Geometrical optics provides an accurate description of electromagnetic phase fluctuations under a wide range of conditions. The phase variance computed in this way is a benchmark parameter for describing propagation in random media. One can calculate this quantity for most situations of practical interest. We shall find that it is proportional to the first moment of the spectrum of irregularities and is therefore sensitive to the small-wavenumber portion of the spectrum. This is the region where energy is fed into the turbulent cascade process. We have no universal physical model for the spectrum in this wavenumber range and phase measurements provide an important way of exploring that region.

In analyzing these situations, we must recognize the anisotropic nature of irregularities in the troposphere and ionosphere. Large structures are highly elongated in both regions and exert a strong influence on phase. These measurements are also sensitive to trends in the data that are caused by nonstationary processes in the atmosphere. Sample length, filtering and other data-processing procedures thus have an important influence on the measured quantities. By contrast, aperture smoothing has a negligible effect.

Single-path phase measurements have been made primarily at microwave frequencies because phase-stable transmitters and receivers were available in these bands. Early experiments were performed on horizontal paths using signals in the frequency range 1–10 GHz. At least one experiment has measured the single-path phase variance at optical wavelengths. Phase-stable signals from navigation satellites and other spacecraft are beginning to provide information about the upper atmosphere.

The first step in studying electromagnetic scintillation is to establish a firm physical foundation. This chapter attempts to do so for the entire work and it will not be repeated in subsequent volumes. We proceed cautiously because the issues are complex and the measured effects are often quite subtle. Section 2.1 explores the way in which Maxwell's equations for the electromagnetic field are modified when the dielectric constant experiences small changes. Because atmospheric fluctuations are much slower than the electromagnetic frequencies employed, their influence can be condensed into a single relationship: the wave equation for random media. This equation is the starting point for all developments in this field.

To proceed further one must characterize the dielectric fluctuations. We want to do so in ways that accurately reflect atmospheric conditions. Because we are dealing with a random medium, we must use statistical methods to describe them and their influence on electromagnetic signals. For instance, we want to know how dielectric fluctuations measured at a single point vary with time. Even more important, we need to describe the way in which fluctuations at separated points in the medium are correlated. There are several ways to do so and they are developed in Section 2.2. These descriptions assume that the random medium is isotropic and homogeneous. Those convenient assumptions are seldom realized in nature and we show how to remove them at the end of this section. Turbulence theory now gives an important but incomplete physical description of these fluctuations.

History

Quivering of stellar images can be observed with the naked eye and was noted by ancient peoples. Aristotle tried but failed to explain it. A related phenomenon noted by early civilizations was the appearance of shadow bands on white walls just before solar eclipses. When telescopes were introduced, scintillation was observed for stars but not for large planets. Newton correctly identified these effects with atmospheric phenomena and recommended that observatories be located on the highest mountains practicable. Despite these occasional observations, the problem did not receive serious attention until modern times.

How it began

Electromagnetic scintillation emerged as an important branch of applied physics after the Second World War. This interest developed in response to the needs of astronomy, communication systems, military applications and atmospheric forecasting. The last fifty years have witnessed a growing and widespread interest in this field, with considerable resources being made available for measurement programs and theoretical research.

Radio signals coming from distant galaxies were detected as this era began, thereby creating the new field of radio astronomy. Microwave receivers developed by the military radar program were used with large apertures to detect these faint signals. Their amplitude varied randomly with time and it was initially suggested that the galactic sources themselves might be changing. Comparison of signals measured at widely separated receivers showed that the scintillation was uncorrelated, indicating that the random modulation was imposed by ionized layers high in the earth's atmosphere.

Introduction

Naturally, the scientific study of matter under extreme conditions is of fundamental interest, but it is also true that its direction and progress are largely determined by technological innovations. Also theorists generally stay within the bounds of what is (nearly) feasible, for even the best theories require verification. The technological development underlying the subject of this book is that of high-power lasers. Particularly the advent of affordable, ultra-short-pulsed lasers has considerably intensified the study of molecules and clusters in intense fields.

Two determining technical advances in this respect were the development of chirped pulse amplification (CPA) and the self-mode-locked Ti: sapphire laser (which has generated pulses as short as 7 fs). It is thus possible to build laboratory-scale systems that produce high-energy pulses (3–4 mJ in 20 fs), even at kilohertz repetition rates. An even more powerful system, a 100-TW, sub-20-fs laser system was demonstrated by Yamakawa et al., but at the lower repetition rate of 10 Hz. Extremely short pulses of only 4.5 fs – but still with energies as high as 70 μJ – were achieved with pulse compression techniques by Nisoli et al.

