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<p dir="ltr">Some of the simplest molecules that are found in abundance in nature, like oxygen, nitrogen, carbon dioxide and water can be playgrounds for complex quantum mechanical phenomenon. Although we can calculate their static properties, like binding energies, equilibrium geometries and ionization/decay rates with extraordinary precision, their dynamics offer new avenues for exploration. Although analytical techniques have been successfully applied in studying single-particle and many-particle systems, few-particle systems like simple molecules are still best understood through a combination of numerical calculations and experimental work. However, the small size of these molecules endows them with dynamics that occur on timescales of a few picoseconds to a few attoseconds, making their experimental study challenging. The overarching goal of this work is the study of such ‘ultrafast’ dynamics in excited state molecules/atoms, by developing and demonstrating novel optical probes of quantum dynamics.</p><p dir="ltr">One way to probe ultrafast dynamics in molecules is by measuring their nonlinear optical response. Such a measurement can potentially track the evolution of the symmetries of excited molecules, shedding light on their transient dynamics. We start chapter 1 with a brief discussion of the formalism behind nonlinear optical spectroscopy. Direct measurement of ultrafast (and ultraweak) optical pulses is discussed as a useful probe of nonlinear processes. After presenting preliminary results on direct electric field reconstruction, experimental work on measuring emitted nonlinear electric fields from impulsively aligned molecules is discussed. In such an experiment, however, contributions from both aligned and unaligned molecules are present, and new experimental capabilities had to be developed to disentangle and measure the ultraweak signal from aligned molecules. Following a detailed discussion of the developed measurement capabilities, results from experiments done on aligned carbon dioxide and nitrogen molecules are discussed.</p><p dir="ltr">Unlike solids, where electronic states can be excited with visible/UV light, binding energies in isolated atoms/molecules are on the order of electron-volts (eVs), and they need vacuum-ultraviolet (VUV) extreme-ultraviolet (EUV) light to excite electronically. Polyatomic molecules, like ethylene, when excited to an electronic state with VUV light, often relax back to the ground state by redistributing energy to their internal degrees of freedom non-adiabatically. These relaxation pathways are important in many chemical and biological systems, and control the yield of chemical reactions ranging from elementary reactions involving few atoms to large biomolecules such as DNA and proteins. For instance, in the photochemical reaction of the protein Rhodopsin, considered to be the primary event in human vision. In chapter 2 we discuss progress made towards extending nonlinear response measurements to study ultrafast dynamics in electronically excited molecules, using a high-harmonic VUV source. Details about the design of the high-harmonic generation beamline, and preliminary experimental data are presented. In chapter 3 we discuss preliminary theoretical work on the development of an EUV entangled-photon source, using two-photon emission from the metastable 2s state in neutral Helium. Such a source, if demonstrated, can possibly even extended to the zeptosecond regime in the future.</p>

At the heart of high harmonic generation lies a combination of optical and collision physics entwined by a strong laser field. An electron, initially tunnel-ionized by the field, driven away then back in the continuum, finally recombines back to rest in its initial ground state via a radiative transition. The emitted attosecond (atto=10^-18) XUV light pulse carries all the information (polarization, amplitude and phase) about the photorecombination continuum-to-ground transition dipolar field. Photorecombination is related to the time-reversed photoionization process. In this perspective, high-harmonic spectroscopy extends well-established photoelectron spectroscopy, based on charged particle detection, to a fully coherent one, based on light characterization. The main achievement presented in this thesis is to use high harmonic generation to probe femtosecond (femto=10^-15) chemical dynamics for the first time. Thanks to the coherence imposed by the strong driving laser field, homodyne detection of attosecond pulses from excited molecules undergoing dynamics is achieved, the signal from unexcited molecules acting as the reference local oscillator. First, applying time-resolved high-harmonic spectroscopy to the photodissociation of a diatomic molecule, Br2 to Br + Br, allows us to follow the break of a chemical bond occurring in a few hundreds of femtoseconds. Second, extending it to a triatomic (NO2) lets us observe both the previously unseen (but predicted) early femtosecond conical intersection dynamics followed by the late picosecond statistical photodissociation taking place in the reaction NO2 to NO + O. Another important realization of this thesis is the development of a complementary technique to time-resolved high-harmonic spectroscopy called LAPIN, for Linked Attosecond Phase INterferometry. When combined together, time-resolved high-harmonic spectroscopy and LAPIN give access to the complex photorecombination dipole of aligned excited molecules. These achievements lay the basis for electron recollision tomographic imaging of a chemical reaction with unprecedented angstrom (1 angstrom= 0.1 nanometer) spatial resolution. Other contributions dedicated to the development of attosecond science and the generalization of high-harmonic spectroscopy as a novel, fully coherent molecular spectroscopy will also be presented in this thesis.

At the heart of high harmonic generation lies a combination of optical and collision physics entwined by a strong laser field. An electron, initially tunnel-ionized by the field, driven away then back in the continuum, finally recombines back to rest in its initial ground state via a radiative transition. The emitted attosecond (atto=10^-18) XUV light pulse carries all the information (polarization, amplitude and phase) about the photorecombination continuum-to-ground transition dipolar field. Photorecombination is related to the time-reversed photoionization process. In this perspective, high-harmonic spectroscopy extends well-established photoelectron spectroscopy, based on charged particle detection, to a fully coherent one, based on light characterization. The main achievement presented in this thesis is to use high harmonic generation to probe femtosecond (femto=10^-15) chemical dynamics for the first time. Thanks to the coherence imposed by the strong driving laser field, homodyne detection of attosecond pulses from excited molecules undergoing dynamics is achieved, the signal from unexcited molecules acting as the reference local oscillator. First, applying time-resolved high-harmonic spectroscopy to the photodissociation of a diatomic molecule, Br2 to Br + Br, allows us to follow the break of a chemical bond occurring in a few hundreds of femtoseconds. Second, extending it to a triatomic (NO2) lets us observe both the previously unseen (but predicted) early femtosecond conical intersection dynamics followed by the late picosecond statistical photodissociation taking place in the reaction NO2 to NO + O. Another important realization of this thesis is the development of a complementary technique to time-resolved high-harmonic spectroscopy called LAPIN, for Linked Attosecond Phase INterferometry. When combined together, time-resolved high-harmonic spectroscopy and LAPIN give access to the complex photorecombination dipole of aligned excited molecules. These achievements lay the basis for electron recollision tomographic imaging of a chemical reaction with unprecedented angstrom (1 angstrom= 0.1 nanometer) spatial resolution. Other contributions dedicated to the development of attosecond science and the generalization of high-harmonic spectroscopy as a novel, fully coherent molecular spectroscopy will also be presented in this thesis.

I present several new methods for the characterisation of ultrashort pulses using interferometry. A generalisation of the concatenation algorithm for spectral shearing interferometry enables interferograms taken at multiple shears to be combined. This improves the precision of the reconstructed phase in the presence of detector noise, and enables the relative phase between disjoint spectral components to be obtained without decreasing the spectral resolution. The algorithm is applied to experimental data from two different implementations of spectral shearing interferometry for ultrashort optical pulses. In one, the shears are acquired sequentially, and in the other they are acquired simultaneously. I develop a form of spatio-temporal ultrashort pulse characterisation which performs both spatial and spectral shearing interferometry simultaneously. It requires a similar geometrical setup to common implementations of spectral phase interferometry for direct electric-field reconstruction, but provides complete amplitude and phase characterisation in time and one spatial dimension. I develop the theory of lateral shearing interferometry for spectrally resolved wavefront sensing of extended ultraviolet and soft x-ray pulses generated using high-harmonic generation. A comprehensive set of wavefront measurements of harmonics 13-25 in Krypton show good agreement with theory, validating the technique. I propose and numerically demonstrate quantum-path interferometry mediated by a weak control field for high harmonic generation. This is a general technique for measuring the amplitude and relative phases of each contributing quantum path. The control field perturbatively modulates the phase of each path. The differing sensitivity of each path to the parameters of the control field allows their contributions to be distinguished from one another.

