OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 21, Iss. 3 — Mar. 1, 2004
  • pp: 439–450

Pulse centroid velocity of the Poynting vector

Natalie A. Cartwright and Kurt E. Oughstun  »View Author Affiliations


JOSA A, Vol. 21, Issue 3, pp. 439-450 (2004)
http://dx.doi.org/10.1364/JOSAA.21.000439


View Full Text Article

Enhanced HTML    Acrobat PDF (244 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

The evolution of the pulse centroid velocity of the Poynting vector for both ultrawideband rectangular and ultrashort Gaussian envelope pulses is presented as a function of the propagation distance in a dispersive, absorptive dielectric material. The index of refraction of the material is described by the Lorentz–Lorenz formula in which a single-resonance Lorentz model is used to describe the mean molecular polarizability. The results show that, as the propagation distance increases above a value that is on the order of an absorption depth at the pulse carrier frequency, the centroid velocity of an ultrawideband/ultrashort pulse tends toward the rate at which the Brillouin precursor travels through the medium. For small propagation distances when the carrier frequency of the optical pulse lies in the absorption band of the material, the centroid velocity can take on superluminal and negative values.

© 2004 Optical Society of America

OCIS Codes
(260.2030) Physical optics : Dispersion
(260.2110) Physical optics : Electromagnetic optics

History
Original Manuscript: September 5, 2003
Revised Manuscript: October 23, 2003
Manuscript Accepted: October 27, 2003
Published: March 1, 2004

Citation
Natalie A. Cartwright and Kurt E. Oughstun, "Pulse centroid velocity of the Poynting vector," J. Opt. Soc. Am. A 21, 439-450 (2004)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-21-3-439


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. Lord Rayleigh, “On progressive waves,” Proc. London Math. Soc. IX, 21–26 (1877). [CrossRef]
  2. E. Wolf, “Significance and measurability of the phase of a spatially coherent optical field,” Opt. Lett. 28, 5–6 (2003). [CrossRef] [PubMed]
  3. W. R. Hamilton, “Researches respecting vibration, connected with the theory of light,” Proc. R. Ir. Acad. 1, 341–349 (1839).
  4. M. Born, E. Wolf, Principles of Optics (Cambridge U. Press, Cambridge, UK, 1999).
  5. A. Sommerfeld, “Über die fortpflanzung des lichtes in disperdierenden medien,” Ann. Phys. (Leipzig) 44, 177–202 (1914). [CrossRef]
  6. H. A. Lorentz, The Theory of Electrons (Tuebner, Leipzig, 1909), Chap. IV; reprinted (Dover, New York, 1952).
  7. L. Brillouin, “Über die fortpflanzung des licht in disperdierenden medien,” Ann. Phys. (Leipzig) 44, 204–240 (1914).
  8. L. Brillouin, Wave Propagation and Group Velocity (Academic, New York, 1960).
  9. P. Debye, “Näherungsformeln für die zylinderfunktionen für grosse werte des arguments und unbeschränkt verander liche werte des index,” Math. Ann. 67, 535–558 (1909). [CrossRef]
  10. H. Baerwald, “Über die fortpflanzung von signalen in disperdierenden medien,” Ann. Phys. 7, 731–760 (1930). [CrossRef]
  11. K. E. Oughstun, G. C. Sherman, “Optical pulse propagation in temporally dispersive Lorentz media,” J. Opt. Soc. Am. 65, 1224A (1975).
  12. F. W. J. Olver, “Why steepest descents?” SIAM (Soc. Ind. Appl. Math.) Rev. 12, 228–247 (1970).
  13. R. Loudon, “The propagation of electromagnetic energy through an absorbing dielectric,” J. Phys. A 3, 233–245 (1970). [CrossRef]
  14. K. E. Oughstun, S. Shen, “Velocity of energy transport for a time-harmonic field in a multiple-resonance Lorentz medium,” J. Opt. Soc. Am. B 5, 2395–2398 (1988). [CrossRef]
  15. K. E. Oughstun, G. C. Sherman, “Propagation of electromagnetic pulses in a linear dispersive medium with absorption (the Lorentz medium),” J. Opt. Soc. Am. B 5, 817–849 (1988). [CrossRef]
  16. S. Shen, K. E. Oughstun, “Dispersive pulse propagation in a double-resonance Lorentz medium,” J. Opt. Soc. Am. B 6, 948–963 (1989). [CrossRef]
  17. K. E. Oughstun, G. C. Sherman, “Uniform asymptotic description of ultrashort rectangular optical pulse propagation in a linear, causally dispersive medium,” Phys. Rev. A 41, 6090–6113 (1990). [CrossRef] [PubMed]
  18. K. Oughstun, G. Sherman, Pulse Propagation in Causal Dielectrics (Springer-Verlag, Berlin, 1994).
  19. G. Sherman, K. E. Oughstun, “Description of pulse dynamics in Lorentz media in terms of the energy velocity and attenuation of time-harmonic waves,” Phys. Rev. Lett. 47, 1451–1454 (1981). [CrossRef]
  20. G. Sherman, K. E. Oughstun, “Energy velocity description of pulse propagation in absorbing, dispersive dielectrics,” J. Opt. Soc. Am. B 12, 229–247 (1995). [CrossRef]
  21. R. Smith, “The velocities of light,” Am. J. Phys. 38, 978–984 (1970). [CrossRef]
  22. M. Lisak, “Energy expressions and energy velocity for wave packets in an absorptive and dispersive medium,” J. Phys. A 9, 1145–1158 (1976). [CrossRef]
  23. J. Peatross, S. A. Glasgow, M. Ware, “Average energy flow of optical pulses in dispersive media,” Phys. Rev. Lett. 84, 2370–2373 (2000). [CrossRef] [PubMed]
  24. M. Ware, S. A. Glasgow, J. Peatross, “Role of group velocity in tracking field energy in linear dielectrics,” Opt. Express 9, 506–518 (2001). [CrossRef] [PubMed]
  25. K. E. Oughstun, J. E. Laurens, “Asymptotic descriptionof ultrashort electromagnetic pulse propagation in a linear, causally dispersive medium,” Radio Sci. 26, 245–258 (1991). [CrossRef]
  26. K. E. Oughstun, G. C. Sherman, “Uniform asymptotic description of electromagnetic pulse propagation in a linear dispersive medium with absorption (the Lorentz medium),” J. Opt. Soc. Am. A 6, 1394–1420 (1989). [CrossRef]
  27. K. E. Oughstun, “Pulse propagation in a linear, causally dispersive medium,” Proc. IEEE 79, 1394–1420 (1991). [CrossRef]
  28. E. T. Copson, Asymptotic Expansions (Cambridge U. Press, London, 1965), Chap. 2.
  29. H. Xiao, K. E. Oughstun, “Failure of the group-velocity description for ultrawideband pulse propagation in a causally dispersive, absorptive dielectric,” J. Opt. Soc. Am. B 16, 1773–1785 (1999). [CrossRef]
  30. K. E. Oughstun, N. A. Cartwright, “On the Lorentz–Lorenz formula and the Lorentz model of dielectric dispersion,” Opt. Express 11, 1541–1546 (2003). [CrossRef] [PubMed]
  31. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941), Sect. 5.12.
  32. E. T. Whittaker, G. N. Watson, A Course of Modern Analysis (Macmillan, New York, 1943), Sect. 5.2.
  33. Here, “dominates the field” refers to the amplitude of the Brillouin precursor being larger than the other contributions to the field when the entire propagated field is considered, as it is in calculating the centroid velocity. However, there are θ domains within the evolved pulse in which the Sommerfeld precursor or the pole contribution is the dominant contribution to the field.
  34. C. M. Balictsis, K. E. Oughstun, “Uniform asymptotic description of ultrashort Gaussian pulse propagation in a causal, dispersive dielectric,” Phys. Rev. E 47, 3645–3669 (1993). [CrossRef]
  35. K. E. Oughstun, C. M. Balictsis, “Gaussian pulse propagation in a dispersive, absorbing dielectric,” Phys. Rev. Lett. 77, 2210–2213 (1996). [CrossRef] [PubMed]
  36. C. M. Balictsis, K. E. Oughstun, “Generalized asymptotic description of the propagated field dynamics in Gaussian pulse propagation in a linear, causally dispersive medium,” Phys. Rev. E 55, 1910–1921 (1997). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited