
  2. R. Briers, O. Leroy, and G. Shkerdin, “Bounded beam interaction with thin inclusions. Characterization by phase differences at Rayleigh angle incidence,” J. Acoust. Soc. Am. 108, 1622–1630(2000).
    [CrossRef]
  3. R. H. Renard, “Total reflection: A new evaluation of the Goos-H¨anchen shift,” J. Opt. Soc. Am. 54, 1190–1197 (1964).
    [CrossRef]
  4. V. K. Ignatovich, “Neutron reflection from condensed matter, the Goos-Hanchen effect and coherence,” Phys. Lett. A 322, 36–46 (2004).
    [CrossRef]
  5. O. Emile, T. Galstyan, A. Le Floch, and F. Bretenaker, “Measurement of the nonlinear Goos–Hanchen effect for Gaussian optical beams,” Phys. Rev. Lett. 75, 1511–1513 (1995).
    [CrossRef]
  6. B. M. Jost, A.-A. R. Al-Rashed, and B. E. A. Saleh, “Observation of the Goos–Hänchen effect in a phase-conjugate mirror,” Phys. Rev. Lett. 81, 2233–2235 (1998).
    [CrossRef]
  7. 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]
  8. P. R. Berman, “Goos–Hanchen shift in negatively refractive media,” Phys. Rev. E 66, 067603 (2002).
    [CrossRef]
  9. I. V. Shadrivov, A. A. Zharov, and Y. S. Kivshar, “Giant Goos–Hänchen effect at the reflection from left-handed metamaterials,” Appl. Phys. Lett. 83, 2713 (2003).
    [CrossRef]
  10. A. Lakhtakia, “On planewave remittances and Goos–Hänchen shifts of planar slabs with negative real permittivity and permeability,” Electromagnetics 23, 71–75 (2003).
    [CrossRef]
  11. C. W. J. Beenakker, R. A. Sepkhanov, A. R. Akhmerov, and J. Tworzydło, “Quantum Goos–Hanchen effect in graphene,” Phys. Rev. Lett. 102, 146804 (2009).
    [CrossRef]
  12. H. M. Lai and S. W. Chan, “Large and negative Goos–Hänchen shift near the Brewster dip on reflection from weakly absorbing media,” Opt. Lett. 27, 680–682 (2002).
    [CrossRef]
  13. 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]
  14. 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]
  15. F. I. Fedorov, “K teorii polnovo otrazenija,” Dokl. Akad. Nauk SSSR 105, 465–467 (1955).
  16. C. Imbert, “Calculation and experimental proof of transverse shift induced by total internal reflection of a circularly polarized-light beam,” Phys. Rev. D 5, 787–796 (1972).
    [CrossRef]
  17. K. Y. Bliokh and Y. P. Bliokh, “Conservation of angular momentum, transverse shift, and spin hall effect in reflection and refraction of an electromagnetic wave packet,” Phys. Rev. Lett. 96, 073903 (2006).
    [CrossRef]
  18. M. Onoda, S. Murakami, and N. Nagaosa, “Hall effect of light,” Phys. Rev. Lett. 93, 083901 (2004).
    [CrossRef]
  19. H. Luo, S. Wen, W. Shu, Z. Tang, Y. Zou, and D. Fan, “Spin Hall effect of a light beam in left-handed materials,” Phys. Rev. A 80, 043810 (2009).
    [CrossRef]
  20. H. Wang and X. D. Zhang, “Unusual spin Hall effect of a light beam in chiral metamaterials,” Phys. Rev. A 83, 053820(2011).
    [CrossRef]
  21. O. Hosten and P. Kwiat, “Observation of the spin Hall effect of light via weak measurements,” Science 319, 787–790 (2008).
    [CrossRef]
  22. M. Merano, A. Aiello, M. P. van Exter, and J. P. Woerdman, “Observing angular deviations in the specular reflection of a light beam,” Nat. Photon. 3, 337–340 (2009).
    [CrossRef]
  23. Y. Qin, Y. Li, H. Y. He, and Q. H. Gong, “Measurement of spin Hall effect of reflected light,” Opt. Lett. 34, 2551–2553 (2009).
    [CrossRef]
  24. W. Pauli, Theory of Relativity (Pergamon, 1958).
  25. J. A. Kong, Theory of Electromagnetic Waves (Wiley, 1975).
  26. T. M. Grzegorczyk and J. A. Kong, “Electrodynamics of moving media inducing positive and negative refraction,” Phys. Rev. B 74, 033102 (2006).
    [CrossRef]
  27. H. Wang and X. D. Zhang, “Magnetic response induced by a moving dielectric slab,” J. Appl. Phys. 107, 104108(2010).
    [CrossRef]
  28. T. G. Mackay and A. Lakhtakia, “Concealment by uniform motion,” J. Eur. Opt. Soc. Rapid Pub. 2, 07003 (2007).
    [CrossRef]

2011

H. Wang and X. D. Zhang, “Unusual spin Hall effect of a light beam in chiral metamaterials,” Phys. Rev. A 83, 053820(2011).
[CrossRef]

2010

H. Wang and X. D. Zhang, “Magnetic response induced by a moving dielectric slab,” J. Appl. Phys. 107, 104108(2010).
[CrossRef]

2009

H. Luo, S. Wen, W. Shu, Z. Tang, Y. Zou, and D. Fan, “Spin Hall effect of a light beam in left-handed materials,” Phys. Rev. A 80, 043810 (2009).
[CrossRef]

Y. Qin, Y. Li, H. Y. He, and Q. H. Gong, “Measurement of spin Hall effect of reflected light,” Opt. Lett. 34, 2551–2553 (2009).
[CrossRef]

