Abstract

We investigate theoretically the phenomenon of so-called fast light in an unconventional regime, using pulses sufficiently short that relaxation effects in a gain medium can be ignored completely. We show that previously recognized gain instabilities, including superfluorescence, can be tolerated in achieving a pulse peak advance of more than one full peak width.

© 2007 Optical Society of America

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  1. S. E. Harris, "Electromagetically induced transparency," Phys. Today 50, 36-42 (1997).
    [CrossRef]
  2. P. W. Milonni, Fast Light, Slow Light and Left-Handed Light (IOP, 2005).
  3. R. W. Boyd and D. J. Gauthier, "Slow and fast light," Prog. Opt. 43, 497-530 (2002).
  4. R. Grobe, F. T. Hioe, and J. H. Eberly, "Formation of shape-preserving pulses in a nonlinear adiabatically integrable system," Phys. Rev. Lett. 73, 3183-3186 (1994).
    [CrossRef] [PubMed]
  5. A. Kasapi, M. Jain, G. Y. Yin, and S. E. Harris, "Electromagnetically induced transparency: propagation dynamics," Phys. Rev. Lett. 74, 2447-2450 (1995).
    [CrossRef] [PubMed]
  6. L. J. Wang, A. Kuzmich, and A. Dogariu, "Gain-assisted superluminal light propagation," Nature 406, 277-279 (2000).
    [CrossRef] [PubMed]
  7. P. G. Kryukov and V. S. Letokhov, "Propagation of a light pulse in a resonantly amplifying (absorbing) medium," Sov. Phys. Usp. 12, 641-672 (1970).
    [CrossRef]
  8. M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, "Superluminal and slow light propagation in a room-temperature solid," Science 301, 200202 (2003).
    [CrossRef]
  9. M. D. Stenner, D. J. Gauthier, and M. A. Neifeld, "The speed of information in a 'fast-light' optical medium," Nature 425, 695-698 (2003).
    [CrossRef] [PubMed]
  10. B. Segev, P. W. Milonni, J. F. Babb, and R. Y. Chiao, "Quantum noise and superluminal propagation," Phys. Rev. A 62, 022114 (2000).
    [CrossRef]
  11. N. G. Basov, R. V. Ambartsumyan, V. S. Zuev, P. G. Kryukov, and V. S. Letokhov, "Nonlinear amplification of light pulses," Sov. Phys. JETP 23, 16-22 (1966).
  12. A. Icsevgi and W. E. Lamb, Jr., "Propagation of light pulses in a laser amplifier," Phys. Rev. 185, 517-545 (1969).
    [CrossRef]
  13. B. D. Clader, Q-Han Park, and J. H. Eberly, "Fast light in fully coherent gain media," Opt. Lett. 31, 2921-2923 (2006).
    [CrossRef] [PubMed]
  14. S. L. McCall and E. L. Hahn, "Self-induced transparency," Phys. Rev. 183, 457-485 (1969).
    [CrossRef]
  15. R. H. Dicke, "Coherence in spontaneous radiation processes," Phys. Rev. 93, 99-110 (1954).
    [CrossRef]
  16. Q. H. F. Vrehen and M. F. H. Schuurmans, "Direct measurement of the effective initial tipping angle in superfluorescence," Phys. Rev. Lett. 42, 224-227 (1979).
    [CrossRef]
  17. A. Crubellier, S. Liberman, and P. Pillet, "Superradiance fluctuations in a j=12-->j′=12 atomic system," J. Phys. B 17, 2771-2780 (1984).
    [CrossRef]
  18. Q. H. Park and H. J. Shin, "Matched pulse propagation in a three-level system," Phys. Rev. A 57, 4643-4653 (1992).
    [CrossRef]
  19. A. V. Andreev, "Optical superradiance: new ideas and new experiments," Sov. Phys. Usp. 33, 997-1020 (1990).
    [CrossRef]
  20. A. Rahman and J. H. Eberly, "Theory of shape-preserving short pulses in inhomogeneously broadened three-level media," Phys. Rev. A 58, R805-R808 (1998).
    [CrossRef]
  21. P. W. Milonni, "Controlling the speed of light pulses," J. Phys. B 35, R31-R56 (2002).
    [CrossRef]
  22. For a discussion and extension of the pioneering works of Sommerfeld and Brillouin, see, for example K.E.Oughston and G.C.Sherman, Electromagnetic Pulse Propagation in Causal Dielectrics, corrected ed. (Springer-Verlag, 1997).
  23. G. L. Lamb, Jr., "Amplification of coherent optical pulses," Phys. Rev. A 12, 2052-2059 (1975).
    [CrossRef]
  24. I. R. Gabitov and S. V. Manakov, "Propagation of ultrashort optical pulses in degenerate laser amplifiers," Phys. Rev. Lett. 50, 495-498 (1983).
    [CrossRef]
  25. D. C. Burnham and R. Y. Chiao, "Coherent resonance fluorescence excited by short light pulses," Phys. Rev. 188, 667-675 (1969).
    [CrossRef]
  26. I. R. Gabitov, V. E. Zakharov, and A. V. Mikhailov, "Maxwell-Bloch equation and the inverse scattering method," Theor. Math. Phys. 63, 328-343 (1985).
    [CrossRef]
  27. R. Bonifacio and L. A. Lugiato, "Cooperative radiation processes in two-level systems: superfluorescence," Phys. Rev. A 11, 1507-1521 (1975).
    [CrossRef]
  28. D. Polder, M. F. H. Schuurmans, and Q. H. F. Vrehen, "Superfluorescence: quantum-mechanical derivation of Maxwell-Bloch description with fluctuating field source," Phys. Rev. A 19, 1192-1203 (1979).
    [CrossRef]
  29. J. C. MacGillivray and M. S. Feld, "Theory of superradiance in an extended, optically thick medium," Phys. Rev. A 14, 1169-1189 (1976).
    [CrossRef]
  30. F. Haake, J. W. Haus, H. King, and G. Schröder, "Delay-time statistics of superfluorescent pulses," Phys. Rev. A 23, 1322-1333 (1981).
    [CrossRef]

