Role of group velocity in tracking field energy in linear dielectrics

doi:10.1364/OE.9.000506

Optics Express

Editor: J. H. Eberly
Vol. 9, Iss. 10 — Nov. 5, 2001
pp: 506–518

Role of group velocity in tracking field energy in linear dielectrics

Michael Ware, S. Glasgow, and Justin Peatross »View Author Affiliations

Optics Express, Vol. 9, Issue 10, pp. 506-518 (2001)
http://dx.doi.org/10.1364/OE.9.000506

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Abstract

A new context for the group delay function (valid for pulses of arbitrary bandwidth) is presented for electromagnetic pulses propagating in a uniform linear dielectric medium. The traditional formulation of group velocity is recovered by taking a narrowband limit of this generalized context. The arrival time of a light pulse at a point in space is defined using a time expectation integral over the Poynting vector. The delay between pulse arrival times at two distinct points consists of two parts: a spectral superposition of group delays and a delay due to spectral reshaping via absorption or amplification. The use of the new context is illustrated for pulses propagating both superluminally and subluminally. The inevitable transition to subluminal behavior for any initially superluminal pulse is also demonstrated.

[Optical Society of America ]

OCIS Codes
(260.2030) Physical optics : Dispersion
(260.2110) Physical optics : Electromagnetic optics
(350.5500) Other areas of optics : Propagation

ToC Category:
Research Papers

History
Original Manuscript: September 19, 2001
Published: November 5, 2001

Citation
Michael Ware, S. Glasgow, and Justin Peatross, "Role of group velocity in tracking field energy in linear dielectrics," Opt. Express 9, 506-518 (2001)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-9-10-506

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References

J. Peatross, S. A. Glasgow, and M. Ware, "Average Energy Flow of Optical Pulses in Dispersive Media," Phys. Rev. Lett. 84, 2370-2373 (2000). [CrossRef] [PubMed]
L. Brillouin, Wave Propagation and Group Velocity (Academic Press, New York, 1960).
M. Born and E. Wolf, Principles of Optics, 7th Ed. (Cambridge, 1999), pp. 19-24.
J. D. Jackson, Classical Electrodynamics, 3rd Ed. (Wiley, New York, 1998), pp. 323, 330-335.
R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, and B. A. Richman, "Measuring Ultrashort Laser Pulses in the Time-Frequency Domain Using Frequency-Resolved Optical Gating," Rev. Sci. Instrum. 68, 3277-3295 (1997). [CrossRef]
K. E. Oughstun and H. Xiao, "Failure of the Quasimonochromatic Approximation for Ultrashort Pulse Propagation in a Dispersive, Attenuative Medium," Phys. Rev. Lett. 78, 642-645 (1997). [CrossRef]
C. G. B. Garrett and D. E. McCumber, "Propagation of a Gaussian Light Pulse through an Anomalous Dispersion Medium," Phys. Rev. A 1, 305-313 (1970). [CrossRef]
R. Y. Chiao, "Superluminal (but Causal) Propagation of Wave Packets in Transparent Media with Inverted Atomic Populations," Phys. Rev. A. 48, R34-R37 (1993). [CrossRef] [PubMed]
E. L. Bolda, J. C. Garrison, and R. Y. Chiao, "Optical Pulse Propagation at Negative Group Velocities due to a Nearby Gain Line," Phys. Rev. A 49, 2938-2947 (1994). [CrossRef] [PubMed]
Y. Chiao and A. M. Steinberg, "Tunneling Times and Superluminality," Progress in Optics 37, pp. 347-406 (Emil Wolf ed., Elsevier, Amsterdam, 1997). [CrossRef]
S. Chu and S. Wong, "Linear Pulse Propagation in an Absorbing Medium," Phys. Rev. Lett. 48, 738-741 (1982). [CrossRef]
L. J. Wang, A. Kuzmmich, and A. Dogariu, "Gain-Assisted Superluminal Light Propagation," Nature 406, 277-279 (2000). [CrossRef] [PubMed]
R. L. Smith, "The Velocities of Light," Am. J. Phys. 38, 978-983 (1970). [CrossRef]
M. Ware, W. E. Dibble, S. A. Glasgow, and J. Peatross, "Energy Flow in Angularly Dispersive Optical Systems," J. Opt. Soc. Am. B 18 839-845 (2001) . [CrossRef]
R. Loudon, "The Propagation of Electromagnetic Energy through an Absorbing Dielectric," J. Phys. A 3, 233-245 (1970). [CrossRef]
Md. Aminul Islam Talukder, Yoshimitsu Amagishi, and Makoto Tomita, "Superluminal to Subluminal Transition in the Pulse Propagation in a Resonantly Absorbing Medium," Phys. Rev. Lett. 86, 3546-3549 (2001). [CrossRef]
M. Ware, S. A. Glasgow, and J. Peatross "Energy Transport in Linear Dielectrics," Opt. Express 9, 519-532 (2001), http://www.opticsexpress.org/oearchive/source/35289.htm

