Abstract

When a three-level atomic wavepacket is obliquely incident on a ”medium slab” consisting of two far-detuned laser beams, there exists lateral shift between reflection and incident points at the surface of a ”medium slab”, analogous to optical Goos-Hänchen effect. We evaluate lateral shifts for reflected and transmitted waves via expansion of reflection and transmission coefficients, in contrast to the stationary phase method. Results show that lateral shifts can be either positive or negative dependent on the incident angle and the atomic internal state. Interestingly, a giant lateral shift of transmitted wave with high transmission probability is observed, which is helpful to observe such lateral shifts experimentally. Different from the two-level atomic wave case, we find that quantum interference between different atomic states plays crucial role on the transmission intensity and corresponding lateral shifts.

© 2014 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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  17. L.W. Zeng and RX Song, “Lateral shift of acoustic wave at interface between double-positive and double-negative media,” Phys. Lett. A 358, 484–486 (2006).
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  18. V Regnier, “Delayed reflection in a stratified acoustic strip,” Mathematical methods in the applied sciences 28, 185–203 (2005).
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2012 (1)

Z.L. Duan and W.P. Zhang, “Failures of the adiabatic approximation in quantum tunneling time,” Phys. Rev. A 86, 064101 (2012).
[CrossRef]

2011 (2)

Ziauddin and Sajid Qamar, “Gain-assisted control of the Goos-Hänchen shift,” Phys. Rev. A 84, 053844 (2011).
[CrossRef]

Y. Wan, Z. Zheng, W. Kong, Y. Liu, Z. Lu, and Y. Bian, “Direct experimental observation of giant Goos-Hänchen shifts from bandgap-enhanced total internal reflection,” Opt Lett. 36, 3539–3541 (2011).
[CrossRef] [PubMed]

2009 (1)

2008 (1)

J. H. Huang, Z. L. Duan, H. Y. Ling, and W. P. Zhang, “Goos-Hänchen-like shifts in atom optics,” Phys. Rev. A 77, 063608 (2008).
[CrossRef]

2006 (3)

L.W. Zeng and RX Song, “Lateral shift of acoustic wave at interface between double-positive and double-negative media,” Phys. Lett. A 358, 484–486 (2006).
[CrossRef]

L.G. Wang and S.Y. Zhu, “Giant Lateral shift of a light beam at the defect mode in One-dimensional photonic crystals,” Opt. Lett. 31, 101–103(2006).
[CrossRef] [PubMed]

X.B. Yin and L Hesselink, “Goos-Hänchen shift surface plasmon resonance sensor,” Appl. Phys. Lett. 89, 261108 (2006).
[CrossRef]

2005 (2)

G.J. Dong, S. Edvadsson, W. Lu, and P.F. Barker, “Super-Gaussian mirror for high-field-seeking molecules,” Phys. Rev. A 72, 031605(R) (2005).
[CrossRef]

V Regnier, “Delayed reflection in a stratified acoustic strip,” Mathematical methods in the applied sciences 28, 185–203 (2005).
[CrossRef]

2004 (2)

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

J. Martina and T. Bastinb, “Transmission of ultracold atoms through a micromaser: detuning effects,” Eur. Phys. J. D 29, 133–137 (2004).
[CrossRef]

2003 (2)

I.V. Shadrivov, A.A. Zharov, and Y.S. Kivshar, “Giant Goos-Hanchen effect at the reflection from left-handed metamaterials,” Appl. Phys. Lett. 83, 2713–2715 (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] [PubMed]

2002 (2)

2000 (1)

T Sakata, H Togo, and F Shimokawa, “Reflection-type 2×2 optical waveguide switch using the Goos-Hdnchen shift effect,” Appl. Phys. Lett. 76, 2841–2843 (2000).
[CrossRef]

1997 (1)

M. Mâaza and B. Pardo, “On the possibility to observe the longitudinal Goos-Hänchen shift with cold neutrons,” Opt. Commun. 142, 84–90 (1997).
[CrossRef]

1996 (2)

M. Morinaga, M. Yasuda, T. Kishimoto, F. Shimizu, J. I. Fujita, and S. Matsui, “Holographic manipulation of a cold atomic beam,” Phys. Rev. Lett. 77, 802–805 (1996).
[CrossRef] [PubMed]

