In 2010 high harmonic generation (HHG) in solids was first observed where high order harmonics of a strong laser field's frequency were observed. HHG in solids is now a rapidly developing field that allows for exciting applications like fully solid state attosecond XUV sources and new ultrafast resolution imaging techniques for quantum dynamics in solids. HHG in solids has been explained by two mechanisms: an interband mechanism, due to polarization associated with separate energy bands, and an intraband mechanism that results from nonlinearities and population changes associated with each individual band. While interband HHG has been seen in wide bandwidth semiconductors, intraband HHG has been observed in narrow bandwidth dielectrics. There has not yet been an explanation of the alternation of mechanisms with material differences. The main goal of this thesis is to attempt to provide a better understanding of the most important mechanisms and where they prevail. Although numerical modelling of HHG requires consideration of multiple energy bands, a two-band model consisting only of a valence band and a single conduction band can explain the most important mechanisms. This model requires a given material's band gap between its valence and conduction bands as well as dipole matrix elements between the bands. In this thesis we follow the Kronig-Penney model to develop a 1D delta-function potential model of solids to obtain these properties required of the two-band model. We implement this in a Wannier quasi-classical (WQC) model of interband HHG in semiconductors that explains the dominant dynamics leading to such through quasi-classical real space electron-hole pair trajectories. Although HHG in solids can be explained to be the result of a resonant process in which an electron-hole pair is generated in the first step, there are also virtual transition processes that lack consideration. These processes do not conserve energy and correspond to transitions to conduction bands resulting from field induced distortions of the ground state. We use methodology introduced by Keldysh for optical field ionization of atoms and solids along with the 1D delta-function potential model to quantify how both resonant and virtual transitions lead to HHG in solids for wide and low bandwidth solids.

In dieser Arbeit wurde die Ionisation einiger zweiatomiger Moleküle (H2, N2 und O2) in intensiven Laserfeldern untersucht. Hierbei wurden verschiedene Modelle zur Beschreibung der Tunnelionisation sowohl untereinander als auch mit der Lösung der zeitabhängigen Schrödingergleichung (TDSE) verglichen. Die kernabstandsabhängige Ionisationswahrscheinlichkeit wurde für verschiedene Intensitäten betrachtet und die Gültigkeit modifizierter atomarer bzw. Molekularer Modelle zur Beschreibung der Tunnelionisation analysiert. Es wurde herausgefunden, dass Modelle, die auf der quasistatischen Näherung beruhen (wo die Ionisation unabhängig von der Frequenz des Laserfeldes ist), nur in einem kleinem Frequenz- und Intensitätsbereich hinreichend genaue Ergebnisse liefern, dem Tunnelregime. Modelle mit einem frequenzabhängigen Faktor stimmen hingegen sowohl im Tunnel- als auch im Mehrphotonenregime mit den genaueren TDSE Ergebnissen überein. Weiterhin wird auch die Abweichung zur Franck-Condon Näherung verdeutlicht. Es wurde ein kleiner Einfluss auf die Revival-Zeit des im Wasserstoffmolekül-Ion gestarteten Wellenpakets gefunden. Die Berücksichtigung von Bond-Softening führt weiterhin zu einer Verringerung der Revival-Zeit mit steigender Spitzenintensität des Lasers. Außerdem wird die Anisotropie der Ionisation von H2 als Funktion der Laserintensität in linear und zirkular polarisiertem Licht mit dem molekularen Tunnelmodell MO-ADK untersucht. Gute Übereinstimmung mit den experimentellen Beobachtungen wurde gefunden, insbesondere wenn der Effekt des Fokusvolumens des Laserfeldes berücksichtigt wird. Die Anwendbarkeit des Zwei-Zentren-Modells auf größere Moleküle, N2 und O2, wird ebenfalls getestet. Es wird beobachtet, dass dies für N2 (symmetrisches HOMO) funktioniert, für O2 (asymmetrisches HOMO) jedoch nicht. / The ionization of some diatomic molecules, H2, N2, and O2, exposed to intense laser fields has been studied by comparing various molecular tunneling–ionization models with each other and with the numerical solution of the time-dependent Schrödinger equation (TDSE). The internuclear-distance dependent ionization yields over a wide range of laser peak intensities are investigated and the validity of the modified atomic and molecular tunneling models is examined. It is found that those models that depend on the quasi-static approximation, where ionization is independent on the oscillation frequency of the applied laser field, are useful for laser-induced ionization processes in only a very small region of the frequency and intensity domain of laser fields, i.e. in the tunneling regime. The models that include a frequency dependent factor are in a good agreement with the accurate TDSE calculations in both the multiphoton and the tunneling ionization regimes. Furthermore, the deviation from Franck-Condon-like distribution is also clarified. A small effect on the revival time of the vibrational wavepacket of hydrogen molecular ion, due to this deviation, has been found. Consideration of the bond-softening effect leads to a decrease in the revival time with increasing laser-peak intensity. The anisotropy of H2 as a function of laser intensity in linear and circular polarized fields using molecular tunneling model (MO-ADK) are also studied and a good agreement with the experimental observations, especially if the focal volume of the laser field is considered, has been obtained. The applicability of the two-center model for larger molecules, N2 and O2, is tested. It is found that it works with N2 (symmetric HOMO) but fails in O2 (ansymmetric HOMO).