M. Merano, A. Aiello, M. P. van Exter, and J. P. Woerdman, “Observing angular deviations in the specular reflection of a light beam,” Nat. Photon. 3, 337–340 (2009).
[CrossRef]

C. W. J. Beenakker, R. A. Sepkhanov, A. R. Akhmerov, and J. Tworzydło, “Quantum Goos–Hanchen effect in graphene,” Phys. Rev. Lett. 102, 146804 (2009).
[CrossRef]

2008

O. Hosten and P. Kwiat, “Observation of the spin Hall effect of light via weak measurements,” Science 319, 787–790 (2008).
[CrossRef]

2007

T. G. Mackay and A. Lakhtakia, “Concealment by uniform motion,” J. Eur. Opt. Soc. Rapid Pub. 2, 07003 (2007).
[CrossRef]

2006

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]

T. M. Grzegorczyk and J. A. Kong, “Electrodynamics of moving media inducing positive and negative refraction,” Phys. Rev. B 74, 033102 (2006).
[CrossRef]

K. Y. Bliokh and Y. P. Bliokh, “Conservation of angular momentum, transverse shift, and spin hall effect in reflection and refraction of an electromagnetic wave packet,” Phys. Rev. Lett. 96, 073903 (2006).
[CrossRef]

2004

M. Onoda, S. Murakami, and N. Nagaosa, “Hall effect of light,” Phys. Rev. Lett. 93, 083901 (2004).
[CrossRef]

V. K. Ignatovich, “Neutron reflection from condensed matter, the Goos-Hanchen effect and coherence,” Phys. Lett. A 322, 36–46 (2004).
[CrossRef]

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]

2003

I. V. Shadrivov, A. A. Zharov, and Y. S. Kivshar, “Giant Goos–Hänchen effect at the reflection from left-handed metamaterials,” Appl. Phys. Lett. 83, 2713 (2003).
[CrossRef]

A. Lakhtakia, “On planewave remittances and Goos–Hänchen shifts of planar slabs with negative real permittivity and permeability,” Electromagnetics 23, 71–75 (2003).
[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]

2002

2000

R. Briers, O. Leroy, and G. Shkerdin, “Bounded beam interaction with thin inclusions. Characterization by phase differences at Rayleigh angle incidence,” J. Acoust. Soc. Am. 108, 1622–1630(2000).
[CrossRef]

1998

B. M. Jost, A.-A. R. Al-Rashed, and B. E. A. Saleh, “Observation of the Goos–Hänchen effect in a phase-conjugate mirror,” Phys. Rev. Lett. 81, 2233–2235 (1998).
[CrossRef]

1995

O. Emile, T. Galstyan, A. Le Floch, and F. Bretenaker, “Measurement of the nonlinear Goos–Hanchen effect for Gaussian optical beams,” Phys. Rev. Lett. 75, 1511–1513 (1995).
[CrossRef]

1972

C. Imbert, “Calculation and experimental proof of transverse shift induced by total internal reflection of a circularly polarized-light beam,” Phys. Rev. D 5, 787–796 (1972).
[CrossRef]

1964

1955

F. I. Fedorov, “K teorii polnovo otrazenija,” Dokl. Akad. Nauk SSSR 105, 465–467 (1955).

1947

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

Aiello, A.

M. Merano, A. Aiello, M. P. van Exter, and J. P. Woerdman, “Observing angular deviations in the specular reflection of a light beam,” Nat. Photon. 3, 337–340 (2009).
[CrossRef]

Akhmerov, A. R.

C. W. J. Beenakker, R. A. Sepkhanov, A. R. Akhmerov, and J. Tworzydło, “Quantum Goos–Hanchen effect in graphene,” Phys. Rev. Lett. 102, 146804 (2009).
[CrossRef]

Al-Rashed, A.-A. R.

B. M. Jost, A.-A. R. Al-Rashed, and B. E. A. Saleh, “Observation of the Goos–Hänchen effect in a phase-conjugate mirror,” Phys. Rev. Lett. 81, 2233–2235 (1998).
[CrossRef]

Beenakker, C. W. J.

C. W. J. Beenakker, R. A. Sepkhanov, A. R. Akhmerov, and J. Tworzydło, “Quantum Goos–Hanchen effect in graphene,” Phys. Rev. Lett. 102, 146804 (2009).
[CrossRef]

Berman, P. R.

P. R. Berman, “Goos–Hanchen shift in negatively refractive media,” Phys. Rev. E 66, 067603 (2002).
[CrossRef]

Bliokh, K. Y.

K. Y. Bliokh and Y. P. Bliokh, “Conservation of angular momentum, transverse shift, and spin hall effect in reflection and refraction of an electromagnetic wave packet,” Phys. Rev. Lett. 96, 073903 (2006).
[CrossRef]

Bliokh, Y. P.

K. Y. Bliokh and Y. P. Bliokh, “Conservation of angular momentum, transverse shift, and spin hall effect in reflection and refraction of an electromagnetic wave packet,” Phys. Rev. Lett. 96, 073903 (2006).
[CrossRef]

Bretenaker, F.

O. Emile, T. Galstyan, A. Le Floch, and F. Bretenaker, “Measurement of the nonlinear Goos–Hanchen effect for Gaussian optical beams,” Phys. Rev. Lett. 75, 1511–1513 (1995).
[CrossRef]

Briers, R.

R. Briers, O. Leroy, and G. Shkerdin, “Bounded beam interaction with thin inclusions. Characterization by phase differences at Rayleigh angle incidence,” J. Acoust. Soc. Am. 108, 1622–1630(2000).
[CrossRef]

Chan, S. W.

