Abstract

We have used a heterodyne Z-scan technique to produce both superluminal and slow light propagation in media that present either thermal or Kerr nonlinearities. The sample position determines the magnitude and sign of the group velocity and this property was used to control it, with an experimental setup much simpler than those previously reported in similar investigations. The observed effect is attributed to the transverse phase modulation produced by a focused Gaussian beam, and is capable of producing both positive and negative group velocities in the range 1.5 m/s <|υg|<c.

© 2006 Optical Society of America

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References

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  1. R. W. Boyd and D. J. Gauthier, “Slow and Fast Light,” Prog. Opt. 43, 496, edited by E. Wolf (Elsevier, Amsterdam, 2002).
  2. A. Kasapiet al., “Electromagnetically induced transparency - propagation dynamics,” Phys. Rev. Lett. 74, 2447 (1995).
    [Crossref] [PubMed]
  3. L. V. Hauet al., “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature (London) 397, 594 (1999).
    [Crossref]
  4. M. M. Kashet al., “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229 (1999).
    [Crossref]
  5. D. Budkeret al., “Nonlinear magneto-optics and reduced group velocity of light in atomic vapor with slow ground state relaxation,” Phys. Rev. Lett. 83, 1767 (1999).
    [Crossref]
  6. S. E. Harris, J. E. Field, and A. Kasapi, “Dispersive properties of electromagnetically induced transparency,” Phys. Rev. A 46, R29 (1992).
    [Crossref] [PubMed]
  7. S. P. Tewari and G. S. Agarwal, “Control of phase matching and nonlinear generation in dense media by resonant fields,” Phys. Rev. Lett. 56, 1811 (1986).
    [Crossref] [PubMed]
  8. R. S. Benninkal., “Enhanced self-action effects by electromagnetically induced transparency in the two-level atom,” Phys. Rev. A 63, 033804 (2001).
    [Crossref]
  9. L. J. Wang, A. Kuzmich, and A. Dogariu, “Gain-assisted superluminal light propagation,” Nature (London) 406, 277 (2000).
    [Crossref]
  10. M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Observation of ultraslow light propagation in a ruby crystal at room temperature,” Phys. Rev. Lett. 90, 113903 (2003).
    [Crossref] [PubMed]
  11. M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Superluminal and slow light propagation in a room-temperature solid,” Science 301, 200 (2003).
    [Crossref] [PubMed]
  12. Q. Yang, J. T. Seo, B. Tabibi, and H. Wang, “Slow light and superluminality in Kerr media without a pump,” Phys. Rev. Lett. 95, 063902 (2005).
    [Crossref] [PubMed]
  13. P. Yeh, “2-wave mixing in nonlinear media,” IEEE J. Quantum Electron. QE-25, 484 (1989).
    [Crossref]
  14. M. Sheik-Bahae, A. A. Said, T. Wei, D. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. QE-26, 760 (1990).
    [Crossref]
  15. J. Penaforte, E. Gouveia, and S. C. Zilio, “Nondegenerate 2-wave mixing in GdAlO3-Cr3+,” Opt. Lett. 16, 452 (1991).
    [Crossref] [PubMed]
  16. S. C. Zilio, J. C. Penaforte, E. A. Gouveia, and M. J. V. Bell, “Nearly degenerate 2-wave mixing in saturable absorbers,” Opt. Commun. 86, 81 (1991).
    [Crossref]
  17. A. Yariv, Quantum Electronics, 3rd edition (John Wiiley and Sons, New York, 1989).
  18. L. C. Oliveira, T. Catunda, and S. C. Zilio, “Saturation effects in Z-scan measurements,” Jpn. J. Appl. Phys. 35, 2649 (1996).
    [Crossref]
  19. J. G. Tian, C. Zhang, G. Zhang, and J. Li, “Position dispersion and optical limiting resulting from thermally-induced nonlinearities in chinese tea liquid,” Appl. Opt. 32, 6628 (1993).
    [Crossref] [PubMed]
  20. Handbook of Optical Materials, edited by M. J. Weber (CRC Press, Boca Raton, 2003).