To capture electronic rearrangements inside a molecule or during chemical reactions, attosecond (as, 1 as =10−18 s) time resolution is needed. To create a light pulse with this duration, the central frequency has to be in the XUV range and cover several tens of eVs. Moreover, the frequency components have to be synchronized. The so called High Harmonic Generation (HHG) in gases well suits this task. During this process a high intensity laser pulse is focused in a gas jet, where its electric field bends the potential barrier of an atom allowing an electron wave packet (EWP) to tunnel ionize. Following the electric field of the laser the EWP gets accelerated, gaining a large kinetic energy that may be released as a high energy (XUV) photon in the event of a re-collision with the ionic core. These recolliding EWP probe the structure and dynamics of the core in a self-probing scheme: the EWP, that is emitted by the molecule at a certain time, probes itself later. More precisely, this "self-probing" scheme gives access to the complex valued recombination dipole moment (RDM) of the molecule which is determined by both the nuclear and electronic structure. The recombination encodes these characteristics into the spectral amplitude, phase and polarization state of the harmonic radiation emitted by the dipole. Due to the coherent nature of HHG it is possible to measure all these three parameters. Moreover, it is in principle possible through a tomographic procedure to reconstruct the radiating orbital.The objective of my thesis was two-fold. By implementing advanced characterization techniques of the harmonic amplitude, phase and polarization we studied i) the electronic structure of N2 and laser induced multi-channel tunnel ionization. We presented the reconstruction of molecular orbitals and revealed the ionization channel dependent ultrafast nuclear vibration. We also studied ii) the reflectivity and dispersion of recently designed chirped XUV mirrors that can shape the temporal profile of attosecond pulses. With these mirrors we could control the spectral phase over 20 eV and compensate the GDD of the harmonics or introduce a TOD. We also proposed a novel attosecond pulse shaper.

At the heart of high harmonic generation lies a combination of optical and collision physics entwined by a strong laser field. An electron, initially tunnel-ionized by the field, driven away then back in the continuum, finally recombines back to rest in its initial ground state via a radiative transition. The emitted attosecond (atto=10^-18) XUV light pulse carries all the information (polarization, amplitude and phase) about the photorecombination continuum-to-ground transition dipolar field. Photorecombination is related to the time-reversed photoionization process. In this perspective, high-harmonic spectroscopy extends well-established photoelectron spectroscopy, based on charged particle detection, to a fully coherent one, based on light characterization. The main achievement presented in this thesis is to use high harmonic generation to probe femtosecond (femto=10^-15) chemical dynamics for the first time. Thanks to the coherence imposed by the strong driving laser field, homodyne detection of attosecond pulses from excited molecules undergoing dynamics is achieved, the signal from unexcited molecules acting as the reference local oscillator. First, applying time-resolved high-harmonic spectroscopy to the photodissociation of a diatomic molecule, Br2 to Br + Br, allows us to follow the break of a chemical bond occurring in a few hundreds of femtoseconds. Second, extending it to a triatomic (NO2) lets us observe both the previously unseen (but predicted) early femtosecond conical intersection dynamics followed by the late picosecond statistical photodissociation taking place in the reaction NO2 to NO + O. Another important realization of this thesis is the development of a complementary technique to time-resolved high-harmonic spectroscopy called LAPIN, for Linked Attosecond Phase INterferometry. When combined together, time-resolved high-harmonic spectroscopy and LAPIN give access to the complex photorecombination dipole of aligned excited molecules. These achievements lay the basis for electron recollision tomographic imaging of a chemical reaction with unprecedented angstrom (1 angstrom= 0.1 nanometer) spatial resolution. Other contributions dedicated to the development of attosecond science and the generalization of high-harmonic spectroscopy as a novel, fully coherent molecular spectroscopy will also be presented in this thesis.