Z. T. Lu, K. L. Corwin, M. J. Renn, M. H. Anderson, E. A. Cornell, and C. E. Wieman, “Low-Velocity Intense Source of Atoms from a Magneto-optical Trap,” Phys. Rev. Lett. 77, 3331–3334 (1996).
[CrossRef] [PubMed]

1995 (2)

T. M. Roach, H. Abele, M. G. Boshier, H. L. Grossman, K. P. Zetie, and E. A. Hinds, “Realization of a Magnetic Mirror for Cold Atoms,” Phys. Rev. Lett. 75, 629–632 (1995).
[CrossRef] [PubMed]

O. Emile, T. Galstyan, A. LeFloch, and F. Bretenaker, “Measurement of the Nonlinear Goos-Hänchen Effect for Gaussian Optical Beams,” Phys. Rev. Lett. 75, 1511–1513 (1995).
[CrossRef] [PubMed]

1994 (1)

W.P. Zhang and B.C. Sanders, “Atomic beamsplitter: reflection and transmission by a laser beam,” J. phys. B 27, 795–808 (1994).
[CrossRef]

1992 (1)

1985 (1)

1974 (2)

D.M. Fradkin and R.J. Kashuba, “Spatial displacement of electrons due to multiple total reflections,” Phys. Rev. D 9, 2775–2788 (1974).
[CrossRef]

A. Gedeon, “Observation of the lateral displacement of surface acoustic beams reflected at boundaries of layered substrates,” Appl. Phys. 3, 397–402 (1974).
[CrossRef]

1972 (1)

S.C. Miller and N. Ashby, “Shifts of Electron Beam Position Due to Total Reflection at a Barrier,” Phys. Rev. Lett. 29, 740–743 (1972).
[CrossRef]

1964 (1)

1960 (1)

H. Hora, “Zur seitenversetzung bei der totalreflexion von matteriewellen,” Optik 17, 409–415 (1960).

1948 (1)

K. Artmann, “Calculation of the Lateral Shift of Totally Reflected Beams,” Ann. Phys.(Leipzig) 2, 87–102 (1948).
[CrossRef]

1947 (1)

F. Goos and H. Hänchen, “Ein neuer und fundamentaler Versuch zur Totalreflexion,” Ann. Phys. 1, 333–346 (1947).
[CrossRef]

1929 (1)

J. Picht, “Beitrag zur Theorie der Totalreflexion,” Ann. Phys.(Leipzig) 3, 433–496 (1929).
[CrossRef]

Abele, H.

T. M. Roach, H. Abele, M. G. Boshier, H. L. Grossman, K. P. Zetie, and E. A. Hinds, “Realization of a Magnetic Mirror for Cold Atoms,” Phys. Rev. Lett. 75, 629–632 (1995).
[CrossRef] [PubMed]

Anderson, M. H.

Z. T. Lu, K. L. Corwin, M. J. Renn, M. H. Anderson, E. A. Cornell, and C. E. Wieman, “Low-Velocity Intense Source of Atoms from a Magneto-optical Trap,” Phys. Rev. Lett. 77, 3331–3334 (1996).
[CrossRef] [PubMed]

Artmann, K.

K. Artmann, “Calculation of the Lateral Shift of Totally Reflected Beams,” Ann. Phys.(Leipzig) 2, 87–102 (1948).
[CrossRef]

Ashby, N.

S.C. Miller and N. Ashby, “Shifts of Electron Beam Position Due to Total Reflection at a Barrier,” Phys. Rev. Lett. 29, 740–743 (1972).
[CrossRef]

Barker, P.F.

G.J. Dong, S. Edvadsson, W. Lu, and P.F. Barker, “Super-Gaussian mirror for high-field-seeking molecules,” Phys. Rev. A 72, 031605(R) (2005).
[CrossRef]

Bastinb, T.

J. Martina and T. Bastinb, “Transmission of ultracold atoms through a micromaser: detuning effects,” Eur. Phys. J. D 29, 133–137 (2004).
[CrossRef]

Bélanger, P.A.

Bian, Y.