2005 (1)

Q. Yang, J. T. Seo, B. Tabibi, and H. Wang, “Slow light and superluminality in Kerr media without a pump,” Phys. Rev. Lett. 95, 063902 (2005).
[Crossref] [PubMed]

2003 (2)

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Observation of ultraslow light propagation in a ruby crystal at room temperature,” Phys. Rev. Lett. 90, 113903 (2003).
[Crossref] [PubMed]

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Superluminal and slow light propagation in a room-temperature solid,” Science 301, 200 (2003).
[Crossref] [PubMed]

2002 (1)

R. W. Boyd and D. J. Gauthier, “Slow and Fast Light,” Prog. Opt. 43, 496, edited by E. Wolf (Elsevier, Amsterdam, 2002).

2001 (1)

R. S. Benninkal., “Enhanced self-action effects by electromagnetically induced transparency in the two-level atom,” Phys. Rev. A 63, 033804 (2001).
[Crossref]

2000 (1)

L. J. Wang, A. Kuzmich, and A. Dogariu, “Gain-assisted superluminal light propagation,” Nature (London) 406, 277 (2000).
[Crossref]

1999 (3)

L. V. Hauet al., “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature (London) 397, 594 (1999).
[Crossref]

M. M. Kashet al., “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229 (1999).
[Crossref]

D. Budkeret al., “Nonlinear magneto-optics and reduced group velocity of light in atomic vapor with slow ground state relaxation,” Phys. Rev. Lett. 83, 1767 (1999).
[Crossref]

1996 (1)

L. C. Oliveira, T. Catunda, and S. C. Zilio, “Saturation effects in Z-scan measurements,” Jpn. J. Appl. Phys. 35, 2649 (1996).
[Crossref]

1995 (1)

A. Kasapiet al., “Electromagnetically induced transparency - propagation dynamics,” Phys. Rev. Lett. 74, 2447 (1995).
[Crossref] [PubMed]

1993 (1)

1992 (1)

S. E. Harris, J. E. Field, and A. Kasapi, “Dispersive properties of electromagnetically induced transparency,” Phys. Rev. A 46, R29 (1992).
[Crossref] [PubMed]

1991 (2)

J. Penaforte, E. Gouveia, and S. C. Zilio, “Nondegenerate 2-wave mixing in GdAlO3-Cr3+,” Opt. Lett. 16, 452 (1991).
[Crossref] [PubMed]

S. C. Zilio, J. C. Penaforte, E. A. Gouveia, and M. J. V. Bell, “Nearly degenerate 2-wave mixing in saturable absorbers,” Opt. Commun. 86, 81 (1991).
[Crossref]

1990 (1)

M. Sheik-Bahae, A. A. Said, T. Wei, D. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. QE-26, 760 (1990).
[Crossref]

1989 (1)

P. Yeh, “2-wave mixing in nonlinear media,” IEEE J. Quantum Electron. QE-25, 484 (1989).
[Crossref]

1986 (1)

S. P. Tewari and G. S. Agarwal, “Control of phase matching and nonlinear generation in dense media by resonant fields,” Phys. Rev. Lett. 56, 1811 (1986).
[Crossref] [PubMed]

Agarwal, G. S.

S. P. Tewari and G. S. Agarwal, “Control of phase matching and nonlinear generation in dense media by resonant fields,” Phys. Rev. Lett. 56, 1811 (1986).
[Crossref] [PubMed]

Bell, M. J. V.

S. C. Zilio, J. C. Penaforte, E. A. Gouveia, and M. J. V. Bell, “Nearly degenerate 2-wave mixing in saturable absorbers,” Opt. Commun. 86, 81 (1991).
[Crossref]

Bennink, R. S.

R. S. Benninkal., “Enhanced self-action effects by electromagnetically induced transparency in the two-level atom,” Phys. Rev. A 63, 033804 (2001).
[Crossref]

Bigelow, M. S.