Particularly energetic laser pulses are required for the study of inertial-confinement fusion (ICF). At the Lawrence Livermore National Laboratory, for example, 660 J in a 440 ± 20-fs pulse can be focused down to an intensity > 7 × 1020 W cm−2.

Introduction

The last decade has seen impressive progress in the understanding of the elementary mechanisms of chemical reactions. The advent of femtosecond (fs) laser sources has allowed the possibility of analysing ultra-fast chemical reactions using lasers. In pump–probe schemes, a first ultra-short pulse initiates a reaction that is monitored by a subsequent probe laser pulse. This method is extremely useful for recording the formation and the evolution of transition states in real time. With the understanding of these fundamental mechanisms, there has emerged a renewal of interest in the control of photo-induced processes using tailored laser pulses.

The ability to control chemical reactions through a variety of means (catalysis, use of various substrates, variation of temperature, pressure, concentration of the initial reactants, etc.) has major beneficial consequences for chemical synthesis and other industrial manufacturing processes. Not only is it normally useful to speed up a reaction but also, in a case with more than one possible outcome, it can be extremely useful to influence the branching ratios of the various fractions. This can result in a far greater yield of the desired product, with the elimination of by-products. Classical methods of chemistry sometimes fail to produce a specific product from a given set of reactants. This is the case, for instance, when the reaction is under thermodynamic control and one wants to produce a metastable species.

Introduction

When an intense laser pulse passes through a gas, the laser–matter interactions are highly non-linear and lead to extensive changes both in the nature of the transmitted light and the medium. Even if the excitation frequencies of the molecule are not in resonance with that of the light, the external electric field can exceed the internal binding forces and allow strong absorption of energy. Subsequently the energy is dissipated through explosive fragmentation of the molecule and by emission of high-frequency light. The physics of strongly correlated many-body quantum systems interacting with intense dynamic external fields is extremely complicated. The understanding of such processes in simple atoms is still in development, so it is fair to say that the mechanisms of multi-electron photodissociative ionisation of molecules are still far from being understood. Naturally the physical process of electron removal is very similar for both types of system. Indeed, the growth in interest in molecular dynamics in intense fields was originally fuelled by speculation on the character of multi-electron ejection from atoms. One of the topical issues of debate in molecular physics focuses on the sequence of the fragmentation; whether the electrons are liberated sequentially or simultaneously and how these processes depend on the nuclear motion. In light atoms the electron correlation in the outer shells is important irrespective of whether the electrons emerge sequentially, whereby the electrons are peeled off the atoms one by one, or escape in groups arising from a multiple collective excitation of the system.

Introduction

The multiple ionisation of small molecules is being studied with various excitation sources, e.g. ionisation by ion or electron impact, synchrotron radiation, beam-foil electron stripping and intense laser pulses. Since multiply charged molecular ions are unstable, the process of ionisation itself is investigated by analysing the multiply charged atomic fragments. The multiple fragmentation channels are determined using various experimental techniques adapted to the excitation sources. These methods present some similarities to other fields in physics, such as particle and nuclear physics, in which the fragmentation of particles and nuclei plays an important role. This chapter starts with some general considerations about the laser excitation of small molecules and then continues to discuss the physics and the experimental techniques that are associated with laser-induced multiple ionisation. The physical quantities are expressed in atomic units (a.u.), MKSA units and practical units such as W cm−2 for the laser intensity. Most of the atomic- and molecular-spectroscopy data are taken from standard textbooks, for instance the books of Herzberg for neutral and singly charged molecules. The transient molecular ions, which remain undetected but appear as the precursors of the observed multiple fragmentation channels, are noted in square brackets, for example [N2O9+].

Timescales

The laser field presents basically two timescales: the optical period T = λ/c, where λ and c are, respectively, the laser wavelength and the speed of light, and the duration of the laser pulse.

Young researchers, when they have just joined a research group, are all too often sent to the library with a photocopying card and the assurance that all the necessary background information can be found in the journals. Those following this advice soon start showing signs of sleepless nights and attacks of panic. The student has studied physics for a number of years, believing it to be the mother of all sciences, but suddenly existential thoughts make all other vocations seem much more relevant. At this stage the risk of dropping out of science is very high. However, those who succeed along this path are destined for a successful academic career and will proudly give the same advice to the next generation. Fortunately, most students are wise enough to approach a young colleague, who is all too familiar with the problem of where to find relevant information for the real beginner.