2006 (1)

2003 (2)

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, "Superluminal and slow light propagation in a room-temperature solid," Science 301, 200202 (2003).
[CrossRef]

M. D. Stenner, D. J. Gauthier, and M. A. Neifeld, "The speed of information in a 'fast-light' optical medium," Nature 425, 695-698 (2003).
[CrossRef] [PubMed]

2002 (2)

R. W. Boyd and D. J. Gauthier, "Slow and fast light," Prog. Opt. 43, 497-530 (2002).

P. W. Milonni, "Controlling the speed of light pulses," J. Phys. B 35, R31-R56 (2002).
[CrossRef]

2000 (2)

B. Segev, P. W. Milonni, J. F. Babb, and R. Y. Chiao, "Quantum noise and superluminal propagation," Phys. Rev. A 62, 022114 (2000).
[CrossRef]

L. J. Wang, A. Kuzmich, and A. Dogariu, "Gain-assisted superluminal light propagation," Nature 406, 277-279 (2000).
[CrossRef] [PubMed]

1998 (1)

A. Rahman and J. H. Eberly, "Theory of shape-preserving short pulses in inhomogeneously broadened three-level media," Phys. Rev. A 58, R805-R808 (1998).
[CrossRef]

1997 (1)

S. E. Harris, "Electromagetically induced transparency," Phys. Today 50, 36-42 (1997).
[CrossRef]

1995 (1)

A. Kasapi, M. Jain, G. Y. Yin, and S. E. Harris, "Electromagnetically induced transparency: propagation dynamics," Phys. Rev. Lett. 74, 2447-2450 (1995).
[CrossRef] [PubMed]

1994 (1)

R. Grobe, F. T. Hioe, and J. H. Eberly, "Formation of shape-preserving pulses in a nonlinear adiabatically integrable system," Phys. Rev. Lett. 73, 3183-3186 (1994).
[CrossRef] [PubMed]

1992 (1)

Q. H. Park and H. J. Shin, "Matched pulse propagation in a three-level system," Phys. Rev. A 57, 4643-4653 (1992).
[CrossRef]

1990 (1)

A. V. Andreev, "Optical superradiance: new ideas and new experiments," Sov. Phys. Usp. 33, 997-1020 (1990).
[CrossRef]

1985 (1)