Le but de cette thèse est d’étudier le processus de la génération d’harmoniques d’ordre élevé (HHG, de l’anglais high-order harmonic generation) dans des solides et la possibilité d’augmenter l’efficacité de la génération en exploitant l’exaltation locale du champ incident dans des nanostructures. La HHG dans les gaz est connue depuis plusieurs décennies et a été étudiée en détails, par contre la HHG dans les solides a été démontrée pour la première fois en 2011. Différents processus comme les oscillations interbandes et intrabandes y jouent un rôle fondamental. Le processus exact est toujours en cours d’investigation et est discuté dans la communauté. Dans ce manuscrit, nous étudions la génération d’harmoniques dans différents cristaux, comme ZnO, CaCO₃ et CdWO₄. Nous confirmons que la HHG dépend de la longueur d’onde génératrice et de l’orientation cristalline. Outre les cristaux 3D nous étudions la HHG dans des matériaux 2D comme le graphène. Grâce à sa grande mobilité électronique et sa structure de bande spécifique la HHG dans graphène est plus efficaces que dans des cristaux 3D.Typiquement des intensités de 10¹² TW/cm² ou plus sont nécessaires pour susciter la HHG. Ces intensités élevées sont généralement atteintes par des méthodes comme l’amplification par dérive de fréquence qui génère des impulsions femtosecondes à des énergies µJ ou mJ. Grâce aux progrès récents des techniques de nanofabrication, il est possible d’exalter un champ électrique laser de plusieurs ordres de grandeurs dans des nanostructures. Alors que la HHG dans les gaz assistée par la plasmonique a été démontrée comme n’étant pas réalisable, des travaux récents démontrent l’amplification de la HHG dans des solides. Dans ce travail, nous étudions l’amplification de la HHG dans différentes configurations. D’abord, nous analysons différents types de nanostructures, à savoir des bow ties, des nano-trous, des réseaux et des résonateurs. Nous comparons ces structures suivant plusieurs critères tels que le volume d’exaltation et l’exaltation crête. Différentes longueurs d’onde et cristaux sont utilisés. Une large amplification de plusieurs ordres de grandeur est démontrée pour la troisième harmonique. En plus, nous discutons l’endommagement des nanostructures causé par l’irradiation laser. Des nanostructures semiconductrices confinant la lumière par guidage sub-longueur d’onde ont plusieurs avantages par rapport aux nanostructures métalliques. Des nanocones semiconducteurs, par exemple, présentent un grand volume d’amplification, supérieur de plusieurs ordres de grandeur à ce qui a été démontré récemment, et évitent la fusion observée dans des nanostructures métalliques. Nous présentons plusieurs itérations de l’expérience avec des nanocones de ZnO en améliorant le système de détection et la géométrie des nanocones entre chaque étape. Nous utilisons différents lasers et différentes géométries de nanocones. Nous avons observé les harmoniques d’un laser à 3.1 µm dans des nanocones de ZnO jusqu’à l’ordre 15. L’amplification de plusieurs ordres de grandeur d’harmoniques perturbatives et non perturbatives, générées à partir des impulsions d’un oscillateur nanojoule à une cadence MHz et une longueur d’onde de 2.1 µm, est démontrée pour la première fois jusqu’à H9. Le facteur d’amplification dépend de l’éclairement du faisceau pompe. Nous étudions également la forte amplification de la luminescence et proposons des méthodes pour séparer sa contribution de la contribution cohérente. En outre, nous démontrons plusieurs applications de la HHG dans les solides. Premièrement, nous proposons une nouvelle méthode pour déduire la distribution spatiale du champ électrique dans des nanostructures en analysant les dommages induits par laser. Deuxièmement, nous utilisons l’émission du nanocone, qui est cohérente spatialement, pour imager des objets avec une résolution à l’échelle nanométrique. Enfin, nous générons des harmoniques portant un moment orbital angulaire contrôlé. / The aim of this dissertation is to study the process of high-order harmonic generation (HHG) in solids and the possibility to amplify solid HHG by exploiting local field enhancements in nanostructures. While HHG in gases has been known for several decades and has been extensively studied, HHG in solids was first reported in 2011. Different processes such as interband and intraband oscillations were identified to play an important role in solid HHG. However, the process is still under investigation and debated in the community. Here, we study the generation of high harmonics in different crystals, such as ZnO, CaCO₃ and CdWO₄. We confirm that HHG depends on the driving wavelengths and on crystalline orientation. Beside 3D