Y. Wan, Z. Zheng, W. Kong, Y. Liu, Z. Lu, and Y. Bian, “Direct experimental observation of giant Goos-Hänchen shifts from bandgap-enhanced total internal reflection,” Opt Lett. 36, 3539–3541 (2011).
[CrossRef] [PubMed]

Bin, Zhao

Boshier, M. G.

T. M. Roach, H. Abele, M. G. Boshier, H. L. Grossman, K. P. Zetie, and E. A. Hinds, “Realization of a Magnetic Mirror for Cold Atoms,” Phys. Rev. Lett. 75, 629–632 (1995).
[CrossRef] [PubMed]

Bretenaker, F.

O. Emile, T. Galstyan, A. LeFloch, and F. Bretenaker, “Measurement of the Nonlinear Goos-Hänchen Effect for Gaussian Optical Beams,” Phys. Rev. Lett. 75, 1511–1513 (1995).
[CrossRef] [PubMed]

Chan, S.W.

Cornell, E. A.

Z. T. Lu, K. L. Corwin, M. J. Renn, M. H. Anderson, E. A. Cornell, and C. E. Wieman, “Low-Velocity Intense Source of Atoms from a Magneto-optical Trap,” Phys. Rev. Lett. 77, 3331–3334 (1996).
[CrossRef] [PubMed]

Corwin, K. L.

Z. T. Lu, K. L. Corwin, M. J. Renn, M. H. Anderson, E. A. Cornell, and C. E. Wieman, “Low-Velocity Intense Source of Atoms from a Magneto-optical Trap,” Phys. Rev. Lett. 77, 3331–3334 (1996).
[CrossRef] [PubMed]

Dong, G.J.

G.J. Dong, S. Edvadsson, W. Lu, and P.F. Barker, “Super-Gaussian mirror for high-field-seeking molecules,” Phys. Rev. A 72, 031605(R) (2005).
[CrossRef]

Duan, Z. L.

J. H. Huang, Z. L. Duan, H. Y. Ling, and W. P. Zhang, “Goos-Hänchen-like shifts in atom optics,” Phys. Rev. A 77, 063608 (2008).
[CrossRef]

Duan, Z.L.

Z.L. Duan and W.P. Zhang, “Failures of the adiabatic approximation in quantum tunneling time,” Phys. Rev. A 86, 064101 (2012).
[CrossRef]

Edvadsson, S.

G.J. Dong, S. Edvadsson, W. Lu, and P.F. Barker, “Super-Gaussian mirror for high-field-seeking molecules,” Phys. Rev. A 72, 031605(R) (2005).
[CrossRef]

Emile, O.

O. Emile, T. Galstyan, A. LeFloch, and F. Bretenaker, “Measurement of the Nonlinear Goos-Hänchen Effect for Gaussian Optical Beams,” Phys. Rev. Lett. 75, 1511–1513 (1995).
[CrossRef] [PubMed]

Fradkin, D.M.

D.M. Fradkin and R.J. Kashuba, “Spatial displacement of electrons due to multiple total reflections,” Phys. Rev. D 9, 2775–2788 (1974).
[CrossRef]

Fujita, J. I.

M. Morinaga, M. Yasuda, T. Kishimoto, F. Shimizu, J. I. Fujita, and S. Matsui, “Holographic manipulation of a cold atomic beam,” Phys. Rev. Lett. 77, 802–805 (1996).
[CrossRef] [PubMed]

Galstyan, T.

O. Emile, T. Galstyan, A. LeFloch, and F. Bretenaker, “Measurement of the Nonlinear Goos-Hänchen Effect for Gaussian Optical Beams,” Phys. Rev. Lett. 75, 1511–1513 (1995).
[CrossRef] [PubMed]

Gao, Lei

Gedeon, A.

A. Gedeon, “Observation of the lateral displacement of surface acoustic beams reflected at boundaries of layered substrates,” Appl. Phys. 3, 397–402 (1974).
[CrossRef]

Goos, F.

F. Goos and H. Hänchen, “Ein neuer und fundamentaler Versuch zur Totalreflexion,” Ann. Phys. 1, 333–346 (1947).
[CrossRef]

Grossman, H. L.

