Abstract

We experimentally and theoretically study the propagation of a 1536nm light pulse superposed on a continuous wave background in a highly doped erbium fiber pumped at 977nm. We observe a transition from subluminal to superluminal propagation with the pulse bandwidth. Furthermore, an improvement of the pulse delay and pulse distortion when increasing the pulse peak and keeping constant the background power is reported. These results are due to the relation between the pump-broadened transparency hole (induced by the coherent population oscillations) and the competition between gain and absorption along the fiber.

© 2011 Optical Society of America

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  1. R. W. Boyd, D. J. Gauthier, and A. L. Gaeta, “Applications of slow light in telecommunications,” Opt. Photon. News 17, 18–23(2006).
    [CrossRef]
  2. C. Peng, Z. Li, and A. Xu, “Rotation sensing based on a slow-light resonating structure with high group dispersion,” Appl. Opt. 46, 4125–4131 (2007).
    [CrossRef] [PubMed]
  3. Z. Shi, R. W. Boyd, D. J. Gauthier, and C. C. Dudley, “Enhancing the spectral sensitivity of interferometers using slow-light media,” Opt. Lett. 32, 915–917 (2007).
    [CrossRef] [PubMed]
  4. 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]
  5. M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Superluminal and slow light propagation in a room-temperature solid,” Science 301, 200–202 (2003).
    [CrossRef] [PubMed]
  6. A. Schweinsberg, N. N. Lepeshkin, M. S. Bigelow, R. W. Boyd, and S. Jarabo, “Observation of superluminal and slow light propagation in erbium-doped optical fiber,” Europhys. Lett. 73, 218–224 (2006).
    [CrossRef]
  7. G. M. Gehring, A. Schweinsberg, C. Barsi, N. Kostinski, and R. W. Boyd, “Observation of backward pulse propagation through a medium with a negative group velocity,” Science 312, 895–897(2006).
    [CrossRef] [PubMed]
  8. P. Wu and D. V. G. L. N. Rao, “Controllable snail-paced light in biological bacteriorhodopsin thin film,” Phys. Rev. Lett. 95, 253601 (2005).
    [CrossRef] [PubMed]
  9. H. Su, P. Kondratko, and S. L. Chuang, “Variable optical delay using population oscillation and four-wave-mixing in semiconductor optical amplifiers,” Opt. Express 14, 4800–4807(2006).
    [CrossRef] [PubMed]
  10. J. Mørk, R. Kjær, M. van der Poel, and K. Yvind, “Slow light in a semiconductor waveguide at gigahertz frequencies,” Opt. Express 13, 8136–8145 (2005).
    [CrossRef] [PubMed]
  11. S. Melle, O. G. Calderón, F. Carreño, E. Cabrera, M. A. Antón, and S. Jarabo, “Effect of ion concentration on slow light propagation in highly doped erbium fibers,” Opt. Commun. 279, 53–63 (2007).
    [CrossRef]
  12. S. Melle, O. G. Calderón, C. E. Caro, E. Cabrera-Granado, M. A. Antón, and F. Carreño, “Modulation-frequency-controlled change from sub- to superluminal regime in highly doped erbium fibers,” Opt. Lett. 33, 827–829 (2008).
    [CrossRef] [PubMed]
  13. O. G. Calderón, S. Melle, M. A. Antón, F. Carreño, F. Arrieta-Yáñez, and E. Cabrera-Granado, “Propagation-induced transition from slow to fast light in highly doped erbium fibers,” Phys. Rev. A 78, 053812 (2008).
    [CrossRef]
  14. H. Shin, A. Schweinsberg, G. Gehring, K. Schwertz, H. J. Chang, R. W. Boyd, Q-H. Park, and D. J. Gauthier, “Reducing pulse distortion in fast light pulse propagation through an erbium doped fiber amplifier,” Opt. Lett. 32, 906–908 (2007).
    [CrossRef] [PubMed]
  15. H. Shin, A. Schweinsberg, and R. W. Boyd, “Reducing pulse distortion in fast-light pulse propagation through and erbium-doped fiber amplifier using a mutually incoherent background field,” Opt. Commun. 282, 2085–2087 (2009).
    [CrossRef]
  16. G. Piredda and R. W. Boyd, “Slow light by means of coherent population oscillations: laser linewidth effects,” J. Eur. Opt. Soc. Rap. Commun. 2, 07004 (2007).
    [CrossRef]
  17. F. Sanchez, P. L. Boudec, P.-L. Francois, and G. Stephan, “Effects of ion pairs on the dynamics of erbium-doped fiber lasers,” Phys. Rev. A 48, 2220–2229 (1993).
    [CrossRef] [PubMed]
  18. J. Li, K. Duan, Y. Wang, W. Zhao, J. Zhu, Y. Guo, and X. Lin, “Modeling and effects of ions pairs in high-concentration-erbium-doped fiber lasers,” J. Mod. Opt. 55, 447–458(2008).
    [CrossRef]
  19. O. G. Calderón, S. Melle, F. Arrieta-Yáñez, M. A. Antón, and F. Carreño, “Effect of ion pairs in fast-light bandwidth in high-concentration erbium-doped fibers,” J. Opt. Soc. Am. B 25, C55–C60 (2008).
    [CrossRef]
  20. S. Wen and S. Chi, “Propagation characteristics of fast light in an erbium-doped fiber amplifier,” J. Opt. Soc. Am. B 25, 1073–1080(2008).
    [CrossRef]
  21. S. Chin, M. Gonzalez-Herraez, and L. Thévanaz, “Zero-gain slow & fast light propagation in an optical fiber,” Opt. Express 14, 10684–10692 (2006).
    [CrossRef] [PubMed]
  22. S. S. Maicas, F. Öhman, J. Capmany, and J. Mørk, “Controlling microwave signals by means of slow and fast light effects in SOA-EA structures,” IEEE Photon. Technol. Lett. 19, 1589–1591(2007).
    [CrossRef]
  23. F. G. Sedgwick, B. Pesala, J. Lin, W. S. Ko, X. Zhao, and C. J. Chang-Hasnain, “THz-bandwidth tunable slow light in semiconductor optical amplifiers,” Opt. Express 15, 747–753(2007).
    [CrossRef] [PubMed]
  24. M. S. Bigelow, N. N. Lepeshkin, H. Shin, and R. W. Boyd, “Propagation of smooth and discontinuous pulses through materials with very large or very small group velocities,” J. Phys. Condens. Matter 18, 3117–3126 (2006).
    [CrossRef]
  25. B. Macke and B. Ségard, “Slow light in saturable absorbers,” Phys. Rev. A 78, 013817 (2008).
    [CrossRef]