Other

J. Peatross, S. A. Glasgow, and M. Ware, "Average Energy Flow of Optical Pulses in Dispersive Media," Phys. Rev. Lett. 84, 2370-2373 (2000). [CrossRef] [PubMed]
L. Brillouin, Wave Propagation and Group Velocity (Academic Press, New York, 1960).
M. Born and E. Wolf, Principles of Optics, 7th Ed. (Cambridge, 1999), pp. 19-24.
J. D. Jackson, Classical Electrodynamics, 3rd Ed. (Wiley, New York, 1998), pp. 323, 330-335.
R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, and B. A. Richman, "Measuring Ultrashort Laser Pulses in the Time-Frequency Domain Using Frequency-Resolved Optical Gating," Rev. Sci. Instrum. 68, 3277-3295 (1997). [CrossRef]
K. E. Oughstun and H. Xiao, "Failure of the Quasimonochromatic Approximation for Ultrashort Pulse Propagation in a Dispersive, Attenuative Medium," Phys. Rev. Lett. 78, 642-645 (1997). [CrossRef]
C. G. B. Garrett and D. E. McCumber, "Propagation of a Gaussian Light Pulse through an Anomalous Dispersion Medium," Phys. Rev. A 1, 305-313 (1970). [CrossRef]
R. Y. Chiao, "Superluminal (but Causal) Propagation of Wave Packets in Transparent Media with Inverted Atomic Populations," Phys. Rev. A. 48, R34-R37 (1993). [CrossRef] [PubMed]
E. L. Bolda, J. C. Garrison, and R. Y. Chiao, "Optical Pulse Propagation at Negative Group Velocities due to a Nearby Gain Line," Phys. Rev. A 49, 2938-2947 (1994). [CrossRef] [PubMed]
Y. Chiao and A. M. Steinberg, "Tunneling Times and Superluminality," Progress in Optics 37, pp. 347-406 (Emil Wolf ed., Elsevier, Amsterdam, 1997). [CrossRef]
S. Chu and S. Wong, "Linear Pulse Propagation in an Absorbing Medium," Phys. Rev. Lett. 48, 738-741 (1982). [CrossRef]
L. J. Wang, A. Kuzmmich, and A. Dogariu, "Gain-Assisted Superluminal Light Propagation," Nature 406, 277-279 (2000). [CrossRef] [PubMed]
R. L. Smith, "The Velocities of Light," Am. J. Phys. 38, 978-983 (1970). [CrossRef]
M. Ware, W. E. Dibble, S. A. Glasgow, and J. Peatross, "Energy Flow in Angularly Dispersive Optical Systems," J. Opt. Soc. Am. B 18 839-845 (2001) . [CrossRef]
R. Loudon, "The Propagation of Electromagnetic Energy through an Absorbing Dielectric," J. Phys. A 3, 233-245 (1970). [CrossRef]
Md. Aminul Islam Talukder, Yoshimitsu Amagishi, and Makoto Tomita, "Superluminal to Subluminal Transition in the Pulse Propagation in a Resonantly Absorbing Medium," Phys. Rev. Lett. 86, 3546-3549 (2001). [CrossRef]
M. Ware, S. A. Glasgow, and J. Peatross "Energy Transport in Linear Dielectrics," Opt. Express 9, 519-532 (2001), http://www.opticsexpress.org/oearchive/source/35289.htm

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