T. M. Roach, H. Abele, M. G. Boshier, H. L. Grossman, K. P. Zetie, and E. A. Hinds, “Realization of a Magnetic Mirror for Cold Atoms,” Phys. Rev. Lett. 75, 629–632 (1995).
[CrossRef] [PubMed]

Hänchen, H.

F. Goos and H. Hänchen, “Ein neuer und fundamentaler Versuch zur Totalreflexion,” Ann. Phys. 1, 333–346 (1947).
[CrossRef]

Hesselink, L

X.B. Yin and L Hesselink, “Goos-Hänchen shift surface plasmon resonance sensor,” Appl. Phys. Lett. 89, 261108 (2006).
[CrossRef]

Hinds, E. A.

T. M. Roach, H. Abele, M. G. Boshier, H. L. Grossman, K. P. Zetie, and E. A. Hinds, “Realization of a Magnetic Mirror for Cold Atoms,” Phys. Rev. Lett. 75, 629–632 (1995).
[CrossRef] [PubMed]

Hora, H.

H. Hora, “Zur seitenversetzung bei der totalreflexion von matteriewellen,” Optik 17, 409–415 (1960).

Hsue, C.W.

Huang, J. H.

J. H. Huang, Z. L. Duan, H. Y. Ling, and W. P. Zhang, “Goos-Hänchen-like shifts in atom optics,” Phys. Rev. A 77, 063608 (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]

Kashuba, R.J.

D.M. Fradkin and R.J. Kashuba, “Spatial displacement of electrons due to multiple total reflections,” Phys. Rev. D 9, 2775–2788 (1974).
[CrossRef]

Kishimoto, T.

M. Morinaga, M. Yasuda, T. Kishimoto, F. Shimizu, J. I. Fujita, and S. Matsui, “Holographic manipulation of a cold atomic beam,” Phys. Rev. Lett. 77, 802–805 (1996).
[CrossRef] [PubMed]

Kivshar, Y.S.

I.V. Shadrivov, A.A. Zharov, and Y.S. Kivshar, “Giant Goos-Hanchen effect at the reflection from left-handed metamaterials,” Appl. Phys. Lett. 83, 2713–2715 (2003).
[CrossRef]

Kong, W.

Y. Wan, Z. Zheng, W. Kong, Y. Liu, Z. Lu, and Y. Bian, “Direct experimental observation of giant Goos-Hänchen shifts from bandgap-enhanced total internal reflection,” Opt Lett. 36, 3539–3541 (2011).
[CrossRef] [PubMed]

Lachance, R.L.

Lai, H.M.

LeFloch, A.

O. Emile, T. Galstyan, A. LeFloch, and F. Bretenaker, “Measurement of the Nonlinear Goos-Hänchen Effect for Gaussian Optical Beams,” Phys. Rev. Lett. 75, 1511–1513 (1995).
[CrossRef] [PubMed]

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] [PubMed]

Ling, H. Y.

J. H. Huang, Z. L. Duan, H. Y. Ling, and W. P. Zhang, “Goos-Hänchen-like shifts in atom optics,” Phys. Rev. A 77, 063608 (2008).
[CrossRef]

Liu, J.S.

Liu, Y.

Y. Wan, Z. Zheng, W. Kong, Y. Liu, Z. Lu, and Y. Bian, “Direct experimental observation of giant Goos-Hänchen shifts from bandgap-enhanced total internal reflection,” Opt Lett. 36, 3539–3541 (2011).
[CrossRef] [PubMed]

Lu, W.

G.J. Dong, S. Edvadsson, W. Lu, and P.F. Barker, “Super-Gaussian mirror for high-field-seeking molecules,” Phys. Rev. A 72, 031605(R) (2005).
[CrossRef]

Lu, Z.

Y. Wan, Z. Zheng, W. Kong, Y. Liu, Z. Lu, and Y. Bian, “Direct experimental observation of giant Goos-Hänchen shifts from bandgap-enhanced total internal reflection,” Opt Lett. 36, 3539–3541 (2011).
[CrossRef] [PubMed]

Lu, Z. T.

