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.