2009 (1)

H. Shin, A. Schweinsberg, and R. W. Boyd, “Reducing pulse distortion in fast-light pulse propagation through and erbium-doped fiber amplifier using a mutually incoherent background field,” Opt. Commun. 282, 2085–2087 (2009).
[CrossRef]

2008 (6)

J. Li, K. Duan, Y. Wang, W. Zhao, J. Zhu, Y. Guo, and X. Lin, “Modeling and effects of ions pairs in high-concentration-erbium-doped fiber lasers,” J. Mod. Opt. 55, 447–458(2008).
[CrossRef]

B. Macke and B. Ségard, “Slow light in saturable absorbers,” Phys. Rev. A 78, 013817 (2008).
[CrossRef]

S. Melle, O. G. Calderón, C. E. Caro, E. Cabrera-Granado, M. A. Antón, and F. Carreño, “Modulation-frequency-controlled change from sub- to superluminal regime in highly doped erbium fibers,” Opt. Lett. 33, 827–829 (2008).
[CrossRef] [PubMed]

S. Wen and S. Chi, “Propagation characteristics of fast light in an erbium-doped fiber amplifier,” J. Opt. Soc. Am. B 25, 1073–1080(2008).
[CrossRef]

O. G. Calderón, S. Melle, F. Arrieta-Yáñez, M. A. Antón, and F. Carreño, “Effect of ion pairs in fast-light bandwidth in high-concentration erbium-doped fibers,” J. Opt. Soc. Am. B 25, C55–C60 (2008).
[CrossRef]

O. G. Calderón, S. Melle, M. A. Antón, F. Carreño, F. Arrieta-Yáñez, and E. Cabrera-Granado, “Propagation-induced transition from slow to fast light in highly doped erbium fibers,” Phys. Rev. A 78, 053812 (2008).
[CrossRef]

2007 (7)

2006 (6)

R. W. Boyd, D. J. Gauthier, and A. L. Gaeta, “Applications of slow light in telecommunications,” Opt. Photon. News 17, 18–23(2006).
[CrossRef]

A. Schweinsberg, N. N. Lepeshkin, M. S. Bigelow, R. W. Boyd, and S. Jarabo, “Observation of superluminal and slow light propagation in erbium-doped optical fiber,” Europhys. Lett. 73, 218–224 (2006).
[CrossRef]

G. M. Gehring, A. Schweinsberg, C. Barsi, N. Kostinski, and R. W. Boyd, “Observation of backward pulse propagation through a medium with a negative group velocity,” Science 312, 895–897(2006).
[CrossRef] [PubMed]

M. S. Bigelow, N. N. Lepeshkin, H. Shin, and R. W. Boyd, “Propagation of smooth and discontinuous pulses through materials with very large or very small group velocities,” J. Phys. Condens. Matter 18, 3117–3126 (2006).
[CrossRef]

H. Su, P. Kondratko, and S. L. Chuang, “Variable optical delay using population oscillation and four-wave-mixing in semiconductor optical amplifiers,” Opt. Express 14, 4800–4807(2006).
[CrossRef] [PubMed]