Z. T. Lu, K. L. Corwin, M. J. Renn, M. H. Anderson, E. A. Cornell, and C. E. Wieman, “Low-Velocity Intense Source of Atoms from a Magneto-optical Trap,” Phys. Rev. Lett. 77, 3331–3334 (1996).
[CrossRef] [PubMed]

Mâaza, M.

M. Mâaza and B. Pardo, “On the possibility to observe the longitudinal Goos-Hänchen shift with cold neutrons,” Opt. Commun. 142, 84–90 (1997).
[CrossRef]

Martina, J.

J. Martina and T. Bastinb, “Transmission of ultracold atoms through a micromaser: detuning effects,” Eur. Phys. J. D 29, 133–137 (2004).
[CrossRef]

Matsui, S.

M. Morinaga, M. Yasuda, T. Kishimoto, F. Shimizu, J. I. Fujita, and S. Matsui, “Holographic manipulation of a cold atomic beam,” Phys. Rev. Lett. 77, 802–805 (1996).
[CrossRef] [PubMed]

Miller, S.C.

S.C. Miller and N. Ashby, “Shifts of Electron Beam Position Due to Total Reflection at a Barrier,” Phys. Rev. Lett. 29, 740–743 (1972).
[CrossRef]

Morinaga, M.

M. Morinaga, M. Yasuda, T. Kishimoto, F. Shimizu, J. I. Fujita, and S. Matsui, “Holographic manipulation of a cold atomic beam,” Phys. Rev. Lett. 77, 802–805 (1996).
[CrossRef] [PubMed]

Newton, I.

I. Newton, Optick (Dover, 1952).

Pardo, B.

M. Mâaza and B. Pardo, “On the possibility to observe the longitudinal Goos-Hänchen shift with cold neutrons,” Opt. Commun. 142, 84–90 (1997).
[CrossRef]

Paré, C.

Picht, J.

J. Picht, “Beitrag zur Theorie der Totalreflexion,” Ann. Phys.(Leipzig) 3, 433–496 (1929).
[CrossRef]

Qamar, Sajid

Ziauddin and Sajid Qamar, “Gain-assisted control of the Goos-Hänchen shift,” Phys. Rev. A 84, 053844 (2011).
[CrossRef]

Regnier, V

V Regnier, “Delayed reflection in a stratified acoustic strip,” Mathematical methods in the applied sciences 28, 185–203 (2005).
[CrossRef]

Renard, R.H.

Renn, M. J.

Z. T. Lu, K. L. Corwin, M. J. Renn, M. H. Anderson, E. A. Cornell, and C. E. Wieman, “Low-Velocity Intense Source of Atoms from a Magneto-optical Trap,” Phys. Rev. Lett. 77, 3331–3334 (1996).
[CrossRef] [PubMed]

Roach, T. M.

T. M. Roach, H. Abele, M. G. Boshier, H. L. Grossman, K. P. Zetie, and E. A. Hinds, “Realization of a Magnetic Mirror for Cold Atoms,” Phys. Rev. Lett. 75, 629–632 (1995).
[CrossRef] [PubMed]

Sakata, T

T Sakata, H Togo, and F Shimokawa, “Reflection-type 2×2 optical waveguide switch using the Goos-Hdnchen shift effect,” Appl. Phys. Lett. 76, 2841–2843 (2000).
[CrossRef]

Sanders, B.C.

W.P. Zhang and B.C. Sanders, “Atomic beamsplitter: reflection and transmission by a laser beam,” J. phys. B 27, 795–808 (1994).
[CrossRef]

Shadrivov, I.V.

I.V. Shadrivov, A.A. Zharov, and Y.S. Kivshar, “Giant Goos-Hanchen effect at the reflection from left-handed metamaterials,” Appl. Phys. Lett. 83, 2713–2715 (2003).
[CrossRef]

Shimizu, F.

M. Morinaga, M. Yasuda, T. Kishimoto, F. Shimizu, J. I. Fujita, and S. Matsui, “Holographic manipulation of a cold atomic beam,” Phys. Rev. Lett. 77, 802–805 (1996).
[CrossRef] [PubMed]

Shimokawa, F

T Sakata, H Togo, and F Shimokawa, “Reflection-type 2×2 optical waveguide switch using the Goos-Hdnchen shift effect,” Appl. Phys. Lett. 76, 2841–2843 (2000).
[CrossRef]

Song, RX

L.W. Zeng and RX Song, “Lateral shift of acoustic wave at interface between double-positive and double-negative media,” Phys. Lett. A 358, 484–486 (2006).
[CrossRef]

Taghizadeh, M.R.