I. R. Gabitov, V. E. Zakharov, and A. V. Mikhailov, "Maxwell-Bloch equation and the inverse scattering method," Theor. Math. Phys. 63, 328-343 (1985).
[CrossRef]

1984 (1)

A. Crubellier, S. Liberman, and P. Pillet, "Superradiance fluctuations in a j=12-->j′=12 atomic system," J. Phys. B 17, 2771-2780 (1984).
[CrossRef]

1983 (1)

I. R. Gabitov and S. V. Manakov, "Propagation of ultrashort optical pulses in degenerate laser amplifiers," Phys. Rev. Lett. 50, 495-498 (1983).
[CrossRef]

1981 (1)

F. Haake, J. W. Haus, H. King, and G. Schröder, "Delay-time statistics of superfluorescent pulses," Phys. Rev. A 23, 1322-1333 (1981).
[CrossRef]

1979 (2)

D. Polder, M. F. H. Schuurmans, and Q. H. F. Vrehen, "Superfluorescence: quantum-mechanical derivation of Maxwell-Bloch description with fluctuating field source," Phys. Rev. A 19, 1192-1203 (1979).
[CrossRef]

Q. H. F. Vrehen and M. F. H. Schuurmans, "Direct measurement of the effective initial tipping angle in superfluorescence," Phys. Rev. Lett. 42, 224-227 (1979).
[CrossRef]

1976 (1)

J. C. MacGillivray and M. S. Feld, "Theory of superradiance in an extended, optically thick medium," Phys. Rev. A 14, 1169-1189 (1976).
[CrossRef]

1975 (2)

R. Bonifacio and L. A. Lugiato, "Cooperative radiation processes in two-level systems: superfluorescence," Phys. Rev. A 11, 1507-1521 (1975).
[CrossRef]

G. L. Lamb, Jr., "Amplification of coherent optical pulses," Phys. Rev. A 12, 2052-2059 (1975).
[CrossRef]

1970 (1)

P. G. Kryukov and V. S. Letokhov, "Propagation of a light pulse in a resonantly amplifying (absorbing) medium," Sov. Phys. Usp. 12, 641-672 (1970).
[CrossRef]

1969 (3)

S. L. McCall and E. L. Hahn, "Self-induced transparency," Phys. Rev. 183, 457-485 (1969).
[CrossRef]

A. Icsevgi and W. E. Lamb, Jr., "Propagation of light pulses in a laser amplifier," Phys. Rev. 185, 517-545 (1969).
[CrossRef]

D. C. Burnham and R. Y. Chiao, "Coherent resonance fluorescence excited by short light pulses," Phys. Rev. 188, 667-675 (1969).
[CrossRef]

1966 (1)

N. G. Basov, R. V. Ambartsumyan, V. S. Zuev, P. G. Kryukov, and V. S. Letokhov, "Nonlinear amplification of light pulses," Sov. Phys. JETP 23, 16-22 (1966).

1954 (1)

R. H. Dicke, "Coherence in spontaneous radiation processes," Phys. Rev. 93, 99-110 (1954).
[CrossRef]

Ambartsumyan, R. V.

N. G. Basov, R. V. Ambartsumyan, V. S. Zuev, P. G. Kryukov, and V. S. Letokhov, "Nonlinear amplification of light pulses," Sov. Phys. JETP 23, 16-22 (1966).

Andreev, A. V.

A. V. Andreev, "Optical superradiance: new ideas and new experiments," Sov. Phys. Usp. 33, 997-1020 (1990).
[CrossRef]

Babb, J. F.

B. Segev, P. W. Milonni, J. F. Babb, and R. Y. Chiao, "Quantum noise and superluminal propagation," Phys. Rev. A 62, 022114 (2000).
[CrossRef]

Basov, N. G.

N. G. Basov, R. V. Ambartsumyan, V. S. Zuev, P. G. Kryukov, and V. S. Letokhov, "Nonlinear amplification of light pulses," Sov. Phys. JETP 23, 16-22 (1966).

Bigelow, M. S.

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, "Superluminal and slow light propagation in a room-temperature solid," Science 301, 200202 (2003).
[CrossRef]

Bonifacio, R.

