Laser Filamentation

Mathematical Methods and Models

  • Andre D. Bandrauk
  • Emmanuel Lorin
  • Jerome V. Moloney

Part of the CRM Series in Mathematical Physics book series (CRM)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Alan C. Newell
    Pages 1-17
  3. Yuri Cher, Magdalena Czubak, Catherine Sulem
    Pages 77-95
  4. Tie-Jun Wang, Shuai Yuan, Jingjing Ju, Heping Zeng, Ruxin Li, Zhizhan Xu et al.
    Pages 121-146
  5. A. Couairon, V. Jukna, J. Darginavičius, D. Majus, N. Garejev, I. Gražulevičiūtė et al.
    Pages 147-165
  6. Paris Panagiotopoulos, Patrick Townsend Whalen, Miroslav Kolesik, Jerome V. Moloney
    Pages 185-213
  7. Back Matter
    Pages 215-216

About this book


This book is focused on the nonlinear theoretical and mathematical problems associated with ultrafast intense laser pulse propagation in gases and in particular, in air. With the aim of understanding the physics of filamentation in gases, solids, the atmosphere, and even biological tissue, specialists in nonlinear optics and filamentation from both physics and mathematics attempt to rigorously derive and analyze relevant non-perturbative models. Modern laser technology allows the generation of ultrafast (few cycle) laser pulses, with intensities exceeding the internal electric field in atoms and molecules (E=5x109 V/cm or intensity I = 3.5 x 1016 Watts/cm2 ). The interaction of such pulses with atoms and molecules leads to new, highly nonlinear nonperturbative regimes, where new physical phenomena, such as High Harmonic Generation (HHG), occur, and from which the shortest (attosecond - the natural time scale of the electron) pulses have been created. One of the major experimental discoveries in this nonlinear nonperturbative regime, Laser Pulse Filamentation, was observed by Mourou and Braun in 1995, as the propagation of pulses over large distances with narrow and intense cones. This observation has led to intensive investigation in physics and applied mathematics of new effects such as self-transformation of these pulses into white light, intensity clamping, and multiple filamentation, as well as to potential applications to wave guide writing, atmospheric remote sensing, lightning guiding, and military long-range weapons.

The increasing power of high performance computers and the mathematical modelling and simulation of photonic systems has enabled many new areas of research. With contributions by theorists and mathematicians, supplemented by active experimentalists who are experts in the field of nonlinear laser molecule interaction and propagation, Laser Filamentation sheds new light on scientific and industrial applications of modern lasers.


Atmospheric Remote Sensing Intense Laser Pulse Propagation in Materials Intensity Clamping Laser Filamentation Laser-guided Medicine Lasers in Planet Earth Laster Filamentation Mathematical Methods and Models Lightning Guiding Maxwell-Schroedinger Equations Military Long-range Weapons Multiple Filamentation Non-perturbative Models Non-perturbative Models Laser Filamentation Nonlinear Nonperturbative Optical Science Nonlinear Optical Processes Lasers Ultrafast Intense Laser Science Ultrafast Lasers Wave Guide Writing

Editors and affiliations

  • Andre D. Bandrauk
    • 1
  • Emmanuel Lorin
    • 2
  • Jerome V. Moloney
    • 3
  1. 1.Faculté des SciencesUniversité de SherbrookeSherbrookeCanada
  2. 2.School of Mathematics and StatisticsCarleton UniversityOttawaCanada
  3. 3.Arizona Center for Mathematical SciencesUniversity of ArizonaTucsonUSA

Bibliographic information