Tamir, T.

Togo, H

T Sakata, H Togo, and F Shimokawa, “Reflection-type 2×2 optical waveguide switch using the Goos-Hdnchen shift effect,” Appl. Phys. Lett. 76, 2841–2843 (2000).
[CrossRef]

Wan, Y.

Y. Wan, Z. Zheng, W. Kong, Y. Liu, Z. Lu, and Y. Bian, “Direct experimental observation of giant Goos-Hänchen shifts from bandgap-enhanced total internal reflection,” Opt Lett. 36, 3539–3541 (2011).
[CrossRef] [PubMed]

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[CrossRef] [PubMed]

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[CrossRef] [PubMed]

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[CrossRef]

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[CrossRef]

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[CrossRef] [PubMed]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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Y. Wan, Z. Zheng, W. Kong, Y. Liu, Z. Lu, and Y. Bian, “Direct experimental observation of giant Goos-Hänchen shifts from bandgap-enhanced total internal reflection,” Opt Lett. 36, 3539–3541 (2011).
[CrossRef] [PubMed]

Zhu, S.Y.

Ziauddin,

Ziauddin and Sajid Qamar, “Gain-assisted control of the Goos-Hänchen shift,” Phys. Rev. A 84, 053844 (2011).
[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

I.V. Shadrivov, A.A. Zharov, and Y.S. Kivshar, “Giant Goos-Hanchen effect at the reflection from left-handed metamaterials,” Appl. Phys. Lett. 83, 2713–2715 (2003).
[CrossRef]

X.B. Yin and L Hesselink, “Goos-Hänchen shift surface plasmon resonance sensor,” Appl. Phys. Lett. 89, 261108 (2006).
[CrossRef]

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J. Martina and T. Bastinb, “Transmission of ultracold atoms through a micromaser: detuning effects,” Eur. Phys. J. D 29, 133–137 (2004).
[CrossRef]

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[CrossRef]

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[CrossRef]

Opt Lett. (1)

Y. Wan, Z. Zheng, W. Kong, Y. Liu, Z. Lu, and Y. Bian, “Direct experimental observation of giant Goos-Hänchen shifts from bandgap-enhanced total internal reflection,” Opt Lett. 36, 3539–3541 (2011).
[CrossRef] [PubMed]

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[CrossRef]

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[CrossRef]

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J. H. Huang, Z. L. Duan, H. Y. Ling, and W. P. Zhang, “Goos-Hänchen-like shifts in atom optics,” Phys. Rev. A 77, 063608 (2008).
[CrossRef]

Ziauddin and Sajid Qamar, “Gain-assisted control of the Goos-Hänchen shift,” Phys. Rev. A 84, 053844 (2011).
[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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Z. T. Lu, K. L. Corwin, M. J. Renn, M. H. Anderson, E. A. Cornell, and C. E. Wieman, “Low-Velocity Intense Source of Atoms from a Magneto-optical Trap,” Phys. Rev. Lett. 77, 3331–3334 (1996).
[CrossRef] [PubMed]

T. M. Roach, H. Abele, M. G. Boshier, H. L. Grossman, K. P. Zetie, and E. A. Hinds, “Realization of a Magnetic Mirror for Cold Atoms,” Phys. Rev. Lett. 75, 629–632 (1995).
[CrossRef] [PubMed]

M. Morinaga, M. Yasuda, T. Kishimoto, F. Shimizu, J. I. Fujita, and S. Matsui, “Holographic manipulation of a cold atomic beam,” Phys. Rev. Lett. 77, 802–805 (1996).
[CrossRef] [PubMed]

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Other (1)

I. Newton, Optick (Dover, 1952).

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Figures (5)

Fig. 1
Fig. 1

(a) Schematic of lateral shift when a three-level atomic wavepacket oblique incident on a Raman laser beams. (b) Energy level structure of atom.