We have investigated processes of ionization, energy absorption and subsequent explosion of atomic and molecular clusters under intense laser illumination using numerical as well as analytical methods. In particular, we focused on the response of composite clusters, those consisting of different atomic elements, to intense light pulses. Another major theme is the effect of the molecular structure of clusters on their Coulomb explosion. The action of intense laser pulses on clusters leads to fundamental, irreversible changes: they turn almost instantaneously into nanoplasmas and subsequently disintegrate into separate ions and electrons. Due to this radical transformation, remarkable new features arise. Transient cluster nanoplasmas are capable of absorbing enormous amounts of laser energy. In some cases more than 90 % of incident laser energy is absorbed by a gas of clusters with a density much smaller than that of a solid. After the efficient absorption, the energy is transformed into production of energetic ions, electrons, photons, and even neutrons. Composite clusters show especially interesting behavior when they interact with intense laser pulses. Nanoplasmas formed in composite clusters may absorb even more laser energy, than those formed in homogeneous clusters, as we demonstrate in this work. One of the most important results of this thesis is the identification of a novel type of plasma resonance. This resonance is enabled by an unusual ellipsoidal shape of the nanoplasma created during the ionization process in a helium droplet doped with just a few xenon atoms. In contrast to the conventional plasma resonance, which requires significant ion motion, here, the resonant energy absorption occurs at a remarkably fast rate, within a few laser cycles. Therefore, this resonance is not only the most efficient (like the conventional resonance), but also, perhaps, the fastest way to transfer laser energy to clusters. Recently, dedicated experimental studies of this effect were performed at the Max Planck Institute in Heidelberg. Their preliminary results confirm our prediction of a strong, avalanche-like ionization of the helium droplet with a small xenon cluster inside. A conventional plasma resonance, which relies on the cluster explosion, also exhibits interesting new properties when it occurs in a composite xenon-helium cluster with a core-shell geometry. We have revealed an intriguing double plasma resonance in this system. This was the first theoretical study of the influence of the helium embedding on the laser- driven nanoplasma dynamics. Our results demonstrate the important role of the interaction between xenon and helium parts of the cluster. Understanding this interaction is necessary in order to correctly interpret the experimental results. We have elucidated several important properties of Coulomb explosion in atomic and molecular clusters. Specifically, it was found that the kinetic energy distribution of ions after the Coulomb explosion of an atomic cluster is quite similar to the initial potential energy distribution of ions and is only weakly influenced by ion overtake effects, as was believed before. For the case of molecular hydrogen clusters, we have shown that the alignment of molecules inside the cluster affects its Coulomb explosion. Investigation of the dynamical processes in composite and molecular clusters induced by intense laser pulses is a step towards understanding them in more complex nano-objects, such as biomolecules or viruses. This is of great interest in the context of x-ray diffractive imaging of biomolecules with atomic resolution, which is one of the main goals of new x-ray free electron laser facilities.