R. Bonifacio and L. A. Lugiato, "Cooperative radiation processes in two-level systems: superfluorescence," Phys. Rev. A 11, 1507-1521 (1975).
[CrossRef]

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, 200202 (2003).
[CrossRef]

R. W. Boyd and D. J. Gauthier, "Slow and fast light," Prog. Opt. 43, 497-530 (2002).

Burnham, D. C.

D. C. Burnham and R. Y. Chiao, "Coherent resonance fluorescence excited by short light pulses," Phys. Rev. 188, 667-675 (1969).
[CrossRef]

Chiao, R. Y.

B. Segev, P. W. Milonni, J. F. Babb, and R. Y. Chiao, "Quantum noise and superluminal propagation," Phys. Rev. A 62, 022114 (2000).
[CrossRef]

D. C. Burnham and R. Y. Chiao, "Coherent resonance fluorescence excited by short light pulses," Phys. Rev. 188, 667-675 (1969).
[CrossRef]

Clader, B. D.

Crubellier, A.

A. Crubellier, S. Liberman, and P. Pillet, "Superradiance fluctuations in a j=12-->j′=12 atomic system," J. Phys. B 17, 2771-2780 (1984).
[CrossRef]

Dicke, R. H.

R. H. Dicke, "Coherence in spontaneous radiation processes," Phys. Rev. 93, 99-110 (1954).
[CrossRef]

Dogariu, A.

L. J. Wang, A. Kuzmich, and A. Dogariu, "Gain-assisted superluminal light propagation," Nature 406, 277-279 (2000).
[CrossRef] [PubMed]

Eberly, J. H.

B. D. Clader, Q-Han Park, and J. H. Eberly, "Fast light in fully coherent gain media," Opt. Lett. 31, 2921-2923 (2006).
[CrossRef] [PubMed]

A. Rahman and J. H. Eberly, "Theory of shape-preserving short pulses in inhomogeneously broadened three-level media," Phys. Rev. A 58, R805-R808 (1998).
[CrossRef]

R. Grobe, F. T. Hioe, and J. H. Eberly, "Formation of shape-preserving pulses in a nonlinear adiabatically integrable system," Phys. Rev. Lett. 73, 3183-3186 (1994).
[CrossRef] [PubMed]

Feld, M. S.

J. C. MacGillivray and M. S. Feld, "Theory of superradiance in an extended, optically thick medium," Phys. Rev. A 14, 1169-1189 (1976).
[CrossRef]

Gabitov, I. R.

I. R. Gabitov, V. E. Zakharov, and A. V. Mikhailov, "Maxwell-Bloch equation and the inverse scattering method," Theor. Math. Phys. 63, 328-343 (1985).
[CrossRef]

I. R. Gabitov and S. V. Manakov, "Propagation of ultrashort optical pulses in degenerate laser amplifiers," Phys. Rev. Lett. 50, 495-498 (1983).
[CrossRef]

Gauthier, D. J.

M. D. Stenner, D. J. Gauthier, and M. A. Neifeld, "The speed of information in a 'fast-light' optical medium," Nature 425, 695-698 (2003).
[CrossRef] [PubMed]

R. W. Boyd and D. J. Gauthier, "Slow and fast light," Prog. Opt. 43, 497-530 (2002).

Grobe, R.

R. Grobe, F. T. Hioe, and J. H. Eberly, "Formation of shape-preserving pulses in a nonlinear adiabatically integrable system," Phys. Rev. Lett. 73, 3183-3186 (1994).
[CrossRef] [PubMed]

Haake, F.

F. Haake, J. W. Haus, H. King, and G. Schröder, "Delay-time statistics of superfluorescent pulses," Phys. Rev. A 23, 1322-1333 (1981).
[CrossRef]

Hahn, E. L.

S. L. McCall and E. L. Hahn, "Self-induced transparency," Phys. Rev. 183, 457-485 (1969).
[CrossRef]

Harris, S. E.

S. E. Harris, "Electromagetically induced transparency," Phys. Today 50, 36-42 (1997).
[CrossRef]

A. Kasapi, M. Jain, G. Y. Yin, and S. E. Harris, "Electromagnetically induced transparency: propagation dynamics," Phys. Rev. Lett. 74, 2447-2450 (1995).
[CrossRef] [PubMed]

Haus, J. W.