Fig. 2
Fig. 2

The lateral shift (upper panel) and reflection(transmission) probability (Lower panel) as a function of incident angle for atomic waves in state |1〉 (solid line) and state |2〉 (dash-dotted line). The incident atomic wave is in state |1〉 through the blue-detuned laser beams with different Rabi frequencies. Other parameters are: L = 30, γ = 0.1, Ω1 = 2.5, Ω2 = 3.5, k0 = 0.8, kL = 0.1.

Fig. 3
Fig. 3

The lateral shift (upper panel) and reflection(transmission) probability (Lower panel) as a function of incident angle for atomic waves in state |1〉 (solid line) and state |2〉 (dash-dotted line). The incident atomic wave is in state |1〉 through the blue-detuned laser beams with equal Rabi frequencies. Other parameters are the same with figure 2.

Fig. 4
Fig. 4

The lateral shift (upper panel) and reflection(transmission) probability (Lower panel) as a function of incident angle for atomic waves in state |1〉 (solid line) and state |2〉 (dash-dotted line). The incident atomic wave is in state ( | 1 + | 2 ) / 2 through the blue-detuned laser beams with equal Rabi frequencies. Other parameters are the same with figure 3.

Fig. 5
Fig. 5

The lateral shift (upper panel) and reflection(transmission) probability (Lower panel) as a function of incident angle for atomic waves in state |1〉 (solid line) and state |2〉 (dash-dotted line) through the red-detuned laser beams with equal Rabi frequencies. the Other parameters are: L = 4, γ = 0.1, Ω1 = 2, Ω2 = 2, k0 = 0.8, kL = 0.1.

Equations (45)