S. Chin, M. Gonzalez-Herraez, and L. Thévanaz, “Zero-gain slow & fast light propagation in an optical fiber,” Opt. Express 14, 10684–10692 (2006).
[CrossRef] [PubMed]

2005 (2)

J. Mørk, R. Kjær, M. van der Poel, and K. Yvind, “Slow light in a semiconductor waveguide at gigahertz frequencies,” Opt. Express 13, 8136–8145 (2005).
[CrossRef] [PubMed]

P. Wu and D. V. G. L. N. Rao, “Controllable snail-paced light in biological bacteriorhodopsin thin film,” Phys. Rev. Lett. 95, 253601 (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, 200–202 (2003).
[CrossRef] [PubMed]

1993 (1)

F. Sanchez, P. L. Boudec, P.-L. Francois, and G. Stephan, “Effects of ion pairs on the dynamics of erbium-doped fiber lasers,” Phys. Rev. A 48, 2220–2229 (1993).
[CrossRef] [PubMed]

Antón, M. A.

O. G. Calderón, S. Melle, M. A. Antón, F. Carreño, F. Arrieta-Yáñez, and E. Cabrera-Granado, “Propagation-induced transition from slow to fast light in highly doped erbium fibers,” Phys. Rev. A 78, 053812 (2008).
[CrossRef]

S. Melle, O. G. Calderón, C. E. Caro, E. Cabrera-Granado, M. A. Antón, and F. Carreño, “Modulation-frequency-controlled change from sub- to superluminal regime in highly doped erbium fibers,” Opt. Lett. 33, 827–829 (2008).
[CrossRef] [PubMed]

O. G. Calderón, S. Melle, F. Arrieta-Yáñez, M. A. Antón, and F. Carreño, “Effect of ion pairs in fast-light bandwidth in high-concentration erbium-doped fibers,” J. Opt. Soc. Am. B 25, C55–C60 (2008).
[CrossRef]

S. Melle, O. G. Calderón, F. Carreño, E. Cabrera, M. A. Antón, and S. Jarabo, “Effect of ion concentration on slow light propagation in highly doped erbium fibers,” Opt. Commun. 279, 53–63 (2007).
[CrossRef]

Arrieta-Yáñez, F.

O. G. Calderón, S. Melle, M. A. Antón, F. Carreño, F. Arrieta-Yáñez, and E. Cabrera-Granado, “Propagation-induced transition from slow to fast light in highly doped erbium fibers,” Phys. Rev. A 78, 053812 (2008).
[CrossRef]

O. G. Calderón, S. Melle, F. Arrieta-Yáñez, M. A. Antón, and F. Carreño, “Effect of ion pairs in fast-light bandwidth in high-concentration erbium-doped fibers,” J. Opt. Soc. Am. B 25, C55–C60 (2008).
[CrossRef]

Barsi, C.

G. M. Gehring, A. Schweinsberg, C. Barsi, N. Kostinski, and R. W. Boyd, “Observation of backward pulse propagation through a medium with a negative group velocity,” Science 312, 895–897(2006).
[CrossRef] [PubMed]

Bigelow, M. S.

M. S. Bigelow, N. N. Lepeshkin, H. Shin, and R. W. Boyd, “Propagation of smooth and discontinuous pulses through materials with very large or very small group velocities,” J. Phys. Condens. Matter 18, 3117–3126 (2006).
[CrossRef]

A. Schweinsberg, N. N. Lepeshkin, M. S. Bigelow, R. W. Boyd, and S. Jarabo, “Observation of superluminal and slow light propagation in erbium-doped optical fiber,” Europhys. Lett. 73, 218–224 (2006).
[CrossRef]

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, 200–202 (2003).
[CrossRef] [PubMed]

Boudec, P. L.

F. Sanchez, P. L. Boudec, P.-L. Francois, and G. Stephan, “Effects of ion pairs on the dynamics of erbium-doped fiber lasers,” Phys. Rev. A 48, 2220–2229 (1993).
[CrossRef] [PubMed]

Boyd, R. W.

H. Shin, A. Schweinsberg, and R. W. Boyd, “Reducing pulse distortion in fast-light pulse propagation through and erbium-doped fiber amplifier using a mutually incoherent background field,” Opt. Commun. 282, 2085–2087 (2009).
[CrossRef]

Z. Shi, R. W. Boyd, D. J. Gauthier, and C. C. Dudley, “Enhancing the spectral sensitivity of interferometers using slow-light media,” Opt. Lett. 32, 915–917 (2007).
[CrossRef] [PubMed]

H. Shin, A. Schweinsberg, G. Gehring, K. Schwertz, H. J. Chang, R. W. Boyd, Q-H. Park, and D. J. Gauthier, “Reducing pulse distortion in fast light pulse propagation through an erbium doped fiber amplifier,” Opt. Lett. 32, 906–908 (2007).
[CrossRef] [PubMed]