This book is aimed primarily at postgraduate students and postdoctoral research assistants. The research area of ‘molecules and clusters in intense laser fields’ is itself quite young and also rapidly developing. Not surprisingly, a proper introduction has been lacking. It seemed appropriate, therefore, to write an introductory text, particularly since interest in the subject is growing. Since the young researcher would normally approach his peers for practical information, it was thought beneficial for the scope of this book if the authors themselves were quite young.

Introduction

Atomic clusters have provoked great interest since their first observation in the mid-1950s. Physicists' and chemists' fascination with them derives from the unique position clusters hold as an intermediate state between molecules and solids. Many studies have been concerned with the optical properties of clusters. An important finding was the discovery of collective electron dynamics in clusters, which is virtually absent from laser–atom interactions. These are responsible for the ‘giant resonance’ seen in absorption spectra of clusters and can lead to remarkable optical properties.

During the last five or so years, the study of laser–cluster interactions has been extended to laser intensities in excess of 1015 W cm−2 (laser pulse widths in the range 0.1–10 ps) in the so-called ‘strong-field’ interaction regime, for which the electric field of the laser is no longer small relative to the atomic field and the interaction becomes highly non-perturbative. This regime, which was made widely accessible by the development of chirped-pulse-amplification (CPA) lasers, had been studied for atoms, small molecules and bulk solids since the late 1980s. In stark contrast to earlier studies of laser–cluster interactions at lower intensities that had revealed dynamics similar to those seen in molecules – with relatively inefficient coupling of laser energy to electrons and ions – studies on the generation of X-rays from gases of clusters (>1000 atoms) at ≃1016 W cm−2 began to reveal startling evidence of a laser–cluster interaction that was very much more energetic.

Introduction

The advent of compact, high-power lasers in the last two decades has opened a rich and challenging research field, aimed at understanding the behaviour of matter under the influence of ultra-intense and extremely short pulses of light. Typical pulse durations of less than 10−13 s are now available with commercial laser systems that are designed to deliver peak powers beyond 1012 W. The focusing of such laser pulses leads to extremely high energy intensities that may exceed 1018 W cm−2. The corresponding electric-field strengths are of the order of several GV cm−1 and megagauss magnetic fields. In terms of photon numbers, at 1017 W cm−2 the irradiation is already so intense that approximately 10000 photons will pass through the volume of one atom during each optical cycle (3 fs).

In the last few decades, extensive strong-laser-field studies have been performed on atomic targets in the gas phase as well as on bulk solidstate targets. Several pertinent phenomena in strong fields were discovered as a result of the non-linear response of matter to intense laser irradiation. For the particular case of atoms in the gas phase, multi-photon ionisation (MPI) and optical field ionisation (OFI) have been studied in great detail both experimentally and theoretically. Moreover, the observation of highly non-linear phenomena such as above-threshold ionisation (ATI) and high-order-harmonic generation (HHG) and their detailed theoretical description have lead to a comprehensive understanding of the principal physical processes that govern the atomic response to intense laser fields.

Introduction

As outlined in earlier chapters, there is currently considerable interest in the interaction of intense, short-duration laser pulses with isolated atomic clusters. Some of the more spectacular recent results reported in the literature have included the observation of mega-electron-volt ions, multi-kilo-electron-volt electrons and extremely high charge states of ions in laser–cluster-interaction experiments. It is clear that, whilst aggregates of more than a few hundred atoms in strong laser fields share some aspects of both solid and monatomic gas-target behaviours, they also exhibit new and quite startling effects that are very specific to atomic clusters. In particular the interaction is extremely energetic compared with that of small molecules and aggregates of a few tens of atoms, for which field and multi-photon ionisation dominate and ions are typically accelerated to energies of only a few tens of electron-volts in weak Coulomb explosions.

An important question to ask is ‘does the energetic behaviour seen in single-cluster experiments hold for extended cluster media, in which a laser pulse interacts with many billions of clusters at the same time and interactions between adjacent clusters become important?’. Are there interesting propagation effects, for example, and can we enhance coherent processes such as high-harmonic generation in cluster media? Finally, can we harness the large energies of ions available from single-cluster interactions for use in heating significant volumes of material to drive applications such as the production of X-rays and thermonuclear fusion.