We have investigated processes of ionization, energy absorption and subsequent explosion of atomic and molecular clusters under intense laser illumination using numerical as well as analytical methods. In particular, we focused on the response of composite clusters, those consisting of different atomic elements, to intense light pulses. Another major theme is the effect of the molecular structure of clusters on their Coulomb explosion. The action of intense laser pulses on clusters leads to fundamental, irreversible changes: they turn almost instantaneously into nanoplasmas and subsequently disintegrate into separate ions and electrons. Due to this radical transformation, remarkable new features arise. Transient cluster nanoplasmas are capable of absorbing enormous amounts of laser energy. In some cases more than 90 % of incident laser energy is absorbed by a gas of clusters with a density much smaller than that of a solid. After the efficient absorption, the energy is transformed into production of energetic ions, electrons, photons, and even neutrons. Composite clusters show especially interesting behavior when they interact with intense laser pulses. Nanoplasmas formed in composite clusters may absorb even more laser energy, than those formed in homogeneous clusters, as we demonstrate in this work. One of the most important results of this thesis is the identification of a novel type of plasma resonance. This resonance is enabled by an unusual ellipsoidal shape of the nanoplasma created during the ionization process in a helium droplet doped with just a few xenon atoms. In contrast to the conventional plasma resonance, which requires significant ion motion, here, the resonant energy absorption occurs at a remarkably fast rate, within a few laser cycles. Therefore, this resonance is not only the most efficient (like the conventional resonance), but also, perhaps, the fastest way to transfer laser energy to clusters. Recently, dedicated experimental studies of this effect were performed at the Max Planck Institute in Heidelberg. Their preliminary results confirm our prediction of a strong, avalanche-like ionization of the helium droplet with a small xenon cluster inside. A conventional plasma resonance, which relies on the cluster explosion, also exhibits interesting new properties when it occurs in a composite xenon-helium cluster with a core-shell geometry. We have revealed an intriguing double plasma resonance in this system. This was the first theoretical study of the influence of the helium embedding on the laser- driven nanoplasma dynamics. Our results demonstrate the important role of the interaction between xenon and helium parts of the cluster. Understanding this interaction is necessary in order to correctly interpret the experimental results. We have elucidated several important properties of Coulomb explosion in atomic and molecular clusters. Specifically, it was found that the kinetic energy distribution of ions after the Coulomb explosion of an atomic cluster is quite similar to the initial potential energy distribution of ions and is only weakly influenced by ion overtake effects, as was believed before. For the case of molecular hydrogen clusters, we have shown that the alignment of molecules inside the cluster affects its Coulomb explosion. Investigation of the dynamical processes in composite and molecular clusters induced by intense laser pulses is a step towards understanding them in more complex nano-objects, such as biomolecules or viruses. This is of great interest in the context of x-ray diffractive imaging of biomolecules with atomic resolution, which is one of the main goals of new x-ray free electron laser facilities.:1. Introduction 1 2. Interaction of clusters with intense laser pulses 5 2.1. Cluster formation and structure . . . . . . . . . . . . . . . . . . 5 2.1.1. Cluster formation . . . . . . . . . . . . . . . . . . . . . . 5 2.1.2. Cluster structure . . . . . . . . . . . . . . . . . . . . . . 6 2.1.3. Composite clusters . . . . . . . . . . . . . . . . . . . . . 7 2.2. Matter in intense light fields . . . . . . . . . . . . . . . . . . . . 9 2.2.1. Laser sources . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2.2. Atoms . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.3. Clusters under intense laser pulses . . . . . . . . . . . . . . . . . 11 2.3.1. Three stages of intense laser-cluster interaction . . . . . 12 2.3.2. Pathways of cluster ionization and energy absorption . . 13 2.3.3. Composite clusters in intense laser fields . . . . . . . . . 14 2.4. Scenarios of cluster explosion . . . . . . . . . . . . . . . . . . . 15 2.4.1. Coulomb explosion vs. quasi-neutral expansion . . . . . 15 2.4.2. Anisotropic explosion . . . . . . . . . . . . . . . . . . . . 17 2.5. Comparison between experiment and theory . . . . . . . . . . . 18 3. Theoretical methods for intense laser-cluster interaction 21 3.1. The Hamiltonian . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.2. Survey of simulation methods . . . . . . . . . . . . . . . . . . . 22 3.2.1. Quantum methods . . . . . . . . . . . . . . . . . . . . . 22 3.2.2. Classical methods . . . . . . . . . . . . . . . . . . . . . . 23 3.3. Our method: classical microscopic molecular dynamics . . . . . 24 3.3.1. Initial configuration . . . . . . . . . . . . . . . . . . . . . 24 3.3.2. Integrating the equations of motion . . . . . . . . . . . . 