Chen, H.

Emile, O.

O. Emile, T. Galstyan, A. Le Floch, and F. Bretenaker, “Measurement of the nonlinear Goos–Hanchen effect for Gaussian optical beams,” Phys. Rev. Lett. 75, 1511–1513 (1995).
[CrossRef]

Fan, D.

H. Luo, S. Wen, W. Shu, Z. Tang, Y. Zou, and D. Fan, “Spin Hall effect of a light beam in left-handed materials,” Phys. Rev. A 80, 043810 (2009).
[CrossRef]

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]

Fedorov, F. I.

F. I. Fedorov, “K teorii polnovo otrazenija,” Dokl. Akad. Nauk SSSR 105, 465–467 (1955).

Galstyan, T.

O. Emile, T. Galstyan, A. Le Floch, and F. Bretenaker, “Measurement of the nonlinear Goos–Hanchen effect for Gaussian optical beams,” Phys. Rev. Lett. 75, 1511–1513 (1995).
[CrossRef]

Gong, Q. H.

Goos, F.

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

Grzegorczyk, T. M.

T. M. Grzegorczyk and J. A. Kong, “Electrodynamics of moving media inducing positive and negative refraction,” Phys. Rev. B 74, 033102 (2006).
[CrossRef]

Hanchen, H.

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

He, H. Y.

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]

Hosten, O.

O. Hosten and P. Kwiat, “Observation of the spin Hall effect of light via weak measurements,” Science 319, 787–790 (2008).
[CrossRef]

Ignatovich, V. K.

V. K. Ignatovich, “Neutron reflection from condensed matter, the Goos-Hanchen effect and coherence,” Phys. Lett. A 322, 36–46 (2004).
[CrossRef]

Imbert, C.

C. Imbert, “Calculation and experimental proof of transverse shift induced by total internal reflection of a circularly polarized-light beam,” Phys. Rev. D 5, 787–796 (1972).
[CrossRef]

Jost, B. M.

B. M. Jost, A.-A. R. Al-Rashed, and B. E. A. Saleh, “Observation of the Goos–Hänchen effect in a phase-conjugate mirror,” Phys. Rev. Lett. 81, 2233–2235 (1998).
[CrossRef]

Kivshar, Y. S.

I. V. Shadrivov, A. A. Zharov, and Y. S. Kivshar, “Giant Goos–Hänchen effect at the reflection from left-handed metamaterials,” Appl. Phys. Lett. 83, 2713 (2003).
[CrossRef]

Kong, J. A.

T. M. Grzegorczyk and J. A. Kong, “Electrodynamics of moving media inducing positive and negative refraction,” Phys. Rev. B 74, 033102 (2006).
[CrossRef]

J. A. Kong, Theory of Electromagnetic Waves (Wiley, 1975).

Kwiat, P.

O. Hosten and P. Kwiat, “Observation of the spin Hall effect of light via weak measurements,” Science 319, 787–790 (2008).
[CrossRef]

Lai, H. M.

Lakhtakia, A.

T. G. Mackay and A. Lakhtakia, “Concealment by uniform motion,” J. Eur. Opt. Soc. Rapid Pub. 2, 07003 (2007).
[CrossRef]

A. Lakhtakia, “On planewave remittances and Goos–Hänchen shifts of planar slabs with negative real permittivity and permeability,” Electromagnetics 23, 71–75 (2003).
[CrossRef]

Le Floch, A.

O. Emile, T. Galstyan, A. Le Floch, and F. Bretenaker, “Measurement of the nonlinear Goos–Hanchen effect for Gaussian optical beams,” Phys. Rev. Lett. 75, 1511–1513 (1995).
[CrossRef]

Leroy, O.

R. Briers, O. Leroy, and G. Shkerdin, “Bounded beam interaction with thin inclusions. Characterization by phase differences at Rayleigh angle incidence,” J. Acoust. Soc. Am. 108, 1622–1630(2000).
[CrossRef]

Li, C.-F.

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]

Li, Y.

Liu, N. H.

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]

Luo, H.

H. Luo, S. Wen, W. Shu, Z. Tang, Y. Zou, and D. Fan, “Spin Hall effect of a light beam in left-handed materials,” Phys. Rev. A 80, 043810 (2009).
[CrossRef]

Mackay, T. G.

T. G. Mackay and A. Lakhtakia, “Concealment by uniform motion,” J. Eur. Opt. Soc. Rapid Pub. 2, 07003 (2007).
[CrossRef]

Merano, M.

M. Merano, A. Aiello, M. P. van Exter, and J. P. Woerdman, “Observing angular deviations in the specular reflection of a light beam,” Nat. Photon. 3, 337–340 (2009).
[CrossRef]

Murakami, S.

M. Onoda, S. Murakami, and N. Nagaosa, “Hall effect of light,” Phys. Rev. Lett. 93, 083901 (2004).
[CrossRef]

Nagaosa, N.

M. Onoda, S. Murakami, and N. Nagaosa, “Hall effect of light,” Phys. Rev. Lett. 93, 083901 (2004).
[CrossRef]

Onoda, M.

M. Onoda, S. Murakami, and N. Nagaosa, “Hall effect of light,” Phys. Rev. Lett. 93, 083901 (2004).
[CrossRef]

Pauli, W.

W. Pauli, Theory of Relativity (Pergamon, 1958).

Qin, Y.

Renard, R. H.

Saleh, B. E. A.

B. M. Jost, A.-A. R. Al-Rashed, and B. E. A. Saleh, “Observation of the Goos–Hänchen effect in a phase-conjugate mirror,” Phys. Rev. Lett. 81, 2233–2235 (1998).
[CrossRef]

Sepkhanov, R. A.

C. W. J. Beenakker, R. A. Sepkhanov, A. R. Akhmerov, and J. Tworzydło, “Quantum Goos–Hanchen effect in graphene,” Phys. Rev. Lett. 102, 146804 (2009).
[CrossRef]

Shadrivov, I. V.

I. V. Shadrivov, A. A. Zharov, and Y. S. Kivshar, “Giant Goos–Hänchen effect at the reflection from left-handed metamaterials,” Appl. Phys. Lett. 83, 2713 (2003).
[CrossRef]

Shkerdin, G.

R. Briers, O. Leroy, and G. Shkerdin, “Bounded beam interaction with thin inclusions. Characterization by phase differences at Rayleigh angle incidence,” J. Acoust. Soc. Am. 108, 1622–1630(2000).
[CrossRef]

Shu, W.

H. Luo, S. Wen, W. Shu, Z. Tang, Y. Zou, and D. Fan, “Spin Hall effect of a light beam in left-handed materials,” Phys. Rev. A 80, 043810 (2009).
[CrossRef]

Tang, Z.

H. Luo, S. Wen, W. Shu, Z. Tang, Y. Zou, and D. Fan, “Spin Hall effect of a light beam in left-handed materials,” Phys. Rev. A 80, 043810 (2009).
[CrossRef]

Tworzydlo, J.

C. W. J. Beenakker, R. A. Sepkhanov, A. R. Akhmerov, and J. Tworzydło, “Quantum Goos–Hanchen effect in graphene,” Phys. Rev. Lett. 102, 146804 (2009).
[CrossRef]

van Exter, M. P.

M. Merano, A. Aiello, M. P. van Exter, and J. P. Woerdman, “Observing angular deviations in the specular reflection of a light beam,” Nat. Photon. 3, 337–340 (2009).
[CrossRef]

Wang, H.

H. Wang and X. D. Zhang, “Unusual spin Hall effect of a light beam in chiral metamaterials,” Phys. Rev. A 83, 053820(2011).
[CrossRef]

H. Wang and X. D. Zhang, “Magnetic response induced by a moving dielectric slab,” J. Appl. Phys. 107, 104108(2010).
[CrossRef]

Wang, L. G.

Wen, S.

H. Luo, S. Wen, W. Shu, Z. Tang, Y. Zou, and D. Fan, “Spin Hall effect of a light beam in left-handed materials,” Phys. Rev. A 80, 043810 (2009).
[CrossRef]

Woerdman, J. P.

M. Merano, A. Aiello, M. P. van Exter, and J. P. Woerdman, “Observing angular deviations in the specular reflection of a light beam,” Nat. Photon. 3, 337–340 (2009).
[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]

Zhang, X. D.

H. Wang and X. D. Zhang, “Unusual spin Hall effect of a light beam in chiral metamaterials,” Phys. Rev. A 83, 053820(2011).
[CrossRef]

H. Wang and X. D. Zhang, “Magnetic response induced by a moving dielectric slab,” J. Appl. Phys. 107, 104108(2010).
[CrossRef]

Zharov, A. A.

I. V. Shadrivov, A. A. Zharov, and Y. S. Kivshar, “Giant Goos–Hänchen effect at the reflection from left-handed metamaterials,” Appl. Phys. Lett. 83, 2713 (2003).
[CrossRef]

Zhu, S. Y.

Zou, Y.

H. Luo, S. Wen, W. Shu, Z. Tang, Y. Zou, and D. Fan, “Spin Hall effect of a light beam in left-handed materials,” Phys. Rev. A 80, 043810 (2009).
[CrossRef]

Ann. Phys.

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

Appl. Phys. Lett.

I. V. Shadrivov, A. A. Zharov, and Y. S. Kivshar, “Giant Goos–Hänchen effect at the reflection from left-handed metamaterials,” Appl. Phys. Lett. 83, 2713 (2003).
[CrossRef]

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]

Dokl. Akad. Nauk SSSR

F. I. Fedorov, “K teorii polnovo otrazenija,” Dokl. Akad. Nauk SSSR 105, 465–467 (1955).

Electromagnetics

A. Lakhtakia, “On planewave remittances and Goos–Hänchen shifts of planar slabs with negative real permittivity and permeability,” Electromagnetics 23, 71–75 (2003).
[CrossRef]

J. Acoust. Soc. Am.

R. Briers, O. Leroy, and G. Shkerdin, “Bounded beam interaction with thin inclusions. Characterization by phase differences at Rayleigh angle incidence,” J. Acoust. Soc. Am. 108, 1622–1630(2000).
[CrossRef]

J. Appl. Phys.

H. Wang and X. D. Zhang, “Magnetic response induced by a moving dielectric slab,” J. Appl. Phys. 107, 104108(2010).
[CrossRef]

J. Eur. Opt. Soc. Rapid Pub.

T. G. Mackay and A. Lakhtakia, “Concealment by uniform motion,” J. Eur. Opt. Soc. Rapid Pub. 2, 07003 (2007).
[CrossRef]

J. Opt. Soc. Am.

Nat. Photon.

M. Merano, A. Aiello, M. P. van Exter, and J. P. Woerdman, “Observing angular deviations in the specular reflection of a light beam,” Nat. Photon. 3, 337–340 (2009).
[CrossRef]

Opt. Lett.

Phys. Lett. A

V. K. Ignatovich, “Neutron reflection from condensed matter, the Goos-Hanchen effect and coherence,” Phys. Lett. A 322, 36–46 (2004).
[CrossRef]

Phys. Rev. A

H. Luo, S. Wen, W. Shu, Z. Tang, Y. Zou, and D. Fan, “Spin Hall effect of a light beam in left-handed materials,” Phys. Rev. A 80, 043810 (2009).
[CrossRef]

H. Wang and X. D. Zhang, “Unusual spin Hall effect of a light beam in chiral metamaterials,” Phys. Rev. A 83, 053820(2011).
[CrossRef]

Phys. Rev. B

T. M. Grzegorczyk and J. A. Kong, “Electrodynamics of moving media inducing positive and negative refraction,” Phys. Rev. B 74, 033102 (2006).
[CrossRef]

Phys. Rev. D

C. Imbert, “Calculation and experimental proof of transverse shift induced by total internal reflection of a circularly polarized-light beam,” Phys. Rev. D 5, 787–796 (1972).
[CrossRef]

Phys. Rev. E

P. R. Berman, “Goos–Hanchen shift in negatively refractive media,” Phys. Rev. E 66, 067603 (2002).
[CrossRef]

Phys. Rev. Lett.

O. Emile, T. Galstyan, A. Le Floch, and F. Bretenaker, “Measurement of the nonlinear Goos–Hanchen effect for Gaussian optical beams,” Phys. Rev. Lett. 75, 1511–1513 (1995).
[CrossRef]

B. M. Jost, A.-A. R. Al-Rashed, and B. E. A. Saleh, “Observation of the Goos–Hänchen effect in a phase-conjugate mirror,” Phys. Rev. Lett. 81, 2233–2235 (1998).
[CrossRef]

K. Y. Bliokh and Y. P. Bliokh, “Conservation of angular momentum, transverse shift, and spin hall effect in reflection and refraction of an electromagnetic wave packet,” Phys. Rev. Lett. 96, 073903 (2006).
[CrossRef]

M. Onoda, S. Murakami, and N. Nagaosa, “Hall effect of light,” Phys. Rev. Lett. 93, 083901 (2004).
[CrossRef]

C. W. J. Beenakker, R. A. Sepkhanov, A. R. Akhmerov, and J. Tworzydło, “Quantum Goos–Hanchen effect in graphene,” Phys. Rev. Lett. 102, 146804 (2009).
[CrossRef]

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Figures (6)

Fig. 1.
Fig. 1.

Geometry of the beam reflection and transmission at the interface between an air and the moving medium. The subscripts i , r , and t represent the incident, reflection, and transmission beams, respectively.

Fig. 2.
Fig. 2.

Normalized IF shifts of the reflection beam ( D r y / λ ) as a function of the incident angle [(a) and (b)] and the velocity of moving medium along y direction (c) for a circularly polarized incident Gaussian beam ( ψ = π / 2 ). The solid line, dashed line, dotted line, and dot-dashed line in (a) correspond to the cases with β = v c = 0 , 0.5, 0.7, and 0.9, respectively, and in (b) to the cases with β = 0 , 0.5 , 0.7 , and 0.9 . The incident angle in (c) is θ i = π / 3 . The other parameters are taken as ε = 2.0 , μ = 1 , and E i s = E i p = 1 .

Fig. 3.
Fig. 3.

Normalized IF shifts of the refraction beam ( D r y / λ ) as a function of the incident angles [(a) and (b)] and the velocity of moving medium along y direction (c) for a circularly polarized incident Gaussian beam ( ψ = π / 2 ). The solid line, dashed line, dotted line, and dot-dashed line in (a) correspond to the cases with β = 0 , 0.5, 0.9, and 0.99, respectively, and in (b) to the cases with β = 0 , 0.5 , 0.9 , and 0.99 . The incident angle in (c) is θ i = π / 3 . The other parameters are identical to those in Fig. 2.

Fig. 4.
Fig. 4.

(a) Normalized GH shifts of the reflection beam ( D r x / λ ) as a function of the incident angle as the medium moves with β = 0.5 (dashed line) and β = 0.9 (solid line) along y direction for a circularly polarized incident Gaussian beam ( ψ = π / 2 ). (b) The corresponding coefficients ( ρ sp = Re [ ln r sp / θ i ] ) as a function of the incident angle. The other parameters are identical to those in Fig. 2.

Fig. 5.
Fig. 5.

Normalized IF shifts of the reflection beam ( D r y / λ ) as a function of the incident angle [(a) and (b)] and the velocity of moving medium along x direction (c) for a circularly polarized incident Gaussian beam ( ψ = π / 2 ). The solid line, dashed line, and dotted line in (a) correspond to the cases with β = 0 , 0.5, and 0.9, respectively, and in (b) to the cases with β = 0 , 0.5 , and 0.9 . The incident angle in (c) is θ i = π / 3 . The other parameters are identical with those in Fig. 2.

Fig. 6.
Fig. 6.

Normalized IF shifts of the transmission beam ( D r y / λ ) as a function of the incident angle [(a) and (b)] and the velocity of moving medium along x direction (c) for a circularly polarized incident Gaussian beam ( ψ = π / 2 ). The solid line, dashed line, and dotted line in (a) correspond to the cases with β = 0 , 0.5, and 0.9, respectively, and in (b) to the cases with β = 0 , 0.5 , and 0.9 . The incident angle in (c) is θ i = π / 3 . The other parameters are identical with those in Fig. 2.

Equations (49)

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E⃗ i ( X i , y , Z i ) = ( E i X e ^ i X + E i y e ^ i y ) exp [ k 0 2 X i 2 + y 2 Z R + j Z i ] .
E⃗ i ( X r , y , Z r ) = d k r X d k r y E ˜ r ( k r X , k r y ) exp [ j ( k r X X r + k r y y + k r Z Z r ) ] ,
E ˜ r ( k r X , k r y ) = ( r p p + k r y k 0 ( r s p r p s ) cot θ i r p s + k r y k 0 ( r p p + r s s ) cot θ i r s p k r y k 0 ( r p p + r s s ) cot θ i r s s + k r y k 0 ( r s p r p s ) cot θ i ) ( E i X E i y ) exp [ Z R ( k r X 2 + k r y 2 ) 2 k 0 ] .
E⃗ r ( X r , y ) = [ r p p ( 1 j X r Z R + j Z r θ i ln r p p ) E i X + r p s ( 1 j X r Z R + j Z r θ i ln r p s ) E i y + j y Z R + j Z r ( r s p r p s ) E i X cot θ i + j y Z R + j Z r ( r p p + r s s ) E i y cot θ i ] exp [ k 0 ( X r 2 + y 2 ) 2 ( Z R + j Z r ) ] e ^ r X + [ r s p ( 1 j X r Z R + j Z r θ i ln r s p ) E i X + r s s ( 1 j X r Z R + j Z r θ i ln r s s ) E i y j y Z R + j Z r ( r p p + r s s ) E i X cot θ i + j y Z R + j Z r ( r s p r p s ) E i y cot θ i ] exp [ k 0 ( X r 2 + y 2 ) 2 ( Z R + i Z r ) ] e ^ r y .
E⃗ t ( X t , y , Z t ) = d k t X d k t y E ˜ t ( k t X , k t y ) exp [ j ( k t X X t + k t y y + k t Z Z t ) ] .
E ˜ t ( k t X , k t y ) = ( t p p k t y k 0 ( t p s + η t s p ) cot θ i t p s + k t y k 0 ( t p p η t s s ) cot θ i t s p + k t y k 0 ( η t p p t s s ) cot θ i t s s + k t y k 0 ( η t p s + t s p ) cot θ i ) · ( E i X E i y ) exp [ Z R X k t X 2 + Z R y k t y 2 2 n k 0 ] ,
E⃗ t ( X t , y ) = [ t p p ( 1 + j n η X t Z t X + j Z t θ i ln t p p ) E i X + t p s ( 1 + j n η X t Z t X + j Z t θ i ln t p s ) E i y j n y Z R y + j Z t ( t p s + η t s p ) E i X cot θ i + j n y Z R y + j Z t ( t p p η t s s ) E i y cot θ i ] exp [ n k 0 2 ( X t 2 Z R X + j Z t + y 2 Z R y + j Z t ) ] e ^ t X + [ t s p ( 1 + j n η X t Z R X + j Z t θ i ln t s p ) E i X + t s s ( 1 + j n η X t Z R X + j Z t θ i ln t s s ) E i y + j n y Z R y + j Z t ( η t p p t s s ) E i X cot θ i + j n y Z R y + j Z t ( t s p + η t p s ) E i y cot θ i ] exp [ n k 0 2 ( X t 2 Z R X + j Z t + y 2 Z R y + j Z t ) ] e ^ t y .
X α = X α I ( X α , y , Z α ) d X α d y I ( X α , y , Z α ) d X α d y , y = y I ( X α , y , Z α ) d X α d y I ( X α , y , Z α ) d X α d y .
D r x = Δ r x k 0 τ + Z r Z R δ r x k 0 τ ,
D r y = Δ r y k 0 τ + Z r Z R δ r y k 0 τ .
D t x = η Δ t x k 0 τ t + Z t Z R X η δ t x k 0 τ t ,
D t y = η Δ t y k 0 τ t + Z t Z R y η δ t y k 0 τ t .
E ˜ r ( k r X , k r y ) = ( r p k r y k 0 ( r p + r s ) cot θ i k r y k 0 ( r p + r s ) cot θ i r s ) ( E i X E i y ) exp [ Z R ( k r X 2 + k r y 2 ) 2 k 0 ] .
E⃗ r ( X r , y ) = [ r p ( 1 j X r Z R + j Z r θ i ln r p ) E i X + j y Z R + j Z r ( r p + r s ) E i y cot θ i ] exp [ k 0 ( X r 2 + y 2 ) 2 ( Z R + j Z r ) ] e ^ r X + [ r s ( 1 j X r Z R + j Z r θ i ln r s ) E i y j y Z R + j Z r ( r p + r s ) E i X cot θ i ] exp [ k 0 ( X r 2 + y 2 ) 2 ( Z R + i Z r ) ] e ^ r y .
E ˜ t ( k t X , k t y ) = ( t p k t y k 0 ( t p η t s ) cot θ i k t y k 0 ( η t p t s ) cot θ i t s ) · ( E i X E i y ) exp [ Z R X k t X 2 + Z R y k t y 2 2 n k 0 ] .