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Observation of ultraslow light propagation in a ruby crystal at room temperature,” Phys. Rev. Lett. 90, 113903 (2003).
[Crossref] [PubMed]

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Superluminal and slow light propagation in a room-temperature solid,” Science 301, 200 (2003).
[Crossref] [PubMed]

Boyd, R. W.

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Superluminal and slow light propagation in a room-temperature solid,” Science 301, 200 (2003).
[Crossref] [PubMed]

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Observation of ultraslow light propagation in a ruby crystal at room temperature,” Phys. Rev. Lett. 90, 113903 (2003).
[Crossref] [PubMed]

R. W. Boyd and D. J. Gauthier, “Slow and Fast Light,” Prog. Opt. 43, 496, edited by E. Wolf (Elsevier, Amsterdam, 2002).

Budker, D.

D. Budkeret al., “Nonlinear magneto-optics and reduced group velocity of light in atomic vapor with slow ground state relaxation,” Phys. Rev. Lett. 83, 1767 (1999).
[Crossref]

Catunda, T.

L. C. Oliveira, T. Catunda, and S. C. Zilio, “Saturation effects in Z-scan measurements,” Jpn. J. Appl. Phys. 35, 2649 (1996).
[Crossref]

Dogariu, A.

L. J. Wang, A. Kuzmich, and A. Dogariu, “Gain-assisted superluminal light propagation,” Nature (London) 406, 277 (2000).
[Crossref]

Field, J. E.

S. E. Harris, J. E. Field, and A. Kasapi, “Dispersive properties of electromagnetically induced transparency,” Phys. Rev. A 46, R29 (1992).
[Crossref] [PubMed]

Gauthier, D. J.

R. W. Boyd and D. J. Gauthier, “Slow and Fast Light,” Prog. Opt. 43, 496, edited by E. Wolf (Elsevier, Amsterdam, 2002).

Gouveia, E.

Gouveia, E. A.

S. C. Zilio, J. C. Penaforte, E. A. Gouveia, and M. J. V. Bell, “Nearly degenerate 2-wave mixing in saturable absorbers,” Opt. Commun. 86, 81 (1991).
[Crossref]

Hagan, D.

M. Sheik-Bahae, A. A. Said, T. Wei, D. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. QE-26, 760 (1990).
[Crossref]

Harris, S. E.

S. E. Harris, J. E. Field, and A. Kasapi, “Dispersive properties of electromagnetically induced transparency,” Phys. Rev. A 46, R29 (1992).
[Crossref] [PubMed]

Hau, L. V.

L. V. Hauet al., “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature (London) 397, 594 (1999).
[Crossref]

Kasapi, A.

A. Kasapiet al., “Electromagnetically induced transparency - propagation dynamics,” Phys. Rev. Lett. 74, 2447 (1995).
[Crossref] [PubMed]

S. E. Harris, J. E. Field, and A. Kasapi, “Dispersive properties of electromagnetically induced transparency,” Phys. Rev. A 46, R29 (1992).
[Crossref] [PubMed]

Kash, M. M.

M. M. Kashet al., “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229 (1999).
[Crossref]

Kuzmich, A.

L. J. Wang, A. Kuzmich, and A. Dogariu, “Gain-assisted superluminal light propagation,” Nature (London) 406, 277 (2000).
[Crossref]

Lepeshkin, N. N.

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Superluminal and slow light propagation in a room-temperature solid,” Science 301, 200 (2003).
[Crossref] [PubMed]

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Observation of ultraslow light propagation in a ruby crystal at room temperature,” Phys. Rev. Lett. 90, 113903 (2003).
[Crossref] [PubMed]

Li, J.

Oliveira, L. C.

L. C. Oliveira, T. Catunda, and S. C. Zilio, “Saturation effects in Z-scan measurements,” Jpn. J. Appl. Phys. 35, 2649 (1996).
[Crossref]

Penaforte, J.

Penaforte, J. C.

S. C. Zilio, J. C. Penaforte, E. A. Gouveia, and M. J. V. Bell, “Nearly degenerate 2-wave mixing in saturable absorbers,” Opt. Commun. 86, 81 (1991).
[Crossref]

Said, A. A.