G. Piredda and R. W. Boyd, “Slow light by means of coherent population oscillations: laser linewidth effects,” J. Eur. Opt. Soc. Rap. Commun. 2, 07004 (2007).
[CrossRef]

R. W. Boyd, D. J. Gauthier, and A. L. Gaeta, “Applications of slow light in telecommunications,” Opt. Photon. News 17, 18–23(2006).
[CrossRef]

A. Schweinsberg, N. N. Lepeshkin, M. S. Bigelow, R. W. Boyd, and S. Jarabo, “Observation of superluminal and slow light propagation in erbium-doped optical fiber,” Europhys. Lett. 73, 218–224 (2006).
[CrossRef]

G. M. Gehring, A. Schweinsberg, C. Barsi, N. Kostinski, and R. W. Boyd, “Observation of backward pulse propagation through a medium with a negative group velocity,” Science 312, 895–897(2006).
[CrossRef] [PubMed]

M. S. Bigelow, N. N. Lepeshkin, H. Shin, and R. W. Boyd, “Propagation of smooth and discontinuous pulses through materials with very large or very small group velocities,” J. Phys. Condens. Matter 18, 3117–3126 (2006).
[CrossRef]

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, 200–202 (2003).
[CrossRef] [PubMed]

Cabrera, E.

S. Melle, O. G. Calderón, F. Carreño, E. Cabrera, M. A. Antón, and S. Jarabo, “Effect of ion concentration on slow light propagation in highly doped erbium fibers,” Opt. Commun. 279, 53–63 (2007).
[CrossRef]

Cabrera-Granado, E.

O. G. Calderón, S. Melle, M. A. Antón, F. Carreño, F. Arrieta-Yáñez, and E. Cabrera-Granado, “Propagation-induced transition from slow to fast light in highly doped erbium fibers,” Phys. Rev. A 78, 053812 (2008).
[CrossRef]

S. Melle, O. G. Calderón, C. E. Caro, E. Cabrera-Granado, M. A. Antón, and F. Carreño, “Modulation-frequency-controlled change from sub- to superluminal regime in highly doped erbium fibers,” Opt. Lett. 33, 827–829 (2008).
[CrossRef] [PubMed]

Calderón, O. G.

S. Melle, O. G. Calderón, C. E. Caro, E. Cabrera-Granado, M. A. Antón, and F. Carreño, “Modulation-frequency-controlled change from sub- to superluminal regime in highly doped erbium fibers,” Opt. Lett. 33, 827–829 (2008).
[CrossRef] [PubMed]

O. G. Calderón, S. Melle, F. Arrieta-Yáñez, M. A. Antón, and F. Carreño, “Effect of ion pairs in fast-light bandwidth in high-concentration erbium-doped fibers,” J. Opt. Soc. Am. B 25, C55–C60 (2008).
[CrossRef]

O. G. Calderón, S. Melle, M. A. Antón, F. Carreño, F. Arrieta-Yáñez, and E. Cabrera-Granado, “Propagation-induced transition from slow to fast light in highly doped erbium fibers,” Phys. Rev. A 78, 053812 (2008).
[CrossRef]

S. Melle, O. G. Calderón, F. Carreño, E. Cabrera, M. A. Antón, and S. Jarabo, “Effect of ion concentration on slow light propagation in highly doped erbium fibers,” Opt. Commun. 279, 53–63 (2007).
[CrossRef]

Capmany, J.

S. S. Maicas, F. Öhman, J. Capmany, and J. Mørk, “Controlling microwave signals by means of slow and fast light effects in SOA-EA structures,” IEEE Photon. Technol. Lett. 19, 1589–1591(2007).
[CrossRef]

Caro, C. E.

Carreño, F.

S. Melle, O. G. Calderón, C. E. Caro, E. Cabrera-Granado, M. A. Antón, and F. Carreño, “Modulation-frequency-controlled change from sub- to superluminal regime in highly doped erbium fibers,” Opt. Lett. 33, 827–829 (2008).
[CrossRef] [PubMed]

O. G. Calderón, S. Melle, F. Arrieta-Yáñez, M. A. Antón, and F. Carreño, “Effect of ion pairs in fast-light bandwidth in high-concentration erbium-doped fibers,” J. Opt. Soc. Am. B 25, C55–C60 (2008).
[CrossRef]

O. G. Calderón, S. Melle, M. A. Antón, F. Carreño, F. Arrieta-Yáñez, and E. Cabrera-Granado, “Propagation-induced transition from slow to fast light in highly doped erbium fibers,” Phys. Rev. A 78, 053812 (2008).
[CrossRef]

S. Melle, O. G. Calderón, F. Carreño, E. Cabrera, M. A. Antón, and S. Jarabo, “Effect of ion concentration on slow light propagation in highly doped erbium fibers,” Opt. Commun. 279, 53–63 (2007).
[CrossRef]

Chang, H. J.

Chang-Hasnain, C. J.

Chi, S.

Chin, S.

Chuang, S. L.

Duan, K.

