Abstract

There have been many recent theoretical and experimental reports on the propagation of light pulses at speeds exceeding the speed of light in vacuum c within media with anomalous dispersion, either opaque or with gain. Superluminal propagation has also been reported within vacuum, in the case of inhomogeneous pulses. In this paper we show that the observations of superluminal and non-causal propagation of evanescent pulses under the conditions of frustrated internal reflection are only apparent, and that they can be simply explained employing an explicitly (sub)luminal causal theory. However, the usual one-dimensional approach to the analysis of pulse propagation has to be abandoned and the spatial extent of the incoming pulse along the directions normal to the propagation direction has to be accounted for to correctly interpret the propagation speed of these evanescent waves. We illustrate our theory with animations of the time development of a pulse built upon the Huygen’s construction.

© 2001 Optical Society of America

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  1. A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Measurement of the single-photon tunneling time,” Phys. Rev. Lett. 71, 708–711 (1993) http://link.aps.org/abstract/PRL/v71/i5/p708.
    [CrossRef] [PubMed]
  2. Ch. Spielmann, R. Szipöcs, A. Stingl, and F. Krausz, “Tunneling of optical pulses through photonic band gaps,” Phys. Rev. Lett. 73, 2308 (1994) http://link.aps.org/abstract/PRL/v73/p2308.
    [CrossRef] [PubMed]
  3. T. H. Hartman, “Tunneling of a wave packet,” J. Appl. Phys. 33, 3427 (1962).
    [CrossRef]
  4. C. G. B. Garret and D. E. McCumber, “Propagation of a Gaussian Light Pulse through an Anomalous Dispersion Medium,” Phys. Rev. A 1, 305 (1970) http://link.aps.org/abstract/PRA/v1/i2/p305.
    [CrossRef]
  5. S. Chu and S. Wong, “Linear Pulse Propagation in an Absorbing Medium,” Phys. Rev. Lett. 48, 738 (1982) http://link.aps.org/abstract/PRL/v48/i11/p738.
    [CrossRef]
  6. A. Katz and R. R. Alfano, “Pulse Propagation in an Absorbing Medium,” Phys. Rev. Lett. 49, 1292 (1982) http://link.aps.org/abstract/PRL/v49/p1292.
    [CrossRef]
  7. Rolf Landauer, “Light faster than light?” Nature 365, 692 (1993).
    [CrossRef]
  8. G. Diener, “Superluminal group velocities and information transfer,” Phys. Lett. A 223, 327–331 (1996).
    [CrossRef]
  9. Léon Brillouin, “Wave Propagation and Group Velocity” (Academic, New york, 1960) Ch. II, III, and IV.
  10. G. Diener, “Energy Transport in Dispersive Media and Superluminal Group Velocities,” Phys. Lett. A 235, 118 (1997).
    [CrossRef]
  11. V. Romero-Rochín, R. P. Duarte-Zamorano, S. Nielsen-Hofseth, and R. G. Barrera, “Superluminal transmission of light pulses through optically opaque barriers,” Phys. Rev. E 63, 027601 (2001) http://link.aps.org/abstract/PRE/v63/e027601.
    [CrossRef]
  12. Richard W. Ziolkowski, “Superluminal Transmission of Information through an Electromagnetic Metamaterial,” Phys. Rev. E 63, 046604 (2001) http://link.aps.org/abstract/PRE/v63/e046604.
    [CrossRef]
  13. A. N. Oraevsky, “Superluminal Waves in Amplifying Media,” Physycs-Uspekhi,  41, 1199 (1998).
    [CrossRef]
  14. L. J. Wang, A. Kuzmich, and A. Dogariu, “Gain-Assisted Superluminal Light Propagation,” Nature 406, 277 (2000).
    [CrossRef] [PubMed]
  15. A. Dogariu, A. Kuzmich, and L. J. Wang, “Transparent anomalous dispersion and superluminal light-pulse propagation at a negative group velocity,” Phys. Rev. A 63, 053806 (2001) http://link.aps.org/abstract/PRA/v63/e053806.
    [CrossRef]
  16. A. Dogariu, Ak. Kuzmich, H. Cao, and L. J. Wang, “Superluminal Light Pulse Propagation Via Rephasing in a Transparent Anomalously Dispersive Medium,” Opt. Express 8, 344 (2001) http://www.opticsexpress.org/oearchive/source/30536.htm.
    [CrossRef] [PubMed]
  17. A. Kuzmich, A. Dogariu, L. J. Wang, P.W. Milonni, and R. Y. Chiao, “Signal Velocity, Causality, and Quantum Noise in Superluminal Light Pulse Propagation,” Phys. Rev. Lett. 86, 3925–3929 (2001) http://link.aps.org/abstract/PRL/v86/p3925.
    [CrossRef] [PubMed]
  18. G. Nimtz, “Evanescent Modes are not Necessarily Einstein Causal,” Eur. Phys. J. B 7, 523 (1999).
    [CrossRef]
  19. Yakir Aharonov, Benni Reznil, and Ady Stern, “Quantum Limitatins on Superluminal Propagation,” Phys. Rev. Lett. 81, 2190 (1998) http://link.aps.org/abstract/PRL/v81/p2190.
    [CrossRef]
  20. P. W. Milonni, K. Furuya, and R. Y. Chiao, “Quantum Theory of Superluminal Pulse Propagation,” Opt. Express 8, 59 (2001) http://www.opticsexpress.org/oearchive/source/27132.htm.
    [CrossRef] [PubMed]
  21. Aephraim M Steinberg, “No thing goes faster than light,” Physics World 133 (2000) http://www.physicsweb.org/article/world/13/9/3.
  22. Peter W. Milonni, “Causal Discussion of Superluminal Pulses,” Physics Today 54, 81 (2001) http://www.physicstoday.org/pt/vol-54/iss-2/p14b.html.
    [CrossRef]
  23. Jacob Broe and Ole Keller, “Superluminality and spatial confinement in optical tunneling,” Opt. Commun. 194, 83 (2001).
    [CrossRef]
  24. A. Ranfagni, D. Mugnai, P. Fabeni, and G. P. Pazzi, “Delay-time measurements in narrowed waveguides as a test of tunneling,” Appl. Phys. Lett. 58, 774 (1991).
    [CrossRef]
  25. A. Enders and G. Nimtz, “Photonic-tunneling experiments,” Phys. Rev. B 47, 9605 (1993) http://link.aps.org/abstract/PRB/v47/p9605.
    [CrossRef]
  26. A. Pablo, L. Barbero, Hugo E. Hernández-Figueroa, and Erasmo Recami, “Propagation Speed of Evanescent Modes,” Phys. Rev. E 62, 8628 (2000) http://link.aps.org/abstract/PRE/v62/p8628.
    [CrossRef]
  27. Klass Wynne, John J. J. Carey, Justyna Zawadzka, and Dino Jaroszynski, “Tunneling of Single-Cycle Terahertz Pulses through Waveguides,” Opt. Commun. 176, 429 (2000).
    [CrossRef]
  28. S. Bosanac, “Propagation of Electromagnetic Wave Packets in Nondispersive Dielectric Media,” Phys. Rev. A 28, 577 (1983) http://link.aps.org/abstract/PRA/v28/p577.
    [CrossRef]
  29. Ph. Balcou and L. Dutriaux, “Dual Optical Tunneling Times in Frustrated Total Internal Reflection,” Phys. Rev. Lett. 78, 851 (1997) http://link.aps.org/abstract/PRL/v78/p851.
    [CrossRef]
  30. John J. Carey, Justyna Zawadzka, Dino A. Jaroszynski, and Klaas Wynne, “Noncausal Time Response in Frustrated Total Internal Reflection?” Phys. Rev. Lett. 84, 1431 (2000) http://link.aps.org/abstract/PRL/v84/p1431.
    [CrossRef] [PubMed]
  31. W. Luis Mochán and Vera L. Brudny, “Comment on Noncausal Time Response in Frustrated Total Internal Reflection?” Phys. Rev. Lett. 87, 119101 (2001) http://link.aps.org/abstract/PRL/v87/e119101.
    [CrossRef]
  32. Vera L. Brudny and W. Luis Mochán, under preparation.
  33. A. Ranfagni, P. Fabeni, G. P. Pazzi, and D. Mugnai “Anomalous pulse delay in microwave propagation: A plausible connection to the tunneling time,” Phys. Rev. E 48, 1453 (1993). http://link.aps.org/abstract/PRE/v48/p1453.
    [CrossRef]
  34. D. Mugnai, A. Ranfagni, and R. Ruggeri, Phys. Rev. Lett. 84, 4830 (2000) http://link.aps.org/abstract/PRL/v84/p4830.
    [CrossRef] [PubMed]