M. Sheik-Bahae, A. A. Said, T. Wei, D. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. QE-26, 760 (1990).
[Crossref]

Seo, J. T.

Q. Yang, J. T. Seo, B. Tabibi, and H. Wang, “Slow light and superluminality in Kerr media without a pump,” Phys. Rev. Lett. 95, 063902 (2005).
[Crossref] [PubMed]

Sheik-Bahae, M.

M. Sheik-Bahae, A. A. Said, T. Wei, D. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. QE-26, 760 (1990).
[Crossref]

Tabibi, B.

Q. Yang, J. T. Seo, B. Tabibi, and H. Wang, “Slow light and superluminality in Kerr media without a pump,” Phys. Rev. Lett. 95, 063902 (2005).
[Crossref] [PubMed]

Tewari, S. P.

S. P. Tewari and G. S. Agarwal, “Control of phase matching and nonlinear generation in dense media by resonant fields,” Phys. Rev. Lett. 56, 1811 (1986).
[Crossref] [PubMed]

Tian, J. G.

Van Stryland, E. W.

M. Sheik-Bahae, A. A. Said, T. Wei, D. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. QE-26, 760 (1990).
[Crossref]

Wang, H.

Q. Yang, J. T. Seo, B. Tabibi, and H. Wang, “Slow light and superluminality in Kerr media without a pump,” Phys. Rev. Lett. 95, 063902 (2005).
[Crossref] [PubMed]

Wang, L. J.

L. J. Wang, A. Kuzmich, and A. Dogariu, “Gain-assisted superluminal light propagation,” Nature (London) 406, 277 (2000).
[Crossref]

Wei, T.

M. Sheik-Bahae, A. A. Said, T. Wei, D. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. QE-26, 760 (1990).
[Crossref]

Yang, Q.

Q. Yang, J. T. Seo, B. Tabibi, and H. Wang, “Slow light and superluminality in Kerr media without a pump,” Phys. Rev. Lett. 95, 063902 (2005).
[Crossref] [PubMed]

Yariv, A.

A. Yariv, Quantum Electronics, 3rd edition (John Wiiley and Sons, New York, 1989).

Yeh, P.

P. Yeh, “2-wave mixing in nonlinear media,” IEEE J. Quantum Electron. QE-25, 484 (1989).
[Crossref]

Zhang, C.

Zhang, G.

Zilio, S. C.

L. C. Oliveira, T. Catunda, and S. C. Zilio, “Saturation effects in Z-scan measurements,” Jpn. J. Appl. Phys. 35, 2649 (1996).
[Crossref]

J. Penaforte, E. Gouveia, and S. C. Zilio, “Nondegenerate 2-wave mixing in GdAlO3-Cr3+,” Opt. Lett. 16, 452 (1991).
[Crossref] [PubMed]

S. C. Zilio, J. C. Penaforte, E. A. Gouveia, and M. J. V. Bell, “Nearly degenerate 2-wave mixing in saturable absorbers,” Opt. Commun. 86, 81 (1991).
[Crossref]

Appl. Opt. (1)

IEEE J. Quantum Electron. (2)

P. Yeh, “2-wave mixing in nonlinear media,” IEEE J. Quantum Electron. QE-25, 484 (1989).
[Crossref]

M. Sheik-Bahae, A. A. Said, T. Wei, D. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. QE-26, 760 (1990).
[Crossref]

Jpn. J. Appl. Phys. (1)

L. C. Oliveira, T. Catunda, and S. C. Zilio, “Saturation effects in Z-scan measurements,” Jpn. J. Appl. Phys. 35, 2649 (1996).
[Crossref]

Nature (London) (2)

L. V. Hauet al., “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature (London) 397, 594 (1999).
[Crossref]

L. J. Wang, A. Kuzmich, and A. Dogariu, “Gain-assisted superluminal light propagation,” Nature (London) 406, 277 (2000).
[Crossref]

