# American Institute of Mathematical Sciences

October  2009, 23(4): 1099-1139. doi: 10.3934/dcds.2009.23.1099

## Modeling ultrashort filaments of light

 1 Département de Physique Théorique et Appliquée, CEA-DAM/Ile de France, B.P. 12, 91680 Bruyères-le-Châtel, France, France

Received  June 2007 Revised  August 2007 Published  November 2008

Laser sources nowadays deliver optical pulses reaching few cycles in duration and peak powers exceeding several terawatt (TW). When such pulses propagate in transparent media, they first self-focus in space, until they generate a tenuous plasma by photo-ionization. These pulses evolve as self-guided objects, resulting from successive equilibria between the Kerr focusing process, the defocusing action of the electron plasma and the chromatic dispersion of the medium. Discovered ten years ago, this self-channeling mechanism reveals a new physics, having direct applications in the long-distance propagation of TW beams in air, supercontinuum emission as well as pulse self-compression. This review presents the major progress in this field. Particular emphasis is laid to the derivation of the propagation equations, for single as well as coupled wave components. Physics is discussed from numerical simulations and explained by analytical arguments. Attention is also paid to the multifilamentation instability, which breaks up broad beams into small-scale cells. Several experimental data validate theoretical descriptions.
Citation: Luc Bergé, Stefan Skupin. Modeling ultrashort filaments of light. Discrete & Continuous Dynamical Systems - A, 2009, 23 (4) : 1099-1139. doi: 10.3934/dcds.2009.23.1099
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