F. Haake, J. W. Haus, H. King, and G. Schröder, "Delay-time statistics of superfluorescent pulses," Phys. Rev. A 23, 1322-1333 (1981).
[CrossRef]

Hioe, F. T.

R. Grobe, F. T. Hioe, and J. H. Eberly, "Formation of shape-preserving pulses in a nonlinear adiabatically integrable system," Phys. Rev. Lett. 73, 3183-3186 (1994).
[CrossRef] [PubMed]

Icsevgi, A.

A. Icsevgi and W. E. Lamb, Jr., "Propagation of light pulses in a laser amplifier," Phys. Rev. 185, 517-545 (1969).
[CrossRef]

Jain, M.

A. Kasapi, M. Jain, G. Y. Yin, and S. E. Harris, "Electromagnetically induced transparency: propagation dynamics," Phys. Rev. Lett. 74, 2447-2450 (1995).
[CrossRef] [PubMed]

Kasapi, A.

A. Kasapi, M. Jain, G. Y. Yin, and S. E. Harris, "Electromagnetically induced transparency: propagation dynamics," Phys. Rev. Lett. 74, 2447-2450 (1995).
[CrossRef] [PubMed]

King, H.

F. Haake, J. W. Haus, H. King, and G. Schröder, "Delay-time statistics of superfluorescent pulses," Phys. Rev. A 23, 1322-1333 (1981).
[CrossRef]

Kryukov, P. G.

P. G. Kryukov and V. S. Letokhov, "Propagation of a light pulse in a resonantly amplifying (absorbing) medium," Sov. Phys. Usp. 12, 641-672 (1970).
[CrossRef]

N. G. Basov, R. V. Ambartsumyan, V. S. Zuev, P. G. Kryukov, and V. S. Letokhov, "Nonlinear amplification of light pulses," Sov. Phys. JETP 23, 16-22 (1966).

Kuzmich, A.

L. J. Wang, A. Kuzmich, and A. Dogariu, "Gain-assisted superluminal light propagation," Nature 406, 277-279 (2000).
[CrossRef] [PubMed]

Lamb, G. L.

G. L. Lamb, Jr., "Amplification of coherent optical pulses," Phys. Rev. A 12, 2052-2059 (1975).
[CrossRef]

Lamb, W. E.

A. Icsevgi and W. E. Lamb, Jr., "Propagation of light pulses in a laser amplifier," Phys. Rev. 185, 517-545 (1969).
[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, 200202 (2003).
[CrossRef]

Letokhov, V. S.

P. G. Kryukov and V. S. Letokhov, "Propagation of a light pulse in a resonantly amplifying (absorbing) medium," Sov. Phys. Usp. 12, 641-672 (1970).
[CrossRef]

N. G. Basov, R. V. Ambartsumyan, V. S. Zuev, P. G. Kryukov, and V. S. Letokhov, "Nonlinear amplification of light pulses," Sov. Phys. JETP 23, 16-22 (1966).

Liberman, S.

A. Crubellier, S. Liberman, and P. Pillet, "Superradiance fluctuations in a j=12-->j′=12 atomic system," J. Phys. B 17, 2771-2780 (1984).
[CrossRef]

Lugiato, L. A.

R. Bonifacio and L. A. Lugiato, "Cooperative radiation processes in two-level systems: superfluorescence," Phys. Rev. A 11, 1507-1521 (1975).
[CrossRef]

MacGillivray, J. C.

J. C. MacGillivray and M. S. Feld, "Theory of superradiance in an extended, optically thick medium," Phys. Rev. A 14, 1169-1189 (1976).
[CrossRef]

Manakov, S. V.

I. R. Gabitov and S. V. Manakov, "Propagation of ultrashort optical pulses in degenerate laser amplifiers," Phys. Rev. Lett. 50, 495-498 (1983).
[CrossRef]

McCall, S. L.

S. L. McCall and E. L. Hahn, "Self-induced transparency," Phys. Rev. 183, 457-485 (1969).
[CrossRef]

Mikhailov, A. V.

I. R. Gabitov, V. E. Zakharov, and A. V. Mikhailov, "Maxwell-Bloch equation and the inverse scattering method," Theor. Math. Phys. 63, 328-343 (1985).
[CrossRef]

Milonni, P. W.

