OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B

| OPTICAL PHYSICS

  • Editor: Henry van Driel
  • Vol. 27, Iss. 8 — Aug. 1, 2010
  • pp: 1664–1670

Optical precursors in the singular and weak dispersion limits

Kurt E. Oughstun, Natalie A. Cartwright, Daniel J. Gauthier, and Heejeong Jeong  »View Author Affiliations


JOSA B, Vol. 27, Issue 8, pp. 1664-1670 (2010)
http://dx.doi.org/10.1364/JOSAB.27.001664


View Full Text Article

Enhanced HTML    Acrobat PDF (507 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

The description of the precursor fields in a single-resonance Lorentz model dielectric is considered in the singular and weak dispersion limits. The singular dispersion limit is obtained as the damping approaches zero and the material dispersion becomes increasingly concentrated about the resonance frequency. The algebraic peak amplitude decay of the Brillouin precursor with propagation distance z > 0 then changes from a z 1 / 2 to a z 1 / 3 behavior. The weak dispersion limit is obtained as the material density decreases to zero. The material dispersion then becomes vanishingly small everywhere and the precursors become increasingly compressed in the space-time domain immediately following the speed-of-light point ( z , t ) = ( z , z / c ) . In order to circumvent the numerical difficulties introduced in this case, an approximate equivalence relation is derived that allows the propagated field evolution due to an ultrawideband signal to be calculated in an equivalent dispersive medium that is highly absorptive.

© 2010 Optical Society of America

OCIS Codes
(260.2030) Physical optics : Dispersion
(320.2250) Ultrafast optics : Femtosecond phenomena
(320.5550) Ultrafast optics : Pulses

ToC Category:
Ultrafast Optics

History
Original Manuscript: May 4, 2010
Revised Manuscript: June 22, 2010
Manuscript Accepted: June 23, 2010
Published: July 29, 2010

Citation
Kurt E. Oughstun, Natalie A. Cartwright, Daniel J. Gauthier, and Heejeong Jeong, "Optical precursors in the singular and weak dispersion limits," J. Opt. Soc. Am. B 27, 1664-1670 (2010)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-27-8-1664


