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.

Studying and using light or "photons" to image and then to control and transmit molecular information is among the most challenging and significant research fields to emerge in recent years. One of the fastest growing areas involves research in the temporal imaging of quantum phenomena, ranging from molecular dynamics in the femto (10-15s) time regime for atomic motion to the atto (10-18s) time scale of electron motion. In fact, the attosecond "revolution" is now recognized as one of the most important recent breakthroughs and innovations in the science of the 21st century. A major participant in the development of ultrafast femto and attosecond temporal imaging of molecular quantum phenomena has been theory and numerical simulation of the nonlinear, non-perturbative response of atoms and molecules to ultrashort laser pulses. Therefore, imaging quantum dynamics is a new frontier of science requiring advanced mathematical approaches for analyzing and solving spatial and temporal multidimensional partial differential equations such as Time-Dependent Schroedinger Equations (TDSE) and Time-Dependent Dirac equations (TDDEs for relativistic phenomena). These equations are also coupled to the photons in Maxwell's equations for collective propagation effects. Inversion of the experimental imaging data of quantum dynamics presents new mathematical challenges in the imaging of quantum wave coherences on subatomic (subnanometer) spatial dimensions and multiple timescales from atto to femto and even nanoseconds. In Quantum Dynamic Imaging: Theoretical and Numerical Methods, leading researchers discuss these exciting state-of-the-art developments and their implications for R&D in view of the promise of quantum dynamic imaging science as the essential tool for controlling matter at the molecular level.

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.

We arepleasedtopresentthesixthvolumeofProgressinUltrafastIntenseLaserS- ence. As the frontiers of ultrafast intense laser science rapidly expand ever outward, there continues to be a growing demand for an introduction to this interdisciplinary research?eldthatisatoncewidelyaccessibleandcapableofdeliveringcutting-edge developments. Our series aims to respond to this call by providing a compilation of concise review-style articles written by researchers at the forefront of this research ?eld, so that researcherswith differentbackgroundsas well as graduatestudentscan easily grasp the essential aspects. As in previousvolumesof PUILS, each chapterof this bookbeginswith an int- ductory part, in which a clear and concise overview of the topic and its signi?cance is given, and moves onto a description of the authors' most recent research results. All the chapters are peer-reviewed. The articles of this sixth volume cover a diverse rangeoftheinterdisciplinaryresearch?eld,andthetopicsmaybegroupedintothree categories: responses of molecules to ultrashort intense laser pulses (Chaps. 1 - 4), generation and characterization of attosecond pulses and high-order harmonics (Chaps. 5 - 8), and?lamentationand laser-plasma interactionand their applications (Chaps. 9 - 11).

This volume contains the lectures and communications presented at the NATO Advanced Research Workshop (NATO ARW 900857) which was held May 5-10, 1991 at McMaster University, Hamilton, Ontario, Canada. A scientific commitee made up of P.P. Lambropoulos (USC & Crete), P.8. Corkum (NRC, Ottawa), and H. B. vL. van den Heuvell (FOM, Amsterdam) guided the organizers, A.D. Bandrauk (Sherbrooke) and S.C. Wallace (Toronto) in preparing a programme which would cover the latest advances in the field of atom and molecule laser interactions. Since the last meeting held in July 1987 on "Atomic and Molecular Processes with Short Intense Laser Pulses", NATO ASI vol 1718 (Plenum Press 1988), considerable progress has been made in understanding high intensity effects on atoms and the concomitant coherence effects. After four years, the emphasis is now shifting more to molecules. The present volume represents therefore this trend with four sections covering the main interests of research endeavours in this area: i) Atoms in Intense Laser-Fields ii) Molecules in Intense Laser Fields iii) Atomic Coherences iv) Molecular Coherences The experience developed over the years in multiphoton atomic processes has been very useful and is the main source of our understanding of similar processes in molecules. Thus ATI (above threshold ionization) has been found to occur in molecules as well as a new phenomenon, ATD (above-threshold dissociation). Laser-induced avoided crossings of molecular electronic surfaces is also now entering the current language of high intensity molecular processes.