Opt. Commun. (1)

S. C. Zilio, J. C. Penaforte, E. A. Gouveia, and M. J. V. Bell, “Nearly degenerate 2-wave mixing in saturable absorbers,” Opt. Commun. 86, 81 (1991).
[Crossref]

Opt. Lett. (1)

Phys. Rev. A (2)

R. S. Benninkal., “Enhanced self-action effects by electromagnetically induced transparency in the two-level atom,” Phys. Rev. A 63, 033804 (2001).
[Crossref]

S. E. Harris, J. E. Field, and A. Kasapi, “Dispersive properties of electromagnetically induced transparency,” Phys. Rev. A 46, R29 (1992).
[Crossref] [PubMed]

Phys. Rev. Lett. (6)

S. P. Tewari and G. S. Agarwal, “Control of phase matching and nonlinear generation in dense media by resonant fields,” Phys. Rev. Lett. 56, 1811 (1986).
[Crossref] [PubMed]

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Observation of ultraslow light propagation in a ruby crystal at room temperature,” Phys. Rev. Lett. 90, 113903 (2003).
[Crossref] [PubMed]

M. M. Kashet al., “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229 (1999).
[Crossref]

D. Budkeret al., “Nonlinear magneto-optics and reduced group velocity of light in atomic vapor with slow ground state relaxation,” Phys. Rev. Lett. 83, 1767 (1999).
[Crossref]

A. Kasapiet al., “Electromagnetically induced transparency - propagation dynamics,” Phys. Rev. Lett. 74, 2447 (1995).
[Crossref] [PubMed]

Q. Yang, J. T. Seo, B. Tabibi, and H. Wang, “Slow light and superluminality in Kerr media without a pump,” Phys. Rev. Lett. 95, 063902 (2005).
[Crossref] [PubMed]

Prog. Opt. (1)

R. W. Boyd and D. J. Gauthier, “Slow and Fast Light,” Prog. Opt. 43, 496, edited by E. Wolf (Elsevier, Amsterdam, 2002).

Science (1)

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Superluminal and slow light propagation in a room-temperature solid,” Science 301, 200 (2003).
[Crossref] [PubMed]

Other (2)

A. Yariv, Quantum Electronics, 3rd edition (John Wiiley and Sons, New York, 1989).

Handbook of Optical Materials, edited by M. J. Weber (CRC Press, Boca Raton, 2003).

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Figures (4)

Fig. 1.
Fig. 1.

Experimental setup used to observe superluminal and slow light. L:lens, S:sample, D:detector, A:aperture.

Fig. 2.
Fig. 2.

Normalized amplitude (a) and phase (b) of the modulation for the ruby sample. The dots correspond to the experimental points while solid lines are plots of Eqs. (4) and (5), with the parameters given in the text.

Fig. 3.
Fig. 3.

Normalized amplitude (a) and phase (b) of the modulation for the DO3 sample at P=0.33 mW. The dots correspond to the experimental points while solid lines are theoretical curves using Eqs. (4) and (5), with the parameters given in the text.

Fig. 4.
Fig. 4.

Group velocity for the DO3 sample as a function of its position (squares) and theoretical fit (solid line).

Equations (6)

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

T ( z , Δ Φ 0 ) = I ( z , Δ Φ 0 ) I ( z , 0 ) = 1 4 Δ Φ 0 ( t ) x ( x 2 + 1 ) ( x 2 + 9 )
Δ n 0 ( t ) = n 2 I 0 { 1 + Γ m 1 + δ 2 sin ( ω m t γ ) }
I ( z , t ) = I 0 [ 1 A ( x ) B ] + I 0 Γ m F ( z , δ ) sin ( ω m t + φ )
φ = t g 1 [ A ( x ) B δ ( 1 + δ 2 ) A ( x ) B ( 2 + δ 2 ) ]
F ( z , δ ) 1 A ( x ) B ( 2 + δ 2 1 + δ 2 )
A ( x ) = 4 x ( x 2 + 1 ) ( x 2 + 9 )

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