2001 (9)

V. Romero-Rochín, R. P. Duarte-Zamorano, S. Nielsen-Hofseth, and R. G. Barrera, “Superluminal transmission of light pulses through optically opaque barriers,” Phys. Rev. E 63, 027601 (2001) http://link.aps.org/abstract/PRE/v63/e027601.
[CrossRef]

Richard W. Ziolkowski, “Superluminal Transmission of Information through an Electromagnetic Metamaterial,” Phys. Rev. E 63, 046604 (2001) http://link.aps.org/abstract/PRE/v63/e046604.
[CrossRef]

A. Dogariu, A. Kuzmich, and L. J. Wang, “Transparent anomalous dispersion and superluminal light-pulse propagation at a negative group velocity,” Phys. Rev. A 63, 053806 (2001) http://link.aps.org/abstract/PRA/v63/e053806.
[CrossRef]

A. Dogariu, Ak. Kuzmich, H. Cao, and L. J. Wang, “Superluminal Light Pulse Propagation Via Rephasing in a Transparent Anomalously Dispersive Medium,” Opt. Express 8, 344 (2001) http://www.opticsexpress.org/oearchive/source/30536.htm.
[CrossRef] [PubMed]

A. Kuzmich, A. Dogariu, L. J. Wang, P.W. Milonni, and R. Y. Chiao, “Signal Velocity, Causality, and Quantum Noise in Superluminal Light Pulse Propagation,” Phys. Rev. Lett. 86, 3925–3929 (2001) http://link.aps.org/abstract/PRL/v86/p3925.
[CrossRef] [PubMed]

P. W. Milonni, K. Furuya, and R. Y. Chiao, “Quantum Theory of Superluminal Pulse Propagation,” Opt. Express 8, 59 (2001) http://www.opticsexpress.org/oearchive/source/27132.htm.
[CrossRef] [PubMed]

Peter W. Milonni, “Causal Discussion of Superluminal Pulses,” Physics Today 54, 81 (2001) http://www.physicstoday.org/pt/vol-54/iss-2/p14b.html.
[CrossRef]

Jacob Broe and Ole Keller, “Superluminality and spatial confinement in optical tunneling,” Opt. Commun. 194, 83 (2001).
[CrossRef]

W. Luis Mochán and Vera L. Brudny, “Comment on Noncausal Time Response in Frustrated Total Internal Reflection?” Phys. Rev. Lett. 87, 119101 (2001) http://link.aps.org/abstract/PRL/v87/e119101.
[CrossRef]

2000 (6)

John J. Carey, Justyna Zawadzka, Dino A. Jaroszynski, and Klaas Wynne, “Noncausal Time Response in Frustrated Total Internal Reflection?” Phys. Rev. Lett. 84, 1431 (2000) http://link.aps.org/abstract/PRL/v84/p1431.
[CrossRef] [PubMed]

D. Mugnai, A. Ranfagni, and R. Ruggeri, Phys. Rev. Lett. 84, 4830 (2000) http://link.aps.org/abstract/PRL/v84/p4830.
[CrossRef] [PubMed]

Aephraim M Steinberg, “No thing goes faster than light,” Physics World 133 (2000) http://www.physicsweb.org/article/world/13/9/3.