J. Li, K. Duan, Y. Wang, W. Zhao, J. Zhu, Y. Guo, and X. Lin, “Modeling and effects of ions pairs in high-concentration-erbium-doped fiber lasers,” J. Mod. Opt. 55, 447–458(2008).
[CrossRef]

Dudley, C. C.

Francois, P.-L.

F. Sanchez, P. L. Boudec, P.-L. Francois, and G. Stephan, “Effects of ion pairs on the dynamics of erbium-doped fiber lasers,” Phys. Rev. A 48, 2220–2229 (1993).
[CrossRef] [PubMed]

Gaeta, A. L.

R. W. Boyd, D. J. Gauthier, and A. L. Gaeta, “Applications of slow light in telecommunications,” Opt. Photon. News 17, 18–23(2006).
[CrossRef]

Gauthier, D. J.

Gehring, G.

Gehring, G. M.

G. M. Gehring, A. Schweinsberg, C. Barsi, N. Kostinski, and R. W. Boyd, “Observation of backward pulse propagation through a medium with a negative group velocity,” Science 312, 895–897(2006).
[CrossRef] [PubMed]

Gonzalez-Herraez, M.

Guo, Y.

J. Li, K. Duan, Y. Wang, W. Zhao, J. Zhu, Y. Guo, and X. Lin, “Modeling and effects of ions pairs in high-concentration-erbium-doped fiber lasers,” J. Mod. Opt. 55, 447–458(2008).
[CrossRef]

Jarabo, S.

S. Melle, O. G. Calderón, F. Carreño, E. Cabrera, M. A. Antón, and S. Jarabo, “Effect of ion concentration on slow light propagation in highly doped erbium fibers,” Opt. Commun. 279, 53–63 (2007).
[CrossRef]

A. Schweinsberg, N. N. Lepeshkin, M. S. Bigelow, R. W. Boyd, and S. Jarabo, “Observation of superluminal and slow light propagation in erbium-doped optical fiber,” Europhys. Lett. 73, 218–224 (2006).
[CrossRef]

Kjær, R.

Ko, W. S.

Kondratko, P.

Kostinski, N.

G. M. Gehring, A. Schweinsberg, C. Barsi, N. Kostinski, and R. W. Boyd, “Observation of backward pulse propagation through a medium with a negative group velocity,” Science 312, 895–897(2006).
[CrossRef] [PubMed]

Lepeshkin, N. N.

M. S. Bigelow, N. N. Lepeshkin, H. Shin, and R. W. Boyd, “Propagation of smooth and discontinuous pulses through materials with very large or very small group velocities,” J. Phys. Condens. Matter 18, 3117–3126 (2006).
[CrossRef]

A. Schweinsberg, N. N. Lepeshkin, M. S. Bigelow, R. W. Boyd, and S. Jarabo, “Observation of superluminal and slow light propagation in erbium-doped optical fiber,” Europhys. Lett. 73, 218–224 (2006).
[CrossRef]

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, 200–202 (2003).
[CrossRef] [PubMed]

Li, J.

J. Li, K. Duan, Y. Wang, W. Zhao, J. Zhu, Y. Guo, and X. Lin, “Modeling and effects of ions pairs in high-concentration-erbium-doped fiber lasers,” J. Mod. Opt. 55, 447–458(2008).
[CrossRef]

Li, Z.

Lin, J.

Lin, X.

J. Li, K. Duan, Y. Wang, W. Zhao, J. Zhu, Y. Guo, and X. Lin, “Modeling and effects of ions pairs in high-concentration-erbium-doped fiber lasers,” J. Mod. Opt. 55, 447–458(2008).
[CrossRef]

Macke, B.

B. Macke and B. Ségard, “Slow light in saturable absorbers,” Phys. Rev. A 78, 013817 (2008).
[CrossRef]

Maicas, S.

S. S. Maicas, F. Öhman, J. Capmany, and J. Mørk, “Controlling microwave signals by means of slow and fast light effects in SOA-EA structures,” IEEE Photon. Technol. Lett. 19, 1589–1591(2007).
[CrossRef]

Melle, S.

O. G. Calderón, S. Melle, M. A. Antón, F. Carreño, F. Arrieta-Yáñez, and E. Cabrera-Granado, “Propagation-induced transition from slow to fast light in highly doped erbium fibers,” Phys. Rev. A 78, 053812 (2008).
[CrossRef]

S. Melle, O. G. Calderón, C. E. Caro, E. Cabrera-Granado, M. A. Antón, and F. Carreño, “Modulation-frequency-controlled change from sub- to superluminal regime in highly doped erbium fibers,” Opt. Lett. 33, 827–829 (2008).
[CrossRef] [PubMed]

O. G. Calderón, S. Melle, F. Arrieta-Yáñez, M. A. Antón, and F. Carreño, “Effect of ion pairs in fast-light bandwidth in high-concentration erbium-doped fibers,” J. Opt. Soc. Am. B 25, C55–C60 (2008).
[CrossRef]

S. Melle, O. G. Calderón, F. Carreño, E. Cabrera, M. A. Antón, and S. Jarabo, “Effect of ion concentration on slow light propagation in highly doped erbium fibers,” Opt. Commun. 279, 53–63 (2007).
[CrossRef]

Mørk, J.