26 3.3.3. Observables . . . . . . . . . . . . . . . . . . . . . . . . . 28 3.4. The role of quantum effects . . . . . . . . . . . . . . . . . . . . 31 4. Cluster nanoplasma: a statistical approach 33 4.1. Vlasov-Poisson formalism . . . . . . . . . . . . . . . . . . . . . . 33 4.2. Nanoplasma electrons at quasi-equilibrium . . . . . . . . . . . . 34 4.2.1. Self-consistent potential and electron density . . . . . . . 34 4.2.2. Energy distribution of nanoplasma electrons . . . . . . . 36 4.3. Harmonic oscillator model . . . . . . . . . . . . . . . . . . . . . 41 4.3.1. Derivation from kinetic equations . . . . . . . . . . . . . 42 4.3.2. Comparison with the molecular dynamics results . . . . 44 4.4. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 5. Ionization and energy absorption in helium droplets doped with xenon clusters 47 5.1. Local ignition and anisotropic nanoplasma growth . . . . . . . . 48 5.1.1. Cluster size dependence . . . . . . . . . . . . . . . . . . 50 5.1.2. Nanoplasma resonance during its anisotropic growth . . 51 5.1.3. Range of laser frequencies and intensities . . . . . . . . . 55 5.1.4. Plasma resonance for circular polarization . . . . . . . . 56 5.1.5. Summary and future work . . . . . . . . . . . . . . . . . 57 5.2. Electron migration and its influence on the cluster expansion . . 59 5.2.1. Charging dynamics . . . . . . . . . . . . . . . . . . . . . 59 5.2.2. Explosion dynamics . . . . . . . . . . . . . . . . . . . . . 61 5.3. Interplay between nanoplasma expansion and its electronic response 63 5.3.1. Single pulse: time-dependence . . . . . . . . . . . . . . . 64 5.3.2. Two pulses: a pump-probe study . . . . . . . . . . . . . 67 5.4. Conclusions and outlook . . . . . . . . . . . . . . . . . . . . . . 71 6. Coulomb explosions of atomic and molecular clusters 75 6.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 6.2. Analytical treatment of the Coulomb explosion . . . . . . . . . . 76 6.2.1. Steplike density profile . . . . . . . . . . . . . . . . . . . 76 6.2.2. Kinetic approach . . . . . . . . . . . . . . . . . . . . . . 79 6.2.3. Gradually decreasing initial density . . . . . . . . . . . . 83 6.3. Coulomb explosions of atomic and molecular hydrogen clusters: a molecular dynamics study . . . . . . . . . . . . . . . . . . . . 84 6.3.1. Kinetic energy distributions of ions (KEDI) . . . . . . . 85 6.3.2. Information loss during the explosion . . . . . . . . . . . 87 6.3.3. Ion overtake processes . . . . . . . . . . . . . . . . . . . 90 6.3.4. Non-radial motion of ions . . . . . . . . . . . . . . . . . 91 6.3.5. Three-body effects in Coulomb explosion . . . . . . . . . 93 6.4. Conclusions and outlook . . . . . . . . . . . . . . . . . . . . . . 96 7. Conclusions and outlook 97 7.1. Physical conclusions . . . . . . . . . . . . . . . . . . . . . . . . 97 7.2. Methodological conclusions . . . . . . . . . . . . . . . . . . . . . 99 7.3. Research perspectives . . . . . . . . . . . . . . . . . . . . . . . . 100 A. Suppression of the cluster barrier 101 B. Structure determination for Xen@Hem clusters 103 C. Calculation of the time-dependent phase shift 107 D. Potential of a uniformly charged spheroid 109 E. On the possibility of molecular alignment inside hydrogen clusters 111 Bibliography

The purpose of this thesis is to advance the understanding of strong-field QED processes in short laser pulses. The processes of non-linear one-photon and two-photon Compton scattering are studied, that is the scattering of photons in the interaction of relativistic electrons with ultra-short high-intensity laser pulses. These investigations are done in view of the present and next generation of ultra-high intensity optical lasers which are supposed to achieve unprecedented intensities of the order of 10^24 W/cm^2 and beyond, with pulse lengths in the order of some femtoseconds. The ultra-high laser intensity requires a non-perturbative description of the interaction of charged particles with the laser field to allow for multi-photon interactions, which is beyond the usual perturbative expansion of QED organized in powers of the fine structure constant. This is achieved in strong-field QED by employing the Furry picture and non-perturbative solutions of the Dirac equation in the presence of a background laser field as initial and final state wave functions, as well as the laser dressed Dirac-Volkov propagator. The primary objective is a realistic description of scattering processes with regard to the finite laser pulse duration beyond the common approximation of infinite plane waves, which is made necessary by the ultra-short pulse length of modern high-intensity lasers. Non-linear finite size effects are identified, which are a result of the interplay between the ultra-high intensity and the ultra-short pulse length. In particular, the frequency spectra and azimuthal photon emission spectra are studied emphasizing the differences between pulsed and infinite laser fields. The proper description of the finite temporal duration of the laser pulse leads to a regularization of unphysical infinities (due to the infinite plane-wave description) of the laser-dressed Dirac-Volkov propagator and in the second-order strong-field process of two-photon Compton scattering. An enhancement of the two-photon process is found in strong laser pulses as compared to the corresponding weak-field process in perturbative QED.