A. Pablo, L. Barbero, Hugo E. Hernández-Figueroa, and Erasmo Recami, “Propagation Speed of Evanescent Modes,” Phys. Rev. E 62, 8628 (2000) http://link.aps.org/abstract/PRE/v62/p8628.
[CrossRef]

Klass Wynne, John J. J. Carey, Justyna Zawadzka, and Dino Jaroszynski, “Tunneling of Single-Cycle Terahertz Pulses through Waveguides,” Opt. Commun. 176, 429 (2000).
[CrossRef]

L. J. Wang, A. Kuzmich, and A. Dogariu, “Gain-Assisted Superluminal Light Propagation,” Nature 406, 277 (2000).
[CrossRef] [PubMed]

1999 (1)

G. Nimtz, “Evanescent Modes are not Necessarily Einstein Causal,” Eur. Phys. J. B 7, 523 (1999).
[CrossRef]

1998 (2)

Yakir Aharonov, Benni Reznil, and Ady Stern, “Quantum Limitatins on Superluminal Propagation,” Phys. Rev. Lett. 81, 2190 (1998) http://link.aps.org/abstract/PRL/v81/p2190.
[CrossRef]

A. N. Oraevsky, “Superluminal Waves in Amplifying Media,” Physycs-Uspekhi,  41, 1199 (1998).
[CrossRef]

1997 (2)

G. Diener, “Energy Transport in Dispersive Media and Superluminal Group Velocities,” Phys. Lett. A 235, 118 (1997).
[CrossRef]

Ph. Balcou and L. Dutriaux, “Dual Optical Tunneling Times in Frustrated Total Internal Reflection,” Phys. Rev. Lett. 78, 851 (1997) http://link.aps.org/abstract/PRL/v78/p851.
[CrossRef]

1996 (1)

G. Diener, “Superluminal group velocities and information transfer,” Phys. Lett. A 223, 327–331 (1996).
[CrossRef]

1994 (1)

Ch. Spielmann, R. Szipöcs, A. Stingl, and F. Krausz, “Tunneling of optical pulses through photonic band gaps,” Phys. Rev. Lett. 73, 2308 (1994) http://link.aps.org/abstract/PRL/v73/p2308.
[CrossRef] [PubMed]

1993 (4)

A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Measurement of the single-photon tunneling time,” Phys. Rev. Lett. 71, 708–711 (1993) http://link.aps.org/abstract/PRL/v71/i5/p708.
[CrossRef] [PubMed]

Rolf Landauer, “Light faster than light?” Nature 365, 692 (1993).
[CrossRef]

A. Enders and G. Nimtz, “Photonic-tunneling experiments,” Phys. Rev. B 47, 9605 (1993) http://link.aps.org/abstract/PRB/v47/p9605.
[CrossRef]

A. Ranfagni, P. Fabeni, G. P. Pazzi, and D. Mugnai “Anomalous pulse delay in microwave propagation: A plausible connection to the tunneling time,” Phys. Rev. E 48, 1453 (1993). http://link.aps.org/abstract/PRE/v48/p1453.
[CrossRef]

1991 (1)

A. Ranfagni, D. Mugnai, P. Fabeni, and G. P. Pazzi, “Delay-time measurements in narrowed waveguides as a test of tunneling,” Appl. Phys. Lett. 58, 774 (1991).
[CrossRef]

1983 (1)

S. Bosanac, “Propagation of Electromagnetic Wave Packets in Nondispersive Dielectric Media,” Phys. Rev. A 28, 577 (1983) http://link.aps.org/abstract/PRA/v28/p577.
[CrossRef]

1982 (2)

S. Chu and S. Wong, “Linear Pulse Propagation in an Absorbing Medium,” Phys. Rev. Lett. 48, 738 (1982) http://link.aps.org/abstract/PRL/v48/i11/p738.
[CrossRef]

A. Katz and R. R. Alfano, “Pulse Propagation in an Absorbing Medium,” Phys. Rev. Lett. 49, 1292 (1982) http://link.aps.org/abstract/PRL/v49/p1292.
[CrossRef]

1970 (1)

C. G. B. Garret and D. E. McCumber, “Propagation of a Gaussian Light Pulse through an Anomalous Dispersion Medium,” Phys. Rev. A 1, 305 (1970) http://link.aps.org/abstract/PRA/v1/i2/p305.
[CrossRef]

1962 (1)

T. H. Hartman, “Tunneling of a wave packet,” J. Appl. Phys. 33, 3427 (1962).
[CrossRef]

Aharonov, Yakir

Yakir Aharonov, Benni Reznil, and Ady Stern, “Quantum Limitatins on Superluminal Propagation,” Phys. Rev. Lett. 81, 2190 (1998) http://link.aps.org/abstract/PRL/v81/p2190.
[CrossRef]

Alfano, R. R.

A. Katz and R. R. Alfano, “Pulse Propagation in an Absorbing Medium,” Phys. Rev. Lett. 49, 1292 (1982) http://link.aps.org/abstract/PRL/v49/p1292.
[CrossRef]

Balcou, Ph.

Ph. Balcou and L. Dutriaux, “Dual Optical Tunneling Times in Frustrated Total Internal Reflection,” Phys. Rev. Lett. 78, 851 (1997) http://link.aps.org/abstract/PRL/v78/p851.
[CrossRef]

Barbero, L.

A. Pablo, L. Barbero, Hugo E. Hernández-Figueroa, and Erasmo Recami, “Propagation Speed of Evanescent Modes,” Phys. Rev. E 62, 8628 (2000) http://link.aps.org/abstract/PRE/v62/p8628.
[CrossRef]

Barrera, R. G.