S. S. Maicas, F. Öhman, J. Capmany, and J. Mørk, “Controlling microwave signals by means of slow and fast light effects in SOA-EA structures,” IEEE Photon. Technol. Lett. 19, 1589–1591(2007).
[CrossRef]

J. Mørk, R. Kjær, M. van der Poel, and K. Yvind, “Slow light in a semiconductor waveguide at gigahertz frequencies,” Opt. Express 13, 8136–8145 (2005).
[CrossRef] [PubMed]

Öhman, F.

S. S. Maicas, F. Öhman, J. Capmany, and J. Mørk, “Controlling microwave signals by means of slow and fast light effects in SOA-EA structures,” IEEE Photon. Technol. Lett. 19, 1589–1591(2007).
[CrossRef]

Park, Q-H.

Peng, C.

Pesala, B.

Piredda, G.

G. Piredda and R. W. Boyd, “Slow light by means of coherent population oscillations: laser linewidth effects,” J. Eur. Opt. Soc. Rap. Commun. 2, 07004 (2007).
[CrossRef]

Rao, D. V. G. L. N.

P. Wu and D. V. G. L. N. Rao, “Controllable snail-paced light in biological bacteriorhodopsin thin film,” Phys. Rev. Lett. 95, 253601 (2005).
[CrossRef] [PubMed]

Sanchez, F.

F. Sanchez, P. L. Boudec, P.-L. Francois, and G. Stephan, “Effects of ion pairs on the dynamics of erbium-doped fiber lasers,” Phys. Rev. A 48, 2220–2229 (1993).
[CrossRef] [PubMed]

Schweinsberg, A.

H. Shin, A. Schweinsberg, and R. W. Boyd, “Reducing pulse distortion in fast-light pulse propagation through and erbium-doped fiber amplifier using a mutually incoherent background field,” Opt. Commun. 282, 2085–2087 (2009).
[CrossRef]

H. Shin, A. Schweinsberg, G. Gehring, K. Schwertz, H. J. Chang, R. W. Boyd, Q-H. Park, and D. J. Gauthier, “Reducing pulse distortion in fast light pulse propagation through an erbium doped fiber amplifier,” Opt. Lett. 32, 906–908 (2007).
[CrossRef] [PubMed]

G. M. Gehring, A. Schweinsberg, C. Barsi, N. Kostinski, and R. W. Boyd, “Observation of backward pulse propagation through a medium with a negative group velocity,” Science 312, 895–897(2006).
[CrossRef] [PubMed]

A. Schweinsberg, N. N. Lepeshkin, M. S. Bigelow, R. W. Boyd, and S. Jarabo, “Observation of superluminal and slow light propagation in erbium-doped optical fiber,” Europhys. Lett. 73, 218–224 (2006).
[CrossRef]

Schwertz, K.

Sedgwick, F. G.

Ségard, B.

B. Macke and B. Ségard, “Slow light in saturable absorbers,” Phys. Rev. A 78, 013817 (2008).
[CrossRef]

Shi, Z.

Shin, H.

H. Shin, A. Schweinsberg, and R. W. Boyd, “Reducing pulse distortion in fast-light pulse propagation through and erbium-doped fiber amplifier using a mutually incoherent background field,” Opt. Commun. 282, 2085–2087 (2009).
[CrossRef]

H. Shin, A. Schweinsberg, G. Gehring, K. Schwertz, H. J. Chang, R. W. Boyd, Q-H. Park, and D. J. Gauthier, “Reducing pulse distortion in fast light pulse propagation through an erbium doped fiber amplifier,” Opt. Lett. 32, 906–908 (2007).
[CrossRef] [PubMed]

M. S. Bigelow, N. N. Lepeshkin, H. Shin, and R. W. Boyd, “Propagation of smooth and discontinuous pulses through materials with very large or very small group velocities,” J. Phys. Condens. Matter 18, 3117–3126 (2006).
[CrossRef]

Stephan, G.

F. Sanchez, P. L. Boudec, P.-L. Francois, and G. Stephan, “Effects of ion pairs on the dynamics of erbium-doped fiber lasers,” Phys. Rev. A 48, 2220–2229 (1993).
[CrossRef] [PubMed]

Su, H.

Thévanaz, L.

van der Poel, M.

Wang, Y.

J. Li, K. Duan, Y. Wang, W. Zhao, J. Zhu, Y. Guo, and X. Lin, “Modeling and effects of ions pairs in high-concentration-erbium-doped fiber lasers,” J. Mod. Opt. 55, 447–458(2008).
[CrossRef]

Wen, S.

Wu, P.

P. Wu and D. V. G. L. N. Rao, “Controllable snail-paced light in biological bacteriorhodopsin thin film,” Phys. Rev. Lett. 95, 253601 (2005).
[CrossRef] [PubMed]

Xu, A.

Yvind, K.

Zhao, W.

J. Li, K. Duan, Y. Wang, W. Zhao, J. Zhu, Y. Guo, and X. Lin, “Modeling and effects of ions pairs in high-concentration-erbium-doped fiber lasers,” J. Mod. Opt. 55, 447–458(2008).
[CrossRef]

Zhao, X.

Zhu, J.

J. Li, K. Duan, Y. Wang, W. Zhao, J. Zhu, Y. Guo, and X. Lin, “Modeling and effects of ions pairs in high-concentration-erbium-doped fiber lasers,” J. Mod. Opt. 55, 447–458(2008).
[CrossRef]

Appl. Opt. (1)

Europhys. Lett. (1)

A. Schweinsberg, N. N. Lepeshkin, M. S. Bigelow, R. W. Boyd, and S. Jarabo, “Observation of superluminal and slow light propagation in erbium-doped optical fiber,” Europhys. Lett. 73, 218–224 (2006).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

S. S. Maicas, F. Öhman, J. Capmany, and J. Mørk, “Controlling microwave signals by means of slow and fast light effects in SOA-EA structures,” IEEE Photon. Technol. Lett. 19, 1589–1591(2007).
[CrossRef]

J. Eur. Opt. Soc. Rap. Commun. (1)

G. Piredda and R. W. Boyd, “Slow light by means of coherent population oscillations: laser linewidth effects,” J. Eur. Opt. Soc. Rap. Commun. 2, 07004 (2007).
[CrossRef]

J. Mod. Opt. (1)

J. Li, K. Duan, Y. Wang, W. Zhao, J. Zhu, Y. Guo, and X. Lin, “Modeling and effects of ions pairs in high-concentration-erbium-doped fiber lasers,” J. Mod. Opt. 55, 447–458(2008).
[CrossRef]

J. Opt. Soc. Am. B (2)

J. Phys. Condens. Matter (1)

M. S. Bigelow, N. N. Lepeshkin, H. Shin, and R. W. Boyd, “Propagation of smooth and discontinuous pulses through materials with very large or very small group velocities,” J. Phys. Condens. Matter 18, 3117–3126 (2006).
[CrossRef]

Opt. Commun. (2)

H. Shin, A. Schweinsberg, and R. W. Boyd, “Reducing pulse distortion in fast-light pulse propagation through and erbium-doped fiber amplifier using a mutually incoherent background field,” Opt. Commun. 282, 2085–2087 (2009).
[CrossRef]

S. Melle, O. G. Calderón, F. Carreño, E. Cabrera, M. A. Antón, and S. Jarabo, “Effect of ion concentration on slow light propagation in highly doped erbium fibers,” Opt. Commun. 279, 53–63 (2007).
[CrossRef]

Opt. Express (4)

Opt. Lett. (3)

Opt. Photon. News (1)

R. W. Boyd, D. J. Gauthier, and A. L. Gaeta, “Applications of slow light in telecommunications,” Opt. Photon. News 17, 18–23(2006).
[CrossRef]

Phys. Rev. A (3)

O. G. Calderón, S. Melle, M. A. Antón, F. Carreño, F. Arrieta-Yáñez, and E. Cabrera-Granado, “Propagation-induced transition from slow to fast light in highly doped erbium fibers,” Phys. Rev. A 78, 053812 (2008).
[CrossRef]

F. Sanchez, P. L. Boudec, P.-L. Francois, and G. Stephan, “Effects of ion pairs on the dynamics of erbium-doped fiber lasers,” Phys. Rev. A 48, 2220–2229 (1993).
[CrossRef] [PubMed]

B. Macke and B. Ségard, “Slow light in saturable absorbers,” Phys. Rev. A 78, 013817 (2008).
[CrossRef]

Phys. Rev. Lett. (2)

P. Wu and D. V. G. L. N. Rao, “Controllable snail-paced light in biological bacteriorhodopsin thin film,” Phys. Rev. Lett. 95, 253601 (2005).
[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]

Science (2)

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Superluminal and slow light propagation in a room-temperature solid,” Science 301, 200–202 (2003).
[CrossRef] [PubMed]

G. M. Gehring, A. Schweinsberg, C. Barsi, N. Kostinski, and R. W. Boyd, “Observation of backward pulse propagation through a medium with a negative group velocity,” Science 312, 895–897(2006).
[CrossRef] [PubMed]

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Figures (9)

Fig. 1
Fig. 1

Energy levels for (a) isolated Er ions and (b) paired ions.

Fig. 2
Fig. 2

Experimental (symbols) and simulated (curves) fractional delay as a function of inverse of the pulse width (FWHM). (a) Different pump powers and a fixed signal background power ( 3.5 mW ). (b) Different signal background powers and a fixed pump power ( 107 mW ).