bulk crystals, we investigate HHG in 2D materials such as graphene. Due to its high electron mobility and its special band structure HHG in graphene is more efficient than in bulk crystals. Typically, intensities of 10¹² TW/cm² or more are needed to trigger HHG. The high intensity is reached by employing schemes like chirped pulse amplification which generates femtosecond pulses with µJ- or mJ-energies. Thanks to recent advances in nanofabrication techniques, nanostructures can enhance a laser electric field by several orders of magnitude. While plasmonically enhanced HHG in gases was shown not to be feasible, recent works reported on the amplification of HHG in solids. In this work, we explore the amplification of crystal HHG under various configurations. We first study different types of plasmonic nanostructures, namely bow ties, nanoholes, gratings and resonators. We compare them with respect to different parameters such as enhancement volume and peak enhancement. Different driving wavelengths and crystals are used. Strong amplification by several orders of magnitude is demonstrated for the third harmonic. Furthermore, we discuss radiation-induced damage of plasmonic nanostructures. Semiconductor nanostructures which confine light by subwavelength waveguiding have several advantages with respect to metallic nanostructures. Semiconductor nanocones for example exhibit a large amplification volume, several orders of magnitudes larger than previously reported and avoid melting observed in metallic nanostructures. We carry out several iterations of experiments with ZnO nanocones where the detection system and the nanocone geometry are improved in each cycle. We use different driving lasers and different optimized nanocone geometries. HHG in ZnO nanocones up to 15th order from a 3.1 µm driving laser is demonstrated. Amplification by several orders of magnitude of both perturbative and non-perturbative harmonics from nanojoule-oscillator pulses at MHz repetition rate and 2.1 µm wavelength is demonstrated, for the first time up to H9. The amplification factor depends on the pump intensity. We also explore the strong amplification of luminescence and propose ways to disentangle its contribution from the coherent one. Furthermore, we explore several applications of crystal HHG. First, we propose a new way to deduce the electric field spatial distribution in nanostructures by analyzing the radiation-induced damage. Secondly, we use the spatially coherent emission from the nanocone to image nanoscale objects with nanometer scale resolution. In addition, we generate solid harmonics that carry an orbital angular momentum.

We are developing a tabletop extreme-ultraviolet source using high harmonic generation at Brigham Young University. The thesis goes over the theory of high harmonic generation using the three-step model. This tabletop source was designed for probing magnetic domains of iron nanoparticles. We present optimization of the 42 eV and 52 eV harmonics through phase matching. Phase matching consists of tuning the intensity of the IR beam and pressure of the gas medium. The target gas medium used for this thesis is argon. The 42 eV harmonic was optimized to 8.2 billion photons per second. This was used with a 1500 mm focal-length lens, 15 mm medium length, laser power of 1.53 Watts, and a pressure of 12 Torr of argon gas. The 52 eV harmonic was optimized to 1.5 billion photons per second with a 1500 mm focal-length lens, 20 mm medium length, laser power of 3.29 W, and 14.9 Torr of argon gas. There are two designs for selection of harmonics: 1) a tunable design consisting of a toroidal mirror and flat diffraction grating and 2) a set of normal-incidence extreme-ultraviolet mirrors designed for 42 or 52 eV photons. Magnetic imaging uses x-ray magnetic circular dichroism to obtain magnetic contrast and use it to visualize magnetic nanosystems. Therefore, the high harmonic source also needs to generate circularly polarized light. Generating circularly polarized high harmonics is possible with a bichromatic beam. This is achieved using an apparatus called the MAZEL-TOV designed by Oren Cohen’s group at Technion University in Israel. The MAZEL-TOV consists of a BBO crystal for second harmonic generation, a pair of pulse delay compensation plates, and a quarter-wave plate. These optics are placed inline with the laser beam. We have successfully optimized the circularly polarized extreme-ultraviolet harmonics with the MAZEL-TOV. A spectrometer was made to calibrate the harmonics in the MAZEL-TOV spectrum. The tabletop source was then used to demonstrated coherent diffraction imaging of two pinholes.

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