WIAS Preprint No. 1359, (2008)

Asymptotic pulse shapes in filamentary propagation of intense femtosecond pulses


  • Krüger, Carsten
  • Demircan, Ayhan
  • Steinmeyer, Günter

2010 Mathematics Subject Classification

  • 78A60 35Q55 37K40 81V80

2008 Physics and Astronomy Classification Scheme

  • 42.65.Tg 42.65.-k 52.38.Hb 42.68Ay


  • Nonlinear Schroedinger equations, Ultrashort pulse propagation




Self-compression of intense ultrashort laser pulses inside a self-guided filament is discussed. The filament self-guiding mechanism requires a balance between diffraction, plasma self-defocusing and Kerr-type self-focusing, which gives rise to asymptotic intensity profiles on axis of the filament. The asymptotic solutions appear as the dominant pulse shaping mechanism in the leading part of the pulse, causing a pinch of the photon density close to zero delay, which substantiates as pulse compression. The simple analytical model is backed up by numerical simulations, confirming the prevalence of spatial coupling mechanisms and explaining the emerging inhomogeneous spatial structure. Numerical simulations confirm that only spatial effects alone may already give rise to filament formation. Consequently, self-compression is explained by a dynamic balance between two optical nonlinearities, giving rise to soliton-like pulse formation inside the filament.

Appeared in

  • Laser Physics, 19 (2009) pp. 330-335.

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