P. W. Milonni, "Controlling the speed of light pulses," J. Phys. B 35, R31-R56 (2002).
[CrossRef]

B. Segev, P. W. Milonni, J. F. Babb, and R. Y. Chiao, "Quantum noise and superluminal propagation," Phys. Rev. A 62, 022114 (2000).
[CrossRef]

P. W. Milonni, Fast Light, Slow Light and Left-Handed Light (IOP, 2005).

Neifeld, M. A.

M. D. Stenner, D. J. Gauthier, and M. A. Neifeld, "The speed of information in a 'fast-light' optical medium," Nature 425, 695-698 (2003).
[CrossRef] [PubMed]

Park, Q. H.

Q. H. Park and H. J. Shin, "Matched pulse propagation in a three-level system," Phys. Rev. A 57, 4643-4653 (1992).
[CrossRef]

Park, Q-Han

Pillet, P.

A. Crubellier, S. Liberman, and P. Pillet, "Superradiance fluctuations in a j=12-->j′=12 atomic system," J. Phys. B 17, 2771-2780 (1984).
[CrossRef]

Polder, D.

D. Polder, M. F. H. Schuurmans, and Q. H. F. Vrehen, "Superfluorescence: quantum-mechanical derivation of Maxwell-Bloch description with fluctuating field source," Phys. Rev. A 19, 1192-1203 (1979).
[CrossRef]

Rahman, A.

A. Rahman and J. H. Eberly, "Theory of shape-preserving short pulses in inhomogeneously broadened three-level media," Phys. Rev. A 58, R805-R808 (1998).
[CrossRef]

Schröder, G.

F. Haake, J. W. Haus, H. King, and G. Schröder, "Delay-time statistics of superfluorescent pulses," Phys. Rev. A 23, 1322-1333 (1981).
[CrossRef]

Schuurmans, M. F. H.

D. Polder, M. F. H. Schuurmans, and Q. H. F. Vrehen, "Superfluorescence: quantum-mechanical derivation of Maxwell-Bloch description with fluctuating field source," Phys. Rev. A 19, 1192-1203 (1979).
[CrossRef]

Q. H. F. Vrehen and M. F. H. Schuurmans, "Direct measurement of the effective initial tipping angle in superfluorescence," Phys. Rev. Lett. 42, 224-227 (1979).
[CrossRef]

Segev, B.

B. Segev, P. W. Milonni, J. F. Babb, and R. Y. Chiao, "Quantum noise and superluminal propagation," Phys. Rev. A 62, 022114 (2000).
[CrossRef]

Shin, H. J.

Q. H. Park and H. J. Shin, "Matched pulse propagation in a three-level system," Phys. Rev. A 57, 4643-4653 (1992).
[CrossRef]

Stenner, M. D.

M. D. Stenner, D. J. Gauthier, and M. A. Neifeld, "The speed of information in a 'fast-light' optical medium," Nature 425, 695-698 (2003).
[CrossRef] [PubMed]

Vrehen, Q. H. F.

Q. H. F. Vrehen and M. F. H. Schuurmans, "Direct measurement of the effective initial tipping angle in superfluorescence," Phys. Rev. Lett. 42, 224-227 (1979).
[CrossRef]

D. Polder, M. F. H. Schuurmans, and Q. H. F. Vrehen, "Superfluorescence: quantum-mechanical derivation of Maxwell-Bloch description with fluctuating field source," Phys. Rev. A 19, 1192-1203 (1979).
[CrossRef]

Wang, L. J.

L. J. Wang, A. Kuzmich, and A. Dogariu, "Gain-assisted superluminal light propagation," Nature 406, 277-279 (2000).
[CrossRef] [PubMed]

Yin, G. Y.

A. Kasapi, M. Jain, G. Y. Yin, and S. E. Harris, "Electromagnetically induced transparency: propagation dynamics," Phys. Rev. Lett. 74, 2447-2450 (1995).
[CrossRef] [PubMed]

Zakharov, V. E.

I. R. Gabitov, V. E. Zakharov, and A. V. Mikhailov, "Maxwell-Bloch equation and the inverse scattering method," Theor. Math. Phys. 63, 328-343 (1985).
[CrossRef]

Zuev, V. S.