Fig. 3
Fig. 3

(a) Simulated signal background (dashed curve) and pump (solid curve) power profiles along 1 m long fiber, normalized to their respective saturation powers. Initial values are 1.8 (signal background power) and 107 mW (pump power). (b) Schematic diagram of the cascade system.

Fig. 4
Fig. 4

Fractional delay versus the inverse of the pulse width in one amplification stage (circles) and in two stages, amplification and absorbtion (triangles). The signal background power was set to 2 mW for both measurements, and the pump power was set to 39 mW in the amplification stage. The theoretical result given by Eq. (17) is also plotted (solid curves).

Fig. 5
Fig. 5

(a) Absorption and (b) phase delay for a pumped EDF (dashed curve), a nonpumped EDF (dotted curve) and for the whole system EDFA + EDF (solid curve) as a function of Ω τ .

Fig. 6
Fig. 6

Spectrum of two pulses (dashed curves) superposed to the refractive index of the system (solid curves). (a) Spectrally narrow pulse (subluminal). (b) Spectrally broad pulse (superluminal).

Fig. 7
Fig. 7

Representative delayed and advanced normalized pulses (solid curve) with their respective reference pulses (dashed curve), for a signal background power of 1.8 mW and a pump power of 107 mW : (a)  1 / τ in = 90 Hz , (b)  1 / τ in = 290 Hz , (c)  1 / τ in = 940 Hz , and (d) magnification of the Gaussian part of the pulse of (c).

Fig. 8
Fig. 8

Measured (dots) and simulated (line) (a) pulse width ratio and (b) distortion versus the inverse of the input pulse width. Both figures correspond to initial powers of 1.8 (background signal) and 107 mW (pump). Pulses (a), (b), and (c) from Fig. 7 correspond to points A, B, and C in this figure.

Fig. 9
Fig. 9

(a) Experimental (symbols) and simulated (curve) maximum fractional delay versus P peak / P b g . (b) Experimental (symbols) and simulated (curve) optimum pulse width, i.e., the pulse width where the maximum fractional delay is achieved versus P peak / P b g .

Equations (18)

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n 1 t = ( 1 2 κ ) n 1 τ + 1 τ P s 2 ( 1 2 κ 2 n 1 ) P p n 1 τ ,
n 11 t = κ n 11 τ + 1 τ P s 2 ( κ 2 n 11 ) P p n 11 τ ,
P s z + n g s c P s t = α s [ 1 2 κ 2 n 1 n 11 ] P s ,
P p z + n g p c P p t = α p [ n 1 + κ ] P p .
n 1 ( t ) = n 1 b g + n 1 m ( t ) = n 1 b g + n ˜ 1 m ( Ω ) e i Ω t d Ω ,
n 11 ( t ) = n 11 b g + n 11 m ( t ) = n 11 b g + n ˜ 11 m ( Ω ) e i Ω t d Ω ,
n 1 b g = ( 1 2 κ ) ( 1 + P b g / 2 ) ω c ,
n 11 b g = 1 + P b g / 2 ω c κ ,
n ˜ 1 m ( Ω ) = ( 1 2 κ ) P ˜ m ( Ω ) / 2 n 1 b g P ˜ m ( Ω ) ω c i Ω τ ,
n ˜ 11 m ( Ω ) = ( P ˜ m ( Ω ) / 2 ) κ n 11 b g P ˜ m ( Ω ) ω c i Ω τ ,
P b g z = α s [ 1 2 κ 2 n 1 b g n 11 b g ] P b g ,
P p z = α p ( n 1 b g + κ ) P p ,
P ˜ m ( Ω ) z = C s P ˜ m ( Ω ) ,
C s = α s ω c [ ( P p 1 ) + κ ( 1 P b g 2 2 P p ) [ ( P p 1 ) + 3 κ 2 ( 1 P p ) ] P b g ω c i Ω τ ] .
φ = L α s P b g Ω τ [ P p 1 ω c 1 ( ω c 1 2 + ( Ω τ ) 2 ) 1 ω c 2 ( ω c 2 2 + ( Ω τ ) 2 ) ] .
α = α s [ P p 1 ω c 1 P b g ( P p 1 ) ω c 1 2 + ( Ω τ ) 2 1 ω c 2 2 + P b g ω c 2 2 + ( Ω τ ) 2 ] .
t d = α s ( P p 1 ) P b g ω c 1 1 ω c 1 2 + 24 ln 2 τ in 2 α s P b g ω c 2 1 ω c 2 2 + 24 ln 2 τ in 2 .
D = ( + | | P out ( t + t d ) | 2 | P in ( t ) | 2 | d t + | P out ( t + t d ) | 2 d t ) 1 / 2 ( + | | P in ( t + δ t ) | 2 | P in ( t ) | 2 | d t + | P out ( t + δ t ) | 2 d t ) 1 / 2 ,

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