American Institute of Mathematical Sciences

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

Modeling ultrashort filaments of light

Luc Bergé 1, and  Stefan Skupin 1,

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.
Keywords: Nonlinear Schroedinger models, nonlinear wave propagation.
Mathematics Subject Classification: Primary: 78A40, 78A60; Secondary: 74J30.
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
[1]

Andrey Shishkov, Laurent Véron. Propagation of singularities of nonlinear heat flow in fissured media. Communications on Pure & Applied Analysis, 2013, 12 (4) : 1769-1782. doi: 10.3934/cpaa.2013.12.1769
[2]

Tai-Chia Lin. Vortices for the nonlinear wave equation. Discrete & Continuous Dynamical Systems - A, 1999, 5 (2) : 391-398. doi: 10.3934/dcds.1999.5.391
[3]

J. M. Cushing. Nonlinear semelparous Leslie models. Mathematical Biosciences & Engineering, 2006, 3 (1) : 17-36. doi: 10.3934/mbe.2006.3.17
[4]

Q-Heung Choi, Tacksun Jung. A nonlinear wave equation with jumping nonlinearity. Discrete & Continuous Dynamical Systems - A, 2000, 6 (4) : 797-802. doi: 10.3934/dcds.2000.6.797
[5]

Út V. Lê. Regularity of the solution of a nonlinear wave equation. Communications on Pure & Applied Analysis, 2010, 9 (4) : 1099-1115. doi: 10.3934/cpaa.2010.9.1099
[6]

Jorge A. Esquivel-Avila. Qualitative analysis of a nonlinear wave equation. Discrete & Continuous Dynamical Systems - A, 2004, 10 (3) : 787-804. doi: 10.3934/dcds.2004.10.787
[7]

Wendi Wang. Epidemic models with nonlinear infection forces. Mathematical Biosciences & Engineering, 2006, 3 (1) : 267-279. doi: 10.3934/mbe.2006.3.267
[8]

Chang-Yeol Jung, Alex Mahalov. Wave propagation in random waveguides. Discrete & Continuous Dynamical Systems - A, 2010, 28 (1) : 147-159. doi: 10.3934/dcds.2010.28.147
[9]

Liu Rui. The explicit nonlinear wave solutions of the generalized $b$-equation. Communications on Pure & Applied Analysis, 2013, 12 (2) : 1029-1047. doi: 10.3934/cpaa.2013.12.1029
[10]

Mark J. Ablowitz, Terry S. Haut, Theodoros P. Horikis, Sean D. Nixon, Yi Zhu. Nonlinear wave dynamics: From lasers to fluids. Discrete & Continuous Dynamical Systems - S, 2011, 4 (5) : 923-955. doi: 10.3934/dcdss.2011.4.923
[11]

Nakao Hayashi, Seishirou Kobayashi, Pavel I. Naumkin. Nonlinear dispersive wave equations in two space dimensions. Communications on Pure & Applied Analysis, 2015, 14 (4) : 1377-1393. doi: 10.3934/cpaa.2015.14.1377
[12]

Gen Nakamura, Michiyuki Watanabe. An inverse boundary value problem for a nonlinear wave equation. Inverse Problems & Imaging, 2008, 2 (1) : 121-131. doi: 10.3934/ipi.2008.2.121
[13]

Geng Chen, Yannan Shen. Existence and regularity of solutions in nonlinear wave equations. Discrete & Continuous Dynamical Systems - A, 2015, 35 (8) : 3327-3342. doi: 10.3934/dcds.2015.35.3327
[14]

Dalibor Pražák. On the dimension of the attractor for the wave equation with nonlinear damping. Communications on Pure & Applied Analysis, 2005, 4 (1) : 165-174. doi: 10.3934/cpaa.2005.4.165
[15]

Carlos E. Kenig. The method of energy channels for nonlinear wave equations. Discrete & Continuous Dynamical Systems - A, 2019, 0 (0) : 1-15. doi: 10.3934/dcds.2019240
[16]

Raul Borsche, Axel Klar, T. N. Ha Pham. Nonlinear flux-limited models for chemotaxis on networks. Networks & Heterogeneous Media, 2017, 12 (3) : 381-401. doi: 10.3934/nhm.2017017
[17]

Akisato Kubo. Nonlinear evolution equations associated with mathematical models. Conference Publications, 2011, 2011 (Special) : 881-890. doi: 10.3934/proc.2011.2011.881
[18]

Eun Heui Kim, Charis Tsikkou. Two dimensional Riemann problems for the nonlinear wave system: Rarefaction wave interactions. Discrete & Continuous Dynamical Systems - A, 2017, 37 (12) : 6257-6289. doi: 10.3934/dcds.2017271
[19]

D. G. Aronson, N. V. Mantzaris, Hans Othmer. Wave propagation and blocking in inhomogeneous media. Discrete & Continuous Dynamical Systems - A, 2005, 13 (4) : 843-876. doi: 10.3934/dcds.2005.13.843
[20]

Shangbing Ai, Wenzhang Huang, Zhi-An Wang. Reaction, diffusion and chemotaxis in wave propagation. Discrete & Continuous Dynamical Systems - B, 2015, 20 (1) : 1-21. doi: 10.3934/dcdsb.2015.20.1

2018 Impact Factor: 1.143

Tools

Metrics

  • PDF downloads (9)
  • HTML views (0)
  • Cited by (7)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences