The European Physical Journal Special Topics

, Volume 147, Issue 1, pp 253–264 | Cite as

The Maxwell-Lorentz model for optical pulses

  • M. P. Sørensen
  • M. Brio


Dynamics of optical pulses, especially of ultra short femtosecond pulses, are of great technological and theoretical interest. The dynamics of optical pulses is usually studied using the nonlinear Schrödinger (NLS) equation model. While such approach works surprisingly well for description of pulse propagation, at least in the femtosecond regime, the full system posses a wealth of new wave phenomena that we explore in this paper: envelope collapse regularization resulting in the orignal pulse splitting; development of infinite gradients in the carrier wave; existence of the stable top hat traveling wave solutions formed by a pair of kink anti-kink shaped optical waves.


Soliton European Physical Journal Special Topic Travel Wave Solution Optical Pulse Carrier Wave 
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  1. C.V. Hile, Wave Motion 24, 1 (1996) Google Scholar
  2. M.P. Sørensen, M. Brio, G.M. Webb, J.V. Moloney, Physica D 170, 287 (2002) Google Scholar
  3. G. Webb, M.P. Sørensen, M. Brio, A.R. Zakharian, J.V. Moloney, Physica D 191, 49 (2004) Google Scholar
  4. G.P. Agrawal, Nonlinear Fiber Optics (Academic Press, New York, 1995) Google Scholar
  5. L. Gilles, S.C. Hagness, L. Vázquez, J. Comput. Phys. 161, 379 (2000) Google Scholar
  6. P.M. Bennett, Parallel Numerical Integration of Maxwell's Full-Vector Equations in Nonlinear Focusing Media, Ph.D. thesis (The University of New Mexico, Albuquerque, New Mexico, 2000) Google Scholar
  7. L. Bergé, Phys. Rep. 303, 259 (1998) Google Scholar
  8. Yu.S. Kivshar, D.E. Pelinovsky, Phys. Rep. 331, 117 (2000) Google Scholar
  9. M.P. Sørensen, G.M. Webb, M. Brio, J.V. Moloney, Phys. Rev. E 71, 036602 (2005) Google Scholar
  10. A. Iserles, A First Course in the Numerical Analysis of Differential Equations (Cambridge University Press, Cambridge Texts in Applied Mathematics, 2002) Google Scholar
  11. K.R. Jackson, Runge-Kutta, Google Scholar
  12. C.V. Hile, W.L. Kath, J. Opt. Soc. Am. B 13, 1135 (1996) Google Scholar
  13. J.E. Rothenberg, D. Grischkowsky, Phys. Rev. Lett. 62, 531 (1989) Google Scholar
  14. R.G. Flesch, A. Pushkarev, J.V. Moloney, Phys. Rev. Lett. 76, 2488 (1996) Google Scholar
  15. L. Gilles, J.V. Moloney, L. Vázquez, Phys. Rev. E 60, 1051 (1999) Google Scholar

Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

Authors and Affiliations

  • M. P. Sørensen
    • 1
  • M. Brio
    • 2
  1. 1.Department of MathematicsTechnical University of DenmarkKongens LyngbyDenmark
  2. 2.Department of Mathematics, Arizona Center for Mathematical SciencesUniversity of ArizonaTucsonUSA

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