V. Romero-Rochín, R. P. Duarte-Zamorano, S. Nielsen-Hofseth, and R. G. Barrera, “Superluminal transmission of light pulses through optically opaque barriers,” Phys. Rev. E 63, 027601 (2001) http://link.aps.org/abstract/PRE/v63/e027601.
[CrossRef]

Bosanac, S.

S. Bosanac, “Propagation of Electromagnetic Wave Packets in Nondispersive Dielectric Media,” Phys. Rev. A 28, 577 (1983) http://link.aps.org/abstract/PRA/v28/p577.
[CrossRef]

Brillouin, Léon

Léon Brillouin, “Wave Propagation and Group Velocity” (Academic, New york, 1960) Ch. II, III, and IV.

Broe, Jacob

Jacob Broe and Ole Keller, “Superluminality and spatial confinement in optical tunneling,” Opt. Commun. 194, 83 (2001).
[CrossRef]

Brudny, Vera L.

W. Luis Mochán and Vera L. Brudny, “Comment on Noncausal Time Response in Frustrated Total Internal Reflection?” Phys. Rev. Lett. 87, 119101 (2001) http://link.aps.org/abstract/PRL/v87/e119101.
[CrossRef]

Vera L. Brudny and W. Luis Mochán, under preparation.

Cao, H.

Carey, John J.

John J. Carey, Justyna Zawadzka, Dino A. Jaroszynski, and Klaas Wynne, “Noncausal Time Response in Frustrated Total Internal Reflection?” Phys. Rev. Lett. 84, 1431 (2000) http://link.aps.org/abstract/PRL/v84/p1431.
[CrossRef] [PubMed]

Carey, John J. J.

Klass Wynne, John J. J. Carey, Justyna Zawadzka, and Dino Jaroszynski, “Tunneling of Single-Cycle Terahertz Pulses through Waveguides,” Opt. Commun. 176, 429 (2000).
[CrossRef]

Chiao, R. Y.

A. Kuzmich, A. Dogariu, L. J. Wang, P.W. Milonni, and R. Y. Chiao, “Signal Velocity, Causality, and Quantum Noise in Superluminal Light Pulse Propagation,” Phys. Rev. Lett. 86, 3925–3929 (2001) http://link.aps.org/abstract/PRL/v86/p3925.
[CrossRef] [PubMed]

P. W. Milonni, K. Furuya, and R. Y. Chiao, “Quantum Theory of Superluminal Pulse Propagation,” Opt. Express 8, 59 (2001) http://www.opticsexpress.org/oearchive/source/27132.htm.
[CrossRef] [PubMed]

A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Measurement of the single-photon tunneling time,” Phys. Rev. Lett. 71, 708–711 (1993) http://link.aps.org/abstract/PRL/v71/i5/p708.
[CrossRef] [PubMed]

Chu, S.

S. Chu and S. Wong, “Linear Pulse Propagation in an Absorbing Medium,” Phys. Rev. Lett. 48, 738 (1982) http://link.aps.org/abstract/PRL/v48/i11/p738.
[CrossRef]

Diener, G.

G. Diener, “Energy Transport in Dispersive Media and Superluminal Group Velocities,” Phys. Lett. A 235, 118 (1997).
[CrossRef]

G. Diener, “Superluminal group velocities and information transfer,” Phys. Lett. A 223, 327–331 (1996).
[CrossRef]

Dogariu, A.

A. Dogariu, A. Kuzmich, and L. J. Wang, “Transparent anomalous dispersion and superluminal light-pulse propagation at a negative group velocity,” Phys. Rev. A 63, 053806 (2001) http://link.aps.org/abstract/PRA/v63/e053806.
[CrossRef]

A. Kuzmich, A. Dogariu, L. J. Wang, P.W. Milonni, and R. Y. Chiao, “Signal Velocity, Causality, and Quantum Noise in Superluminal Light Pulse Propagation,” Phys. Rev. Lett. 86, 3925–3929 (2001) http://link.aps.org/abstract/PRL/v86/p3925.
[CrossRef] [PubMed]

A. Dogariu, Ak. Kuzmich, H. Cao, and L. J. Wang, “Superluminal Light Pulse Propagation Via Rephasing in a Transparent Anomalously Dispersive Medium,” Opt. Express 8, 344 (2001) http://www.opticsexpress.org/oearchive/source/30536.htm.
[CrossRef] [PubMed]

L. J. Wang, A. Kuzmich, and A. Dogariu, “Gain-Assisted Superluminal Light Propagation,” Nature 406, 277 (2000).
[CrossRef] [PubMed]

Duarte-Zamorano, R. P.

V. Romero-Rochín, R. P. Duarte-Zamorano, S. Nielsen-Hofseth, and R. G. Barrera, “Superluminal transmission of light pulses through optically opaque barriers,” Phys. Rev. E 63, 027601 (2001) http://link.aps.org/abstract/PRE/v63/e027601.
[CrossRef]

Dutriaux, L.

Ph. Balcou and L. Dutriaux, “Dual Optical Tunneling Times in Frustrated Total Internal Reflection,” Phys. Rev. Lett. 78, 851 (1997) http://link.aps.org/abstract/PRL/v78/p851.
[CrossRef]

Enders, A.

A. Enders and G. Nimtz, “Photonic-tunneling experiments,” Phys. Rev. B 47, 9605 (1993) http://link.aps.org/abstract/PRB/v47/p9605.
[CrossRef]

Fabeni, P.

A. Ranfagni, P. Fabeni, G. P. Pazzi, and D. Mugnai “Anomalous pulse delay in microwave propagation: A plausible connection to the tunneling time,” Phys. Rev. E 48, 1453 (1993). http://link.aps.org/abstract/PRE/v48/p1453.
[CrossRef]

A. Ranfagni, D. Mugnai, P. Fabeni, and G. P. Pazzi, “Delay-time measurements in narrowed waveguides as a test of tunneling,” Appl. Phys. Lett. 58, 774 (1991).
[CrossRef]

Furuya, K.

Garret, C. G. B.

C. G. B. Garret and D. E. McCumber, “Propagation of a Gaussian Light Pulse through an Anomalous Dispersion Medium,” Phys. Rev. A 1, 305 (1970) http://link.aps.org/abstract/PRA/v1/i2/p305.
[CrossRef]

Hartman, T. H.

T. H. Hartman, “Tunneling of a wave packet,” J. Appl. Phys. 33, 3427 (1962).
[CrossRef]

Hernández-Figueroa, Hugo E.

A. Pablo, L. Barbero, Hugo E. Hernández-Figueroa, and Erasmo Recami, “Propagation Speed of Evanescent Modes,” Phys. Rev. E 62, 8628 (2000) http://link.aps.org/abstract/PRE/v62/p8628.
[CrossRef]

Jaroszynski, Dino

Klass Wynne, John J. J. Carey, Justyna Zawadzka, and Dino Jaroszynski, “Tunneling of Single-Cycle Terahertz Pulses through Waveguides,” Opt. Commun. 176, 429 (2000).
[CrossRef]

Jaroszynski, Dino A.

John J. Carey, Justyna Zawadzka, Dino A. Jaroszynski, and Klaas Wynne, “Noncausal Time Response in Frustrated Total Internal Reflection?” Phys. Rev. Lett. 84, 1431 (2000) http://link.aps.org/abstract/PRL/v84/p1431.
[CrossRef] [PubMed]

Katz, A.

A. Katz and R. R. Alfano, “Pulse Propagation in an Absorbing Medium,” Phys. Rev. Lett. 49, 1292 (1982) http://link.aps.org/abstract/PRL/v49/p1292.
[CrossRef]

Keller, Ole

Jacob Broe and Ole Keller, “Superluminality and spatial confinement in optical tunneling,” Opt. Commun. 194, 83 (2001).
[CrossRef]

Krausz, F.

Ch. Spielmann, R. Szipöcs, A. Stingl, and F. Krausz, “Tunneling of optical pulses through photonic band gaps,” Phys. Rev. Lett. 73, 2308 (1994) http://link.aps.org/abstract/PRL/v73/p2308.
[CrossRef] [PubMed]

Kuzmich, A.

A. Dogariu, A. Kuzmich, and L. J. Wang, “Transparent anomalous dispersion and superluminal light-pulse propagation at a negative group velocity,” Phys. Rev. A 63, 053806 (2001) http://link.aps.org/abstract/PRA/v63/e053806.
[CrossRef]

A. Kuzmich, A. Dogariu, L. J. Wang, P.W. Milonni, and R. Y. Chiao, “Signal Velocity, Causality, and Quantum Noise in Superluminal Light Pulse Propagation,” Phys. Rev. Lett. 86, 3925–3929 (2001) http://link.aps.org/abstract/PRL/v86/p3925.
[CrossRef] [PubMed]

L. J. Wang, A. Kuzmich, and A. Dogariu, “Gain-Assisted Superluminal Light Propagation,” Nature 406, 277 (2000).
[CrossRef] [PubMed]

Kuzmich, Ak.

Kwiat, P. G.

A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Measurement of the single-photon tunneling time,” Phys. Rev. Lett. 71, 708–711 (1993) http://link.aps.org/abstract/PRL/v71/i5/p708.
[CrossRef] [PubMed]

Landauer, Rolf

Rolf Landauer, “Light faster than light?” Nature 365, 692 (1993).
[CrossRef]

Luis Mochán, W.

W. Luis Mochán and Vera L. Brudny, “Comment on Noncausal Time Response in Frustrated Total Internal Reflection?” Phys. Rev. Lett. 87, 119101 (2001) http://link.aps.org/abstract/PRL/v87/e119101.
[CrossRef]

Vera L. Brudny and W. Luis Mochán, under preparation.

McCumber, D. E.

C. G. B. Garret and D. E. McCumber, “Propagation of a Gaussian Light Pulse through an Anomalous Dispersion Medium,” Phys. Rev. A 1, 305 (1970) http://link.aps.org/abstract/PRA/v1/i2/p305.
[CrossRef]

Milonni, P. W.

Milonni, P.W.

A. Kuzmich, A. Dogariu, L. J. Wang, P.W. Milonni, and R. Y. Chiao, “Signal Velocity, Causality, and Quantum Noise in Superluminal Light Pulse Propagation,” Phys. Rev. Lett. 86, 3925–3929 (2001) http://link.aps.org/abstract/PRL/v86/p3925.
[CrossRef] [PubMed]

Milonni, Peter W.

Peter W. Milonni, “Causal Discussion of Superluminal Pulses,” Physics Today 54, 81 (2001) http://www.physicstoday.org/pt/vol-54/iss-2/p14b.html.
[CrossRef]

Mugnai, D.

D. Mugnai, A. Ranfagni, and R. Ruggeri, Phys. Rev. Lett. 84, 4830 (2000) http://link.aps.org/abstract/PRL/v84/p4830.
[CrossRef] [PubMed]

A. Ranfagni, P. Fabeni, G. P. Pazzi, and D. Mugnai “Anomalous pulse delay in microwave propagation: A plausible connection to the tunneling time,” Phys. Rev. E 48, 1453 (1993). http://link.aps.org/abstract/PRE/v48/p1453.
[CrossRef]

A. Ranfagni, D. Mugnai, P. Fabeni, and G. P. Pazzi, “Delay-time measurements in narrowed waveguides as a test of tunneling,” Appl. Phys. Lett. 58, 774 (1991).
[CrossRef]

Nielsen-Hofseth, S.