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. H. A. Lorentz, Theory of Electrons (Teubner, 1906), Chap. IV.
  2. A. Sommerfeld, “Über die fortpflanzung des lichtes in disperdierenden medien,” Ann. Phys. (Leipzig) 44, 177–202 (1914).
  3. L. Brillouin, “Über die fortpflanzung des licht in disperdierenden medien,” Ann. Phys. (Leipzig) 44, 203–240 (1914).
  4. L. Brillouin, Wave Propagation and Group Velocity (Academic, 1960).
  5. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941), Sec. 5.18.
  6. K. E. Oughstun and G. C. Sherman, Electromagnetic Pulse Propagation in Causal Dielectrics (Springer-Verlag, 1994).
  7. K. E. Oughstun, Electromagnetic & Optical Pulse Propagation 1: Spectral Representations in Temporally Dispersive Media (Springer, 2006). [PubMed]
  8. K. E. Oughstun, Electromagnetic & Optical Pulse Propagation 2: Temporal Pulse Dynamics in Dispersive Attenuative Media (Springer, 2009).
  9. H. M. Nussenzveig, Causality and Dispersion Relations (Academic, 1972), Chap. 1.
  10. K. E. Oughstun and 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]
  11. K. E. Oughstun and 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]
  12. N. A. Cartwright and K. E. Oughstun, “Uniform asymptotics applied to ultrawideband pulse propagation,” SIAM Rev. 49, 628–648 (2007). [CrossRef]
  13. There are several definitions of what an ultrawideband signal is; see, for example, Section 11.2.2 of . We take here the simple physical definition to mean a temporal pulse whose frequency spectrum along the positive real frequency axis is nonzero as ω→0 and which goes to zero as 1/ω or less as ω→∞.
  14. P. D. Smith and K. E. Oughstun, “Electromagnetic energy dissipation and propagation of an ultrawideband plane wave pulse in a causally dispersive dielectric,” Radio Sci. 33, 1489–1504 (1998). [CrossRef]
  15. The Beer–Lambert–Bouger law was originally discovered by P. Bouger, Essai d’Optique sur la Gradation de la Lumiere (Claude Jombert, 1729) and subsequently cited by J. H. Lambert, Photometri (V. E. Klett, 1760); the result was then extended by A. Beer, Einleitung in die höhere Optik (Friedrich Viewig, 1853) to include the concentration of solutions in the expression of the absorption coefficient for the intensity of light.
  16. K. E. Oughstun, “Dynamical evolution of the Brillouin precursor in Rocard–Powles–Debye model dielectrics,” IEEE Trans. Antennas Propag. 53, 1582–1590 (2005). [CrossRef]
  17. M. Pieraccini, A. Bicci, D. Mecatti, G. Macaluso, and C. Atzeni, “Propagation of large bandwidth microwave signals in water,” IEEE Trans. Antennas Propag. 57, 3612–3618 (2009). [CrossRef]
  18. In the group velocity description, the “strength” of the material dispersion is typically measured through the derivative dnr(ω)/dω as that is what appears in the coefficients β1≡(nr+ωdnr/dω)/c and β2≡(2dnr/dω+ωd2nr/dω2)/c in the Taylor series expansion of the real propagation factor β(ω)≡R{k̃(ω)} in a hypothetical “lossless” dispersive medium. It is directly found from Eq. that this first derivative is directly proportional to the number density N so that these coefficients can always be made as small as desired at any real ω simply by choosing N sufficiently small.
  19. H. Jeong, A. M. C. Dawes, and D. J. Gauthier, “Direct observation of optical precursors in a region of anomalous dispersion,” Phys. Rev. Lett. 96, 143901 (2006). [CrossRef] [PubMed]
  20. B. Macke and B. Ségard, “Optical precursors in transparent media,” Phys. Rev. A 80, 011803 (2009). [CrossRef]
  21. H. Jeong and S. Du, “Two-way transparency in the light-matter interaction: Optical precursors with electromagnetically induced transparency,” Phys. Rev. A 79, 011802 (2009). [CrossRef]
  22. D. Wei, J. F. Chen, M. M. T. Loy, G. K. L. Wong, and S. Du, “Optical precursors with electromagnetically induced transparency in cold atoms,” Phys. Rev. Lett. 103, 093602 (2009). [CrossRef] [PubMed]
  23. B. Macke and B. Ségard, “Optical precursors with self-induced transparency,” Phys. Rev. A 81, 015803 (2010). [CrossRef]
  24. J. F. Chen, S. Wang, D. Wei, M. M. T. Loy, G. K. L. Wong, and S. Du, “Optical coherent transients in cold atoms: from free induction decay to optical precursors,” Phys. Rev. A 81, 033844 (2010). [CrossRef]
  25. H. Jeong and S. Du, “Slow-light-induced interference with stacked optical precursors for square input pulses,” Opt. Lett. 35, 124–126 (2010). [CrossRef] [PubMed]
  26. W. R. LeFew, S. Venakides, and D. J. Gauthier, “Accurate description of optical precursors and their relation to weak-field coherent optical transients,” Phys. Rev. A 79, 063842 (2009). [CrossRef]
  27. M. D. Crisp, “Propagation of small-area pulses of coherent light through a resonant medium,” Phys. Rev. A 1, 1604–1611 (1970). [CrossRef]
  28. B. Macke and B. Ségard, “Comment on “Direct observation of optical precursors in a region of anomalous dispersion”,” arXiv:physics/0605039.
  29. K. E. Oughstun, “Noninstantaneous, finite rise-time effects on the precursor field formation in linear dispersive pulse propagation,” J. Opt. Soc. Am. A 12, 1715–1729 (1995). [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