La génération d'harmoniques d'ordre élevé en milieu gazeux est un phénomène habituellement décrit par un modèle à trois étapes : sous l'effet d'un champ laser intense, un atome (ou une molécule) est ionisé par effet tunnel. L'électron éjecté est accéléré dans le champ laser, puis il se recombine sur son ion parent en émettant un photon XUV. Ce rayonnement XUV, émis sous la forme d'impulsions attosecondes (1 as = 10-18 s), est un outil idéal pour sonder la structure électronique des atomes ou des molécules, avec une résolution temporelle de l'ordre de l'attoseconde. Néanmoins, l'intensité de ce rayonnement n'est en général pas suffisante pour induire des effets non-linéaires (transitions à deux photons).Au cours des travaux réalisés pendant cette thèse, nous avons développé une source harmonique capable de produire un rayonnement XUV intense qui doit permettre d'accéder à la physique non-linéaire dans cette gamme de longueur d'onde. Pour parvenir à ces résultats, un travail important sur les impulsions infrarouges génératrices a été nécessaire, aussi bien dans le domaine spatial que dans le domaine temporel. Une technique de mise en forme spatiale de faisceaux laser intenses a donc été développée, ainsi qu'une technique de post compression adaptée aux impulsions laser intenses. Ce travail de thèse se divise donc en trois étapes : - Le développement de la source harmonique haute énergie et des diagnostics associés. Cette source est basée sur l'utilisation d'une chaîne laser Titane-Saphir qui délivre des impulsions de 150 mJ pour des durées de 40 fs à une cadence de 10 Hz. De bonnes conditions d'optimisation ont été obtenues, donnant lieu à des impulsions XUV dont l'énergie est de l'ordre du µJ lors de la génération dans l'argon.- Le développement d'une technique de mise en forme spatiale adaptée aux faisceaux laser intenses et à la génération d'harmoniques. Le dispositif est basé sur une optique en réflexion et sur les interférences à deux faisceaux. Il permet de produire, dans la région focale, des faisceaux dont le profil d'intensité est radialement constant (faisceaux flat top) et ainsi d'apporter un contrôle supplémentaire sur la génération d'harmoniques d'ordre élevé.- Le développement d'une technique de post compression en propagation guidée basée sur l'élargissement spectral induit par ionisation. Cette technique est adaptée pour des impulsions intenses (3.5 TW) et permet de produire des impulsions de puissance crête supérieure au Térawatt dans le domaine sub-10 fs. Cette technique fournit donc une source unique pour la génération d'harmoniques d'ordre élevé.Ces deux approches ont été testées et validées pour la génération d'harmoniques d'ordre élevé, et les résultats obtenus ouvrent d'intéressantes perspectives telles que la génération d'impulsions attosecondes isolées de haute énergie (> 100 nJ). / The generation of high order harmonics in a gaseous medium is a phenomenon conveniently described by a three steps model : subject to a strong laser field irradiation, an atom (or molecule) can undergo a tunneling ionization. The ejected electron is accelerated in the laser field and recombine on its parent ion leading to the emission of an XUV photon. The XUV radiation can be emitted as attosecond pulses (1 as = 10-18 s), and it is then an ideal tool to probe the electronic structure of atoms or molecules which require the highest time resolution. However, the intensity of this radiation is usually not sufficient to induce non-linear processes (two-photon transitions).In the frame of this work, we have developed a harmonic source capable of producing an intense XUV radiation to access non-linear physics in this wavelength domain.To achieve these results, significant work on the infrared generating pulses was necessary, both in the spatial and temporal domain. We have developed a technique for spatial shaping of intense laser beams, and a post compression technique fitted to high energy pulses.This thesis is therefore divided into three parts:- The development of an high energy harmonic source and related diagnostics. We use a Ti: sapphire laser system for this source which delivers 40-fs pulses up to an energy of 150 mJ at 10 Hz repetition rate. Good optimization conditions were obtained, leading to XUV pulse energies of the order of μJ in the case of generation in argon.- The development of a spatial shaping technique adapted to intense laser beams and to harmonic generation. The device is based on reflection optics and the interferences of two beams. It can produce, in the focal region, beams with a radially constant intensity over a large volume (flat top beams) and thus provide additional control of the harmonics generating process.- The development of a post compression technique in guided geometry based on the ionization induced spectral broadening. This technique is suitable for intense pulses (3.5 TW) and produces pulses above the terawatt level in the 10-fs range. This technique therefore provides a unique source for harmonic generation.These two approaches have been tested and validated for high order harmonics generation, and the results open interesting perspectives such as the generation of isolated attosecond pulses of high energy (> 100 nJ).