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i h ¯ t Ψ 1 ( r , t ) = h ¯ 2 2 m 2 Ψ 1 ( r , t ) h ¯ 2 Ω 1 ( x ) e i k L 1 y Ψ 3 ( r , t )
i h ¯ t Ψ 2 ( r , t ) = h ¯ 2 2 m 2 Ψ 2 ( r , t ) h ¯ δ 0 ψ 2 ( r , t ) h ¯ 2 Ω 2 ( x ) e i k L 2 y Ψ 3 ( r , t )
i h ¯ t Ψ 3 ( r , t ) = h ¯ 2 2 m 2 Ψ 3 ( r , t ) h ¯ ( Δ 0 + i γ 2 ) Ψ 3 ( r , t ) h ¯ 2 Ω 1 ( x ) e i k L 1 y Ψ 1 ( r , t ) h ¯ 2 Ω 2 ( x ) e i k L 2 y Ψ 2 ( r , t )
Ω 1 , 2 ( x ) = { Ω 1 , 2 , 0 x L 0 , x < 0 , x > L .
Ψ 1 ( r , t ) = d k y d k z ψ 1 ( x , t ) e i k y y i h ¯ ( k y 2 + k z 2 ) t / 2 m ,
Ψ 2 ( r , t ) = d k y d k z ψ 2 ( x , t ) e i ( k y + k L 1 + k L 2 ) y i h ¯ ( k y 2 + k z 2 ) t / 2 m ,
Ψ 3 ( r , t ) = d k y d k z ψ 3 ( x , t ) e i ( k y + k L 1 ) y i h ¯ ( k y 2 + k z 2 ) t / 2 m .
i h ¯ t ψ ( x , t ) = ( h ¯ 2 2 m 2 x 2 I ^ + V ^ ) ψ ( x , t )
V ^ = h ¯ 2 ( 0 0 Ω 1 0 2 δ Ω 2 Ω 1 Ω 2 2 Δ ) ,
Δ = Δ 0 h ¯ 2 m ( 2 k L 1 k y + k L 1 2 ) + i 2 γ
δ = δ 0 + h ¯ 2 m k y 2 h ¯ 2 m ( k L 1 + k L 2 + k y ) 2
U = ( Ω 1 Δ Δ ˜ Ω 2 Ω 1 Ω 1 Δ + Δ ˜ Ω 2 Δ Δ ˜ 1 Ω 2 Δ + Δ ˜ 1 0 1 )
ψ in ( r , t ) = f ( k ) exp ( i k r i E / h ¯ t ) d k
ψ in ( r , t ) = ( 1 2 π A 2 ) 3 / 4 exp ( ( r h ¯ k 0 t / m ) 2 4 A 2 + i k 0 ( r h ¯ k 0 2 m t ) )
ψ t ( r , t ) = T f ( k ) exp ( i k r i E / h ¯ t ) d k
ψ t ( r , t ) = ( 1 2 π A 2 ) 3 / 4 | T ( k 0 ) | exp ( λ 2 4 W 2 ) × exp ( ( r h ¯ k 0 t / m ) 2 4 A 2 + i k 0 ( r ϕ h ¯ k 0 2 m t ) )
y + ϕ t y h ¯ k y 0 t / m = 0
L + ϕ t x h ¯ k x 0 t / m = 0
D t = k y 0 k x 0 ( L + ϕ t x ) ϕ t y
D t = k y 0 k x 0 ( L + ϕ t x ) ϕ t y
D r = k y 0 k x 0 ϕ r x ϕ r y
k x 0 = ( cos ( θ ) k 0 sin ( θ ) k 0 θ )
k y 0 = ( sin ( θ ) k 0 + cos ( θ ) k 0 θ )
D r , t = 1 cos ( θ ) k 0 ϕ r , t θ
| 1 Ω 1 | + + Ω 2 | 0 Ω 1 2 + Ω 2 2
| 2 Ω 2 | + Ω 1 | 0 Ω 1 2 + Ω 2 2
| 3 |
( ψ 1 ψ 2 ψ 3 ) = { ( In 1 e i k 1 x + R 1 e i k 1 x In 2 e i k 2 x + R 2 e i k 2 x In 3 e i k 3 x + R 3 e i k 3 x ) e i E x t / h ¯ , x 0 ( T 1 e i k 1 x T 2 e i k 2 x T 3 e i k 3 x ) e i E x t / h ¯ , x L
| ± = ( Ω 1 | 1 + Ω 2 | 2 + ( Δ Δ ˜ ) | 3 ) Ω 1 2 + Ω 2 2 + ( Δ Δ ˜ ) 2
| 0 = 1 Ω 1 2 + Ω 2 2 ( Ω 2 | 1 Ω 1 | 2 )
( ψ 1 ψ 2 ψ 3 ) = U ( A + e p + x + B + e p + x A 0 e p 0 x + B 0 e p 0 x A e p x + B e p x ) e i E x t / h ¯
( In 1 In 2 In 3 ) + ( R 1 R 2 R 3 ) = U ( A + + B + A 0 + B 0 A + B )
i ( k 1 In 1 k 2 In 2 k 3 In 3 ) i ( k 1 R 1 k 2 R 2 k 3 R 3 ) = U ( p + A + p + B + p 0 A 0 p 0 B 0 p A p B )
U ( A + e p + L + B + e p + L A 0 e p 0 L + B 0 e p 0 L A e p L + B e p L ) = ( T 1 e i k 1 L T 2 e i k 1 L T 3 e i k 3 L )
U ( p + A + e p + L p + B + e p + L p 0 A 0 e p 0 L p 0 B 0 e p 0 L p A e p L p B e p L ) = ( i k 1 T 1 e i k 1 L i k 1 T 2 e i k 1 L i k 3 T 3 e i k 3 L )
W = ( e p + L 0 0 0 e p 0 L 0 0 0 e p L ) K = ( i k 1 0 0 0 i k 2 0 0 0 i k 3 ) E = ( e i k 1 L 0 0 0 e i k 2 L 0 0 0 e i k 3 L ) P = ( p + 0 0 0 p 0 0 0 0 p )
In + R = U ( A + B )
K ( In R ) = U P ( A B )
U ( W A + W 1 B ) = T
U P ( W A W 1 B ) = K T
T = 4 F 1 K In
F = ( K U + U P ) W 1 ( U 1 + P 1 U 1 K ) + ( K U U P ) W ( U 1 P 1 U 1 K )
R = G 1 D In
G = ( K U U P ) W ( U 1 P 1 U 1 K ) + ( K U + U P ) W 1 ( U 1 + P 1 U 1 K )
D = ( K U U P ) W ( U 1 + P 1 U 1 K ) + ( K U + U P ) W 1 ( U 1 P 1 U 1 K )

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