Studying and using light or "photons" to image and then to control and transmit molecular information is among the most challenging and significant research fields to emerge in recent years. One of the fastest growing areas involves research in the temporal imaging of quantum phenomena, ranging from molecular dynamics in the femto (10-15s) time regime for atomic motion to the atto (10-18s) time scale of electron motion. In fact, the attosecond "revolution" is now recognized as one of the most important recent breakthroughs and innovations in the science of the 21st century. A major participant in the development of ultrafast femto and attosecond temporal imaging of molecular quantum phenomena has been theory and numerical simulation of the nonlinear, non-perturbative response of atoms and molecules to ultrashort laser pulses. Therefore, imaging quantum dynamics is a new frontier of science requiring advanced mathematical approaches for analyzing and solving spatial and temporal multidimensional partial differential equations such as Time-Dependent Schroedinger Equations (TDSE) andTime-Dependent Dirac equations (TDDEs for relativistic phenomena). These equations are also coupled to the photons in Maxwell's equations for collective propagation effects. Inversion of the experimental imaging data of quantum dynamics presents new mathematical challenges in the imaging of quantum wave coherences on subatomic (subnanometer) spatial dimensions and multiple timescales from atto to femto and even nanoseconds.In "Quantum Dynamic Imaging: Theoretical and Numerical Methods," leading researchers discuss these exciting state-of-the-art developments and theirimplications for R&D in view of the promise of quantum dynamic imagingscience as the essential tool for controlling matter at the molecular level."

We arepleasedtopresentthesixthvolumeofProgressinUltrafastIntenseLaserS- ence. As the frontiers of ultrafast intense laser science rapidly expand ever outward, there continues to be a growing demand for an introduction to this interdisciplinary research?eldthatisatoncewidelyaccessibleandcapableofdeliveringcutting-edge developments. Our series aims to respond to this call by providing a compilation of concise review-style articles written by researchers at the forefront of this research ?eld, so that researcherswith differentbackgroundsas well as graduatestudentscan easily grasp the essential aspects. As in previousvolumesof PUILS, each chapterof this bookbeginswith an int- ductory part, in which a clear and concise overview of the topic and its signi?cance is given, and moves onto a description of the authors' most recent research results. All the chapters are peer-reviewed. The articles of this sixth volume cover a diverse rangeoftheinterdisciplinaryresearch?eld,andthetopicsmaybegroupedintothree categories: responses of molecules to ultrashort intense laser pulses (Chaps. 1 - 4), generation and characterization of attosecond pulses and high-order harmonics (Chaps. 5 - 8), and?lamentationand laser-plasma interactionand their applications (Chaps. 9 - 11).

Atoms in Intense Laser Fields: Inhibition of Atomic Ionization in Strong Laser Fields; B. Piraux, E. Huens. Optical Analogs of Model Atoms in Fields; P.W. Milonni. Molecules in Intense Laser Fields: Intense Field Dynamics of Diatomic Molecules; L.F. DiMauro, et al. Excitation of Molecular Hydrogen in Intense Laser Fields; H. Helm, et al. High Intensity Molecular Multiphoton Ionization; G.N. Gibson, et al. Atomic Coherences: Coherence in Strong Field Harmonic Generation; A. L'Huillier, et al. Coherent Interactions within the Atomic Continuum; P. Lambropoulos, et al. Molecular Coherences: Femtosecond Pulse Shaping and Excitation of Molecular Coherences; A.M. Weiner, et al. Coherence in the Control of Molecular Processes; P. Brumer, M. Shapiro. Optimal Control of Molecular Motion; H. Rabitz. 25 additional articles. Index.

In view of the rapid growth in both experimental and theoretical studies of multiphoton processes and multiphoton spectroscopy of atoms, ions, and molecules in chemistry, physics, biology, materials sciences, etc., it is desirable to publish an Advanced Series that contains review papers readable not only by active researchers in these areas, but also by those who are not experts in the field but who intend to enter the field. The present series attempts to serve this purpose. Each review article is written in a self-contained manner by the experts in the area so that the readers can grasp the knowledge in the area without too much preparation. This volume will be useful not only to active researchers but also to other scientists in the area of biology, chemistry, materials science, and physics.