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.

This book attempts to give a discussion of the physics and current and potential applications of the self-focusing of an intense femtosecond laser pulse in a tra- parent medium. Although self-focusing is an old subject of nonlinear optics, the consequence of self-focusing of intense femtosecond laser pulses is totally new and unexpected. Thus, new phenomena are observed, such as long range lam- tation, intensity clamping, white light laser pulse, self-spatial ltering, self-group phase locking, self-pulse compression, clean nonlinear uorescence, and so on. Long range propagation at high intensity, which is seemingly against the law of diffraction, is probably one of the most exciting consequences of this new sub- eld of nonlinear optics. Because the intensity inside the lament core is high, new ways of doing nonlinear optics inside the lament become possible. We call this lamentation nonlinear optics. We shall describe the generation of pulses at other wavelengths in the visible and ultraviolet (UV) starting from the near infrared pump pulse at 800 nm through four-wave-mixing and third harmonic generation, all in gases. Remotely sensing uorescence from the fragments of chemical and biological agents in all forms, gaseous, aerosol or solid, inside the laments in air is demonstrated in the labo- tory. The results will be shown in the last part of the book. Through analyzing the uorescence of gas molecules inside the lament, an unexpected physical process pertaining to the interaction of synchrotron radiation with molecules is observed.

Laser filamentation is a highly complex and dynamic nonlinear process that is sensitive to many physical parameters. The basic properties that define a filament consist of (i) a narrow, high intensity core that persists for distances much greater than the Rayleigh distance, (ii) a low density plasma channel existing within the filament core, and (iii) a supercontinuum generated over the course of filamentation. However, there remain many questions pertaining to how these basic properties are affected by changes in the conditions in which the filaments are formed; that is the premise of the work presented in this dissertation. To examine the effects of anomalous dispersion and of different multi-photon ionization regimes, filaments were formed in solids with different laser wavelengths. The results provided a better understanding of supercontinuum generation in the anomalous dispersion regime, and of how multi-photon ionization can affect the formation of filaments. Three different experiments were carried out on filamentation in air. The first was an investigation into the effects of geometrical focusing. A simplified theoretical model was derived to determine the transition of filamentation in the linear-focusing and nonlinear-focusing regimes. The second examined the effects of polarization on supercontinuum generation, where a polarization-dependent anomalous spectral broadening phenomenon due to molecular effects was identified. The third involved the characterization of filaments in the ultraviolet. The combination of physical mechanisms responsible for filamentation in the ultraviolet was found to be different from that in the near infrared.

This thesis provides deep insights into currently controversial questions in laser filamentation, a highly complex phenomenon involving nonlinear optical effects and plasma physics. First, based on the concrete picture of a femtosecond laser beam which self-pinches its radial intensity distribution, the thesis delivers a novel explanation for the remarkable and previously unexplained phenomenon of pulse self-compression in filaments. Moreover, the work addresses the impact of a non-adiabatic change of both nonlinearity and dispersion on such an intense femtosecond pulse transiting from a gaseous dielectric material to a solid one. Finally, and probably most importantly, the author presents a simple and highly practical theoretical approach for quantitatively estimating the influence of higher-order nonlinear optical effects in optics. These results shed new light on recent experimental observations, which are still hotly debated and may completely change our understanding of filamentation, causing a paradigm change concerning the role of higher-order nonlinearities in optics.

This book covers a diverse cross section of this interdisciplinary research field, with contributions grouped into four categories: laser-induced filamentation; atoms and molecules in a laser field; interaction of solid materials with a coherent light field; and ion acceleration and ionization of atoms in super intense laser fields. This book series presents up-to-date reviews of advances in this interdisciplinary research field, spanning atomic and molecular physics, as well as molecular and optical science, which have been stimulated by the recent developments in ultrafast laser technologies. Each book compiles peer-reviewed articles by researchers at the forefront of their particular subfields. All the chapters include an overview to allow graduate students and researchers unfamiliar with the subfield to grasp the importance and attractions of the topic covered, followed by reports of cutting-edge discoveries.

Digest contains the materials on the research and applications of pulsed lasers. Abstracts are interesting for researches and engineers in the field of quantum electronics, spectroscopy, plasma physics, medicine, remote sensing and laser technologies.

This textbook provides a comprehensive introduction to the physics of laser-plasma interactions (LPI), based on a graduate course taught by the author. The emphasis is on high-energy-density physics (HEDP) and inertial confinement fusion (ICF), with a comprehensive description of the propagation, absorption, nonlinear effects and parametric instabilities of high energy lasers in plasmas. The recent demonstration of a burning plasma on the verge of nuclear fusion ignition at the National Ignition Facility in Livermore, California, has marked the beginning of a new era of ICF and fusion research. These new developments make LPI more relevant than ever, and the resulting influx of new scientists necessitates new pedagogical material on the subject. In contrast to the classical textbooks on LPI, this book provides a complete description of all wave-coupling instabilities in unmagnetized plasmas in the kinetic as well as fluid pictures, and includes a comprehensive description of the optical smoothing techniques used on high-power lasers and their impact on laser-plasma instabilities. It summarizes all the key developments from the 1970s to the present day in view of the current state of LPI and ICF research; it provides a derivation of the key LPI metrics and formulas from first principles, and connects the theory to experimental observables. With exercises and plenty of illustrations, this book is ideal as a textbook for a course on laser-plasma interactions or as a supplementary text for graduate introductory plasma physics course. Students and researchers will also find it to be an invaluable reference and self-study resource.