V. Romero-Rochín, R. P. Duarte-Zamorano, S. Nielsen-Hofseth, and R. G. Barrera, “Superluminal transmission of light pulses through optically opaque barriers,” Phys. Rev. E 63, 027601 (2001) http://link.aps.org/abstract/PRE/v63/e027601.
[CrossRef]

Nimtz, G.

G. Nimtz, “Evanescent Modes are not Necessarily Einstein Causal,” Eur. Phys. J. B 7, 523 (1999).
[CrossRef]

A. Enders and G. Nimtz, “Photonic-tunneling experiments,” Phys. Rev. B 47, 9605 (1993) http://link.aps.org/abstract/PRB/v47/p9605.
[CrossRef]

Oraevsky, A. N.

A. N. Oraevsky, “Superluminal Waves in Amplifying Media,” Physycs-Uspekhi,  41, 1199 (1998).
[CrossRef]

Pablo, A.

A. Pablo, L. Barbero, Hugo E. Hernández-Figueroa, and Erasmo Recami, “Propagation Speed of Evanescent Modes,” Phys. Rev. E 62, 8628 (2000) http://link.aps.org/abstract/PRE/v62/p8628.
[CrossRef]

Pazzi, G. P.

A. Ranfagni, P. Fabeni, G. P. Pazzi, and D. Mugnai “Anomalous pulse delay in microwave propagation: A plausible connection to the tunneling time,” Phys. Rev. E 48, 1453 (1993). http://link.aps.org/abstract/PRE/v48/p1453.
[CrossRef]

A. Ranfagni, D. Mugnai, P. Fabeni, and G. P. Pazzi, “Delay-time measurements in narrowed waveguides as a test of tunneling,” Appl. Phys. Lett. 58, 774 (1991).
[CrossRef]

Ranfagni, A.

D. Mugnai, A. Ranfagni, and R. Ruggeri, Phys. Rev. Lett. 84, 4830 (2000) http://link.aps.org/abstract/PRL/v84/p4830.
[CrossRef] [PubMed]

A. Ranfagni, P. Fabeni, G. P. Pazzi, and D. Mugnai “Anomalous pulse delay in microwave propagation: A plausible connection to the tunneling time,” Phys. Rev. E 48, 1453 (1993). http://link.aps.org/abstract/PRE/v48/p1453.
[CrossRef]

A. Ranfagni, D. Mugnai, P. Fabeni, and G. P. Pazzi, “Delay-time measurements in narrowed waveguides as a test of tunneling,” Appl. Phys. Lett. 58, 774 (1991).
[CrossRef]

Recami, Erasmo

A. Pablo, L. Barbero, Hugo E. Hernández-Figueroa, and Erasmo Recami, “Propagation Speed of Evanescent Modes,” Phys. Rev. E 62, 8628 (2000) http://link.aps.org/abstract/PRE/v62/p8628.
[CrossRef]

Reznil, Benni

Yakir Aharonov, Benni Reznil, and Ady Stern, “Quantum Limitatins on Superluminal Propagation,” Phys. Rev. Lett. 81, 2190 (1998) http://link.aps.org/abstract/PRL/v81/p2190.
[CrossRef]

Romero-Rochín, V.

V. Romero-Rochín, R. P. Duarte-Zamorano, S. Nielsen-Hofseth, and R. G. Barrera, “Superluminal transmission of light pulses through optically opaque barriers,” Phys. Rev. E 63, 027601 (2001) http://link.aps.org/abstract/PRE/v63/e027601.
[CrossRef]

Ruggeri, R.

D. Mugnai, A. Ranfagni, and R. Ruggeri, Phys. Rev. Lett. 84, 4830 (2000) http://link.aps.org/abstract/PRL/v84/p4830.
[CrossRef] [PubMed]

Spielmann, Ch.

Ch. Spielmann, R. Szipöcs, A. Stingl, and F. Krausz, “Tunneling of optical pulses through photonic band gaps,” Phys. Rev. Lett. 73, 2308 (1994) http://link.aps.org/abstract/PRL/v73/p2308.
[CrossRef] [PubMed]

Steinberg, A. M.

A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Measurement of the single-photon tunneling time,” Phys. Rev. Lett. 71, 708–711 (1993) http://link.aps.org/abstract/PRL/v71/i5/p708.
[CrossRef] [PubMed]

Steinberg, Aephraim M

Aephraim M Steinberg, “No thing goes faster than light,” Physics World 133 (2000) http://www.physicsweb.org/article/world/13/9/3.

Stern, Ady

Yakir Aharonov, Benni Reznil, and Ady Stern, “Quantum Limitatins on Superluminal Propagation,” Phys. Rev. Lett. 81, 2190 (1998) http://link.aps.org/abstract/PRL/v81/p2190.
[CrossRef]

Stingl, A.

Ch. Spielmann, R. Szipöcs, A. Stingl, and F. Krausz, “Tunneling of optical pulses through photonic band gaps,” Phys. Rev. Lett. 73, 2308 (1994) http://link.aps.org/abstract/PRL/v73/p2308.
[CrossRef] [PubMed]

Szipöcs, R.

Ch. Spielmann, R. Szipöcs, A. Stingl, and F. Krausz, “Tunneling of optical pulses through photonic band gaps,” Phys. Rev. Lett. 73, 2308 (1994) http://link.aps.org/abstract/PRL/v73/p2308.
[CrossRef] [PubMed]

Wang, L. J.