E⃗ t ( X t , y ) = [ t p ( 1 + j n η X t Z t X + j Z t θ i ln t p ) E i X + j n y Z R y + j Z t ( t p η t s ) E i y cot θ i ] exp [ n k 0 2 ( X t 2 Z R X + j Z t + y 2 Z R y + j Z t ) ] e ^ t X + [ t s ( 1 + j n η X t Z R X + j Z t θ i ln t s ) E i y + j n y Z R y + j Z t ( η t p t s ) E i X cot θ i ] exp [ n k 0 2 ( X t 2 Z R X + j Z t + y 2 Z R y + j Z t ) ] e ^ t y .
D r x = Δ r x k 0 τ + Z r Z R δ r x k 0 τ ,
D r y = Δ r y k 0 τ + Z r Z R δ r y k 0 τ .
D t x = η Δ t x k 0 τ t + Z t Z R X η δ t x k 0 τ t ,
D t y = η Δ t y k 0 τ t + Z t Z R y η δ t y k 0 τ t .
j r z = Δ r y k r sin θ r + σ r cos θ r ,
j t z = Δ t y k t sin θ t + σ t cos θ t ,
σ r = 2 E i s E i p [ | r s p | | r p s | sin ( ϕ s p ϕ p s ψ ) + | r s s | | r p p | sin ( ϕ s s ϕ p p + ψ ) ] ( E i s ) 2 ( | r s s | 2 + | r p s | 2 ) + ( E i p ) 2 ( | r p p | 2 + | r s p | 2 ) ,
σ t = 2 E i s E i p [ | t s p | | t p s | sin ( φ s p φ p s ψ ) + | t s s | | t p p | sin ( φ s s φ p p + ψ ) ] ( E i p ) 2 ( a | t p p | 2 + | t s p | 2 ) + ( E i s ) 2 ( | t s s | 2 + a | t p s | 2 ) .
Q r j r z + Q t j t z = j i z .
σ r = 2 E i s E i p | r s | | r p | sin ( ϕ s ϕ p + ψ ) ( E i s ) 2 | r s | 2 + ( E i p ) 2 | r p | 2 ,
σ t = 2 E i s E i p | t s | | t p | sin ( φ s φ p + ψ ) a ( E i p ) 2 | t p | 2 + ( E i s ) 2 | t s | 2 .
Q r = ( E i s ) 2 | r s | 2 + ( E i p ) 2 | r p | 2 ,
Q t = n η [ a ( E i p ) 2 | t p | 2 + ( E i s ) 2 | t s | 2 ] .
Δ r x = ( E i s ) 2 ( | r s s | 2 ξ s s + | r p s | 2 ξ p s ) + ( E i p ) 2 ( | r p p | 2 ξ p p + | r s p | 2 ξ s p ) + E i p E i s [ | r s s | | r s p | ( ξ s s + ξ s p ) cos ( ϕ s s ϕ s p + ψ ) + | r p p | | r p s | ( ξ p p + ξ p s ) cos ( ϕ p s ϕ p p + ψ ) + | r p p | | r p s | ( ρ p s ρ p p ) sin ( ϕ p s ϕ p p + ψ ) + | r s s | | r s p | ( ρ s p ρ s s ) sin ( ϕ s p ϕ s s ψ ) ] .
δ r x = ( E i s ) 2 ( | r s s | 2 ρ s s + | r p s | 2 ρ p s ) ( E i p ) 2 ( | r p p | 2 ρ p p + | r s p | 2 ρ s p ) + E i s E i p [ | r s s | | r s p | ( ρ s s + ρ s p ) cos ( ϕ s s ϕ s p + ψ ) | r p p | | r p s | ( ρ p p + ρ p s ) cos ( ϕ p s ϕ p p + ψ ) + | r p p | | r p s | ( ξ p s ξ p p ) sin ( ϕ p s ϕ p p + ψ ) + | r s p | | r s s | ( ξ s p ξ s s ) sin ( ϕ s p ϕ s s ψ ) ] .
Δ r y = cot θ i [ ( ( E i s ) 2 + ( E i p ) 2 ) | r s s | | r s p | sin ( ϕ s p ϕ s s ) + 2 ( E i s ) 2 | r s s | | r p s | sin ( ϕ s s ϕ p s ) + ( E i p ) 2 | r s p | | r p p | sin ( ϕ s p ϕ p p ) + ( ( E i p ) 2 + ( E i s ) 2 ) | r p s | | r p p | sin ( ϕ p p ϕ p s ) + 2 E i s E i p | r s p | | r p s | sin ( ϕ s p ϕ p s ψ ) + 2 E i s E i p | r s s | | r p p | sin ( ϕ s s ϕ p p + ψ ) + E i s E i p ( | r p p | 2 + | r p s | 2 + | r s p | 2 + | r s s | 2 ) sin ψ ] .
δ r y = cot θ i [ ( ( E i p ) 2 ( E i s ) 2 ) ( | r p p | | r p s | cos ( ϕ p s ϕ p p ) + | r s p | | r s s | cos ( ϕ s p ϕ s s ) ) + E i s E i p ( | r s s | 2 | r s p | 2 + | r p s | 2 | r p p | 2 ) cos ψ ] .
τ = ( E i s ) 2 ( | r s s | 2 + | r p s | 2 ) + ( E i p ) 2 ( | r p p | 2 + | r s p | 2 ) + 2 E i p E i s [ | r s s | | r s p | cos ( ϕ s s ϕ s p + ψ ) + | r p p | | r p s | cos ( ϕ p s ϕ p p + ψ ) ] .
Δ t x = ( E i p ) 2 ζ p p | t p p | 2 + ( E i s ) 2 ζ p s | t p s | 2 + ( ( E i p ) 2 ζ s p | t s p | 2 + ( E i s ) 2 ζ s s | t s s | 2 ) / a + E i p E i s [ | t p p | | t p s | cos ( φ p p φ p s ψ ) ( ζ p p + ζ p s ) + | t s s | | t s p | cos ( φ s p φ s s + ψ ) ( ζ s s + ζ s p ) / a ] + E i p E i s [ | t p p | | t p s | sin ( φ p p φ p s ψ ) ( χ p p + χ p s ) + | t s s | | t s p | sin ( φ s p φ s s + ψ ) ( χ s s + χ s p ) / a ] + Ω y [ ( E i p ) 2 | t p p | | t s p | sin ( φ p p φ s p ψ ) + ( E i s ) 2 | t s s | | t p s | sin ( φ s s φ p s ψ ) + E i p E i s ( | t s p | | t p s | sin ( φ p s φ s p + ψ ) + | t p p | | t s s | sin ( φ s s φ p p + ψ ) ) ] / 2 a n η ,