N. G. Basov, R. V. Ambartsumyan, V. S. Zuev, P. G. Kryukov, and V. S. Letokhov, "Nonlinear amplification of light pulses," Sov. Phys. JETP 23, 16-22 (1966).

J. Phys. B (2)

A. Crubellier, S. Liberman, and P. Pillet, "Superradiance fluctuations in a j=12-->j′=12 atomic system," J. Phys. B 17, 2771-2780 (1984).
[CrossRef]

P. W. Milonni, "Controlling the speed of light pulses," J. Phys. B 35, R31-R56 (2002).
[CrossRef]

Nature (2)

M. D. Stenner, D. J. Gauthier, and M. A. Neifeld, "The speed of information in a 'fast-light' optical medium," Nature 425, 695-698 (2003).
[CrossRef] [PubMed]

L. J. Wang, A. Kuzmich, and A. Dogariu, "Gain-assisted superluminal light propagation," Nature 406, 277-279 (2000).
[CrossRef] [PubMed]

Opt. Lett. (1)

Phys. Rev. (4)

S. L. McCall and E. L. Hahn, "Self-induced transparency," Phys. Rev. 183, 457-485 (1969).
[CrossRef]

R. H. Dicke, "Coherence in spontaneous radiation processes," Phys. Rev. 93, 99-110 (1954).
[CrossRef]

A. Icsevgi and W. E. Lamb, Jr., "Propagation of light pulses in a laser amplifier," Phys. Rev. 185, 517-545 (1969).
[CrossRef]

D. C. Burnham and R. Y. Chiao, "Coherent resonance fluorescence excited by short light pulses," Phys. Rev. 188, 667-675 (1969).
[CrossRef]

Phys. Rev. A (8)

G. L. Lamb, Jr., "Amplification of coherent optical pulses," Phys. Rev. A 12, 2052-2059 (1975).
[CrossRef]

A. Rahman and J. H. Eberly, "Theory of shape-preserving short pulses in inhomogeneously broadened three-level media," Phys. Rev. A 58, R805-R808 (1998).
[CrossRef]

R. Bonifacio and L. A. Lugiato, "Cooperative radiation processes in two-level systems: superfluorescence," Phys. Rev. A 11, 1507-1521 (1975).
[CrossRef]

D. Polder, M. F. H. Schuurmans, and Q. H. F. Vrehen, "Superfluorescence: quantum-mechanical derivation of Maxwell-Bloch description with fluctuating field source," Phys. Rev. A 19, 1192-1203 (1979).
[CrossRef]

J. C. MacGillivray and M. S. Feld, "Theory of superradiance in an extended, optically thick medium," Phys. Rev. A 14, 1169-1189 (1976).
[CrossRef]

F. Haake, J. W. Haus, H. King, and G. Schröder, "Delay-time statistics of superfluorescent pulses," Phys. Rev. A 23, 1322-1333 (1981).
[CrossRef]

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[CrossRef]

Q. H. Park and H. J. Shin, "Matched pulse propagation in a three-level system," Phys. Rev. A 57, 4643-4653 (1992).
[CrossRef]

Phys. Rev. Lett. (4)

Q. H. F. Vrehen and M. F. H. Schuurmans, "Direct measurement of the effective initial tipping angle in superfluorescence," Phys. Rev. Lett. 42, 224-227 (1979).
[CrossRef]

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[CrossRef] [PubMed]

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[CrossRef] [PubMed]

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[CrossRef]

Phys. Today (1)

S. E. Harris, "Electromagetically induced transparency," Phys. Today 50, 36-42 (1997).
[CrossRef]

Prog. Opt. (1)

R. W. Boyd and D. J. Gauthier, "Slow and fast light," Prog. Opt. 43, 497-530 (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, 200202 (2003).
[CrossRef]

Sov. Phys. JETP (1)

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Other (2)

For a discussion and extension of the pioneering works of Sommerfeld and Brillouin, see, for example K.E.Oughston and G.C.Sherman, Electromagnetic Pulse Propagation in Causal Dielectrics, corrected ed. (Springer-Verlag, 1997).