A. Dogariu, A. Kuzmich, and L. J. Wang, “Transparent anomalous dispersion and superluminal light-pulse propagation at a negative group velocity,” Phys. Rev. A 63, 053806 (2001) http://link.aps.org/abstract/PRA/v63/e053806.
[CrossRef]

A. Kuzmich, A. Dogariu, L. J. Wang, P.W. Milonni, and R. Y. Chiao, “Signal Velocity, Causality, and Quantum Noise in Superluminal Light Pulse Propagation,” Phys. Rev. Lett. 86, 3925–3929 (2001) http://link.aps.org/abstract/PRL/v86/p3925.
[CrossRef] [PubMed]

A. Dogariu, Ak. Kuzmich, H. Cao, and L. J. Wang, “Superluminal Light Pulse Propagation Via Rephasing in a Transparent Anomalously Dispersive Medium,” Opt. Express 8, 344 (2001) http://www.opticsexpress.org/oearchive/source/30536.htm.
[CrossRef] [PubMed]

L. J. Wang, A. Kuzmich, and A. Dogariu, “Gain-Assisted Superluminal Light Propagation,” Nature 406, 277 (2000).
[CrossRef] [PubMed]

Wong, S.

S. Chu and S. Wong, “Linear Pulse Propagation in an Absorbing Medium,” Phys. Rev. Lett. 48, 738 (1982) http://link.aps.org/abstract/PRL/v48/i11/p738.
[CrossRef]

Wynne, Klaas

John J. Carey, Justyna Zawadzka, Dino A. Jaroszynski, and Klaas Wynne, “Noncausal Time Response in Frustrated Total Internal Reflection?” Phys. Rev. Lett. 84, 1431 (2000) http://link.aps.org/abstract/PRL/v84/p1431.
[CrossRef] [PubMed]

Wynne, Klass

Klass Wynne, John J. J. Carey, Justyna Zawadzka, and Dino Jaroszynski, “Tunneling of Single-Cycle Terahertz Pulses through Waveguides,” Opt. Commun. 176, 429 (2000).
[CrossRef]

Zawadzka, Justyna

Klass Wynne, John J. J. Carey, Justyna Zawadzka, and Dino Jaroszynski, “Tunneling of Single-Cycle Terahertz Pulses through Waveguides,” Opt. Commun. 176, 429 (2000).
[CrossRef]

John J. Carey, Justyna Zawadzka, Dino A. Jaroszynski, and Klaas Wynne, “Noncausal Time Response in Frustrated Total Internal Reflection?” Phys. Rev. Lett. 84, 1431 (2000) http://link.aps.org/abstract/PRL/v84/p1431.
[CrossRef] [PubMed]

Ziolkowski, Richard W.

Richard W. Ziolkowski, “Superluminal Transmission of Information through an Electromagnetic Metamaterial,” Phys. Rev. E 63, 046604 (2001) http://link.aps.org/abstract/PRE/v63/e046604.
[CrossRef]

Appl. Phys. Lett. (1)

A. Ranfagni, D. Mugnai, P. Fabeni, and G. P. Pazzi, “Delay-time measurements in narrowed waveguides as a test of tunneling,” Appl. Phys. Lett. 58, 774 (1991).
[CrossRef]

Eur. Phys. J. B (1)

G. Nimtz, “Evanescent Modes are not Necessarily Einstein Causal,” Eur. Phys. J. B 7, 523 (1999).
[CrossRef]

J. Appl. Phys. (1)

T. H. Hartman, “Tunneling of a wave packet,” J. Appl. Phys. 33, 3427 (1962).
[CrossRef]

Nature (2)

Rolf Landauer, “Light faster than light?” Nature 365, 692 (1993).
[CrossRef]

L. J. Wang, A. Kuzmich, and A. Dogariu, “Gain-Assisted Superluminal Light Propagation,” Nature 406, 277 (2000).
[CrossRef] [PubMed]

Opt. Commun. (2)

Jacob Broe and Ole Keller, “Superluminality and spatial confinement in optical tunneling,” Opt. Commun. 194, 83 (2001).
[CrossRef]

Klass Wynne, John J. J. Carey, Justyna Zawadzka, and Dino Jaroszynski, “Tunneling of Single-Cycle Terahertz Pulses through Waveguides,” Opt. Commun. 176, 429 (2000).
[CrossRef]

Opt. Express (2)

Phys. Lett. A (2)

G. Diener, “Energy Transport in Dispersive Media and Superluminal Group Velocities,” Phys. Lett. A 235, 118 (1997).
[CrossRef]

G. Diener, “Superluminal group velocities and information transfer,” Phys. Lett. A 223, 327–331 (1996).
[CrossRef]

Phys. Rev. A (3)

C. G. B. Garret and D. E. McCumber, “Propagation of a Gaussian Light Pulse through an Anomalous Dispersion Medium,” Phys. Rev. A 1, 305 (1970) http://link.aps.org/abstract/PRA/v1/i2/p305.
[CrossRef]

A. Dogariu, A. Kuzmich, and L. J. Wang, “Transparent anomalous dispersion and superluminal light-pulse propagation at a negative group velocity,” Phys. Rev. A 63, 053806 (2001) http://link.aps.org/abstract/PRA/v63/e053806.
[CrossRef]

S. Bosanac, “Propagation of Electromagnetic Wave Packets in Nondispersive Dielectric Media,” Phys. Rev. A 28, 577 (1983) http://link.aps.org/abstract/PRA/v28/p577.
[CrossRef]

Phys. Rev. B (1)

A. Enders and G. Nimtz, “Photonic-tunneling experiments,” Phys. Rev. B 47, 9605 (1993) http://link.aps.org/abstract/PRB/v47/p9605.
[CrossRef]

Phys. Rev. E (4)

A. Pablo, L. Barbero, Hugo E. Hernández-Figueroa, and Erasmo Recami, “Propagation Speed of Evanescent Modes,” Phys. Rev. E 62, 8628 (2000) http://link.aps.org/abstract/PRE/v62/p8628.
[CrossRef]

A. Ranfagni, P. Fabeni, G. P. Pazzi, and D. Mugnai “Anomalous pulse delay in microwave propagation: A plausible connection to the tunneling time,” Phys. Rev. E 48, 1453 (1993). http://link.aps.org/abstract/PRE/v48/p1453.
[CrossRef]

V. Romero-Rochín, R. P. Duarte-Zamorano, S. Nielsen-Hofseth, and R. G. Barrera, “Superluminal transmission of light pulses through optically opaque barriers,” Phys. Rev. E 63, 027601 (2001) http://link.aps.org/abstract/PRE/v63/e027601.
[CrossRef]

Richard W. Ziolkowski, “Superluminal Transmission of Information through an Electromagnetic Metamaterial,” Phys. Rev. E 63, 046604 (2001) http://link.aps.org/abstract/PRE/v63/e046604.
[CrossRef]

Phys. Rev. Lett. (10)

A. Kuzmich, A. Dogariu, L. J. Wang, P.W. Milonni, and R. Y. Chiao, “Signal Velocity, Causality, and Quantum Noise in Superluminal Light Pulse Propagation,” Phys. Rev. Lett. 86, 3925–3929 (2001) http://link.aps.org/abstract/PRL/v86/p3925.
[CrossRef] [PubMed]

S. Chu and S. Wong, “Linear Pulse Propagation in an Absorbing Medium,” Phys. Rev. Lett. 48, 738 (1982) http://link.aps.org/abstract/PRL/v48/i11/p738.
[CrossRef]

A. Katz and R. R. Alfano, “Pulse Propagation in an Absorbing Medium,” Phys. Rev. Lett. 49, 1292 (1982) http://link.aps.org/abstract/PRL/v49/p1292.
[CrossRef]

A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Measurement of the single-photon tunneling time,” Phys. Rev. Lett. 71, 708–711 (1993) http://link.aps.org/abstract/PRL/v71/i5/p708.
[CrossRef] [PubMed]

Ch. Spielmann, R. Szipöcs, A. Stingl, and F. Krausz, “Tunneling of optical pulses through photonic band gaps,” Phys. Rev. Lett. 73, 2308 (1994) http://link.aps.org/abstract/PRL/v73/p2308.
[CrossRef] [PubMed]

D. Mugnai, A. Ranfagni, and R. Ruggeri, Phys. Rev. Lett. 84, 4830 (2000) http://link.aps.org/abstract/PRL/v84/p4830.
[CrossRef] [PubMed]

Ph. Balcou and L. Dutriaux, “Dual Optical Tunneling Times in Frustrated Total Internal Reflection,” Phys. Rev. Lett. 78, 851 (1997) http://link.aps.org/abstract/PRL/v78/p851.
[CrossRef]

John J. Carey, Justyna Zawadzka, Dino A. Jaroszynski, and Klaas Wynne, “Noncausal Time Response in Frustrated Total Internal Reflection?” Phys. Rev. Lett. 84, 1431 (2000) http://link.aps.org/abstract/PRL/v84/p1431.
[CrossRef] [PubMed]

W. Luis Mochán and Vera L. Brudny, “Comment on Noncausal Time Response in Frustrated Total Internal Reflection?” Phys. Rev. Lett. 87, 119101 (2001) http://link.aps.org/abstract/PRL/v87/e119101.
[CrossRef]

Yakir Aharonov, Benni Reznil, and Ady Stern, “Quantum Limitatins on Superluminal Propagation,” Phys. Rev. Lett. 81, 2190 (1998) http://link.aps.org/abstract/PRL/v81/p2190.
[CrossRef]

Physics Today (1)

Peter W. Milonni, “Causal Discussion of Superluminal Pulses,” Physics Today 54, 81 (2001) http://www.physicstoday.org/pt/vol-54/iss-2/p14b.html.
[CrossRef]

Physics World (1)

Aephraim M Steinberg, “No thing goes faster than light,” Physics World 133 (2000) http://www.physicsweb.org/article/world/13/9/3.

Physycs-Uspekhi (1)

A. N. Oraevsky, “Superluminal Waves in Amplifying Media,” Physycs-Uspekhi,  41, 1199 (1998).
[CrossRef]

Other (2)

Léon Brillouin, “Wave Propagation and Group Velocity” (Academic, New york, 1960) Ch. II, III, and IV.

Vera L. Brudny and W. Luis Mochán, under preparation.

Supplementary Material (2)

» Media 1: MPG (790 KB)     
» Media 2: MPG (720 KB)     

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Figures (2)

Fig. 1.
Fig. 1.

Animation illustrating the non-evanescent transmission of light across an air gap from ∑1 to ∑2 separating two semi-infinite dielectrics (1.9Mb). A single incoming narrow plane wavefront, with angle of incidence θ, excites secondary waves w 1 within the air gap, which grow with speed c around successive points p 1 at the surface ∑1. As they sweep points p 2 on the other side of the air gap ∑2, these waves in turn excite further secondary waves w 2 within the second dielectric growing with speed c/n. S 1 and S 2 are perfectly opaque screens. The nominal propagation directions are indicated by red arrows. The dots indicate the centers of the secondary waves launched at equally spaced times. The figure corresponds to n=2 and θ=27°<θc .

Fig. 2.
Fig. 2.

Animation illustrating the evanescent transmission of light across an air gap separating two semi-infinite dielectrics (2.1Mb), as in Fig. 1, but with θ=34°>θc . The vertical dashed line connects the point at which the incident wavefront intersects the front face of the air gap i with the corresponding point on the back face t. The thin black arrow connects the superluminally excited position t to its true field source s.

Equations (3)

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

P ( x , z , t ) = c π z Θ ( ct x 2 + z 2 ) ( ct ) 2 x 2 z 2
ϕ ( x , z , t ) = { 0 t < T ( x , z ; x 1 s ) ϕ 0 F ( x , z , t ; x 1 s ) T ( x , z ; x 1 s ) < t < T ( x , z ; x 2 s ) ϕ 0 ( F ( x , z , t ; x 1 s ) F ( x , z , t ; x 2 s ) ) t > T ( x , z ; x 2 s ) ,
F 0 ( x , z , t ) = γ z π γ 2 ( x v t ) 2 + z 2

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