δ t x = ( E i p ) 2 χ p p | t p p | 2 + ( E i s ) 2 χ p s | t p s | 2 + ( ( E i p ) 2 χ s p | t s p | 2 + ( E i s ) 2 χ s s | t s s | 2 ) / a + E i p E i s [ | t p p | | t p s | cos ( φ p p φ p s ψ ) ( χ p p + χ p s ) + | t s s | | t s p | cos ( φ s p φ s s + ψ ) ( χ s s + χ s p ) / a ] + E i p E i s [ | t p p | | t p s | sin ( φ p p φ p s ψ ) ( ζ p p ζ p s ) + | t s s | | t s p | sin ( φ s p φ s s + ψ ) ( ζ s s ζ s p ) / a ] + Ω y [ ( E i p ) 2 | t p p | | t s p | cos ( φ p p φ s p ψ ) + ( E i s ) 2 | t s s | | t p s | cos ( φ s s φ p s ψ ) + E i p E i s ( | t s p | | t p s | cos ( φ p s φ s p + ψ ) + | t p p | | t s s | cos ( φ s s φ p p + ψ ) ) ] / 2 a n η ,
Δ t y = E i p E i s { cot θ i [ ( | t p p | 2 + | t p s | 2 + ( | t s s | 2 + | t s p | 2 ) / a ) sin ψ + ( η | t p p | | t s s | sin ( φ p p φ s s ψ ) + η | t p s | | t s p | sin ( φ p s φ s p + ψ ) ) ( 1 + 1 / a ) ] + Ω y ( a | t p p | 2 sin ( φ p p + ψ ) + | t s s | 2 sin ( φ s s + ψ ) + | t s p | | t p s | sin ( φ s p φ p s + ψ ) + | t s p | | t p s | sin ( φ p s φ s p + ψ ) ) / 2 a n } + ( ( E i p ) 2 + ( E i s ) 2 ) ( | t p p | | t p s | sin ( φ p p φ p s ) + | t s s | | t s p | sin ( φ s s φ p s ) / a ) cot θ i ,
δ t y = E i p E i s { cot θ i ( η cos ψ ( | t p p | 2 | t s s | 2 / a + 2 | t p p | | t s s | / a ) ) Ω y ( a | t p p | 2 cos ( φ p p + ψ ) + | t s s | 2 cos ( φ s s + ψ ) + | t s p | | t p s | cos ( φ s p φ p s + ψ ) + | t s p | | t p s | cos ( φ p s φ s p + ψ ) ) / 2 a n } + ( ( E i p ) 2 + ( E i s ) 2 ) ( | t p p | | t p s | cos ( φ p p φ p s ) + | t s s | | t s p | cos ( φ s s φ p s ) / a ) cot θ i .
τ t = [ ( E i p ) 2 ( a | t p p | 2 + | t s p | 2 ) + ( E i s ) 2 ( | t s s | 2 + a | t p s | 2 ) + 2 E i p E i s ( a | t p p | | t p s | cos ( φ p p φ p s ψ ) + | t s s | | t s p | cos ( φ s p φ s s ψ ) ) ] / a ,
Δ r x = ( E i p ) 2 ξ p | r p | 2 + ( E i s ) 2 ξ s | r s | 2 ,
δ r x = ( E i s ) 2 ρ s | r s | 2 ( E i p ) 2 ρ p | r p | 2 ,
Δ r y = E i s E i p cot θ i [ ( | r s | 2 + | r p | 2 ) sin ψ 2 | r s | | r p | sin ( ϕ p ϕ s ψ ) ] ,
δ r y = E i s E i p ( | r p | 2 | r s | 2 ) cos ψ cot θ i ,
τ = ( E i s ) 2 | r s | 2 + ( E i p ) 2 | r p | 2 ,
Δ t x = ( E i p ) 2 ζ p | t p | 2 + a ( E i s ) 2 ζ s | t s | 2 + Ω x ( ( E i p ) 2 | t p | 2 sin φ p + a ( E i s ) 2 | t s | 2 sin φ s ) / 2 a n η ,
δ t x = ( E i p ) 2 χ p | t p | 2 + a ( E i s ) 2 χ s | t s | 2 Ω x ( ( E i p ) 2 | t p | 2 cos φ p + a ( E i s ) 2 | t s | 2 cos φ s ) / 2 a n η ,
Δ t y = E i s E i p cot θ i [ ( | t p | 2 + a | t s | 2 ) sin ψ + 2 ( 1 + a ) η | t s | | t p | sin ( φ p φ s ψ ) ] + Ω x E i s E i p | t s | | t p | sin ( φ p φ s ψ ) / 2 a n ,
δ t y = E i s E i p [ ( | t p | 2 a | t s | 2 ) cos ψ cot θ i + ( a 1 ) η | t s | | t p | cos ( φ p φ s ψ ) ] Ω x E i s E i p | t s | | t p | cos ( φ p φ s ψ ) / 2 a n ,
τ t = ( E i s ) 2 | t s | 2 + ( E i p ) 2 | t p | 2 / a ,

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