P. W. Milonni, Fast Light, Slow Light and Left-Handed Light (IOP, 2005).

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Figures (8)

Fig. 1
Fig. 1

Two-level atom with level 1 connected to level 2 via the Rabi frequency Ω of a laser field detuned from resonance by an amount Δ and a sketch of significant pulse advance in an inverted two-level gain medium of length L and cross-sectional area σ.

Fig. 2
Fig. 2

Snapshots of the analytic solutions given in Eq. (4). The horizontal axis is x in units of c τ . The shaded region indicates the location of the medium, which is taken to be 2 c τ in length. The parameters of the pulse and medium are described in the text. For an EIT comparison, see Fig. 15 in Ref. [21].

Fig. 3
Fig. 3

Left frame shows the sech pulse used in numerical simulations. The right frame zooms in on the front edge of the pulse showing a sharp front edge 10 units from the pulse peak. The horizontal and vertical axes are the same as those in the analytic and numerical solution figures.

Fig. 4
Fig. 4

Snapshots during evolution of the numerical pulse solution to Eqs. (2, 3) with the same parameters as for Fig. 2, but for a pulse initially entirely outside the medium with abrupt edges at ± 10 units from the peak. The pulse peak advances 2.5 units forward, which is still well behind the front edge of the pulse, which is marked by the arrows.

Fig. 5
Fig. 5

Time-integrated area of the pulse from the numerical solution shown in Fig. 4. The horizontal axis is the position in units of c τ , and the vertical axis is the area of the pulse, as given in Eq. (8) in units of π.

Fig. 6
Fig. 6

Plot of the delay time, τ D of the SF pulse given in Eq. (10) and the total pulse transit time given in Eq. (7). The horizontal axis is the length of the medium in units of c τ , and the vertical axis is time in units of τ. The dashed curve is τ D , and the solid curve is τ adv . Each data point is an average delay time from 20 numerical solutions, showing excellent agreement with the theoretical delay time in Eq. (10). Pulse advance is predicted for a medium of up to 5 c τ , giving pulse advances of up to 6.5 τ .

Fig. 7
Fig. 7

Snapshots during evolution of the numerical pulse solution to Eqs. (2, 3) with the same parameters as for Fig. 2, but with initial probability amplitudes as given in Eq. (A1). The pulse is initially entirely outside the medium with sharp edges at ± 10 units from the peak, with the front edge indicated by the arrows. The following peak advance is 2.5 units forward, in agreement with Eq. (7). This advanced pulse is also ahead of the SF pulse shown in Fig. 8.

Fig. 8
Fig. 8

Snapshots during evolution of the numerical pulse solution to Eqs. (2, 3) but with no input pulse, and with initial probability amplitudes as given in Eq. (A1). A SF pulse emerges from the medium with delay time τ D . The time of each snapshot is the same as in all other figures.

Equations (14)

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H = Ω 2 1 2 Ω * 2 2 1 + Δ 2 2 ,
c 1 t = i Ω 2 c 2 ,
c 2 t = i Ω 2 c 1 i Δ c 2 .
( c x + t ) Ω = i g c 1 c 2 * = i g d Δ F ( Δ ) c 1 c 2 * ,
Ω ( x , t ) = { 2 τ sech 1 τ ( t x c ) , x < x 0 2 τ sech 1 τ ( t x v g + ϕ 0 ) , x 0 x x 1 , 2 τ sech 1 τ ( t x c + ϕ 1 ) , x > x 1 )
1 c v g = g 2 F ( Δ ) d Δ Δ 2 + ( 1 τ ) 2 g τ 2 2 ,
c 1 ( x , t ) = i sech 1 τ ( t x v g + ϕ 0 ) ,
c 2 ( x , t ) = tanh 1 τ ( t x v g + ϕ 0 ) .
τ adv L c L v g = L 2 c g τ 2 ,
θ ( x ) = Ω ( x , t ) d t ,
θ ( x ) x = α 2 sin θ ( x ) ,
T D = π τ 0 V 4 N a λ 2 L ( ln ( 2 π N a ) ) 2 = 3 c 4 g L [ ln ( L L 0 ) ] 2 ,
c 1 ( x i , t = ) = sin ( θ 0 ( x i ) 2 ) e i ϕ ( x i ) ,
c 2 ( x i , t = ) = cos ( θ 0 ( x i ) 2 ) ,

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