Attosecond pulses have been developed as a means for investigating phenomena that proceed on the order of the atomic unit of time (24 as). Unfortunately, these extreme ultraviolet (XUV) pulses by themselves contain too few photons to initiate nonlinear dynamics or dress states in an attosecond pump--attosecond probe scheme. As a result, most attosecond experiments thus far have featured complementary near infrared (NIR) femtosecond lasers for instigating electron dynamics. In order to access the benefits of all-attosecond measurements and open attosecond physics to new fields of exploration, the photon flux of these pulses must be increased. One way to boost the attosecond pulse energy is to scale up the energy of the NIR pulse responsible for driving high-harmonic generation (HHG). With generalized double optical gating (GDOG), isolated attosecond pulses can be generated with multi-cycle laser systems, wherein the pulse energy can be boosted more easily than in the few-cycle laser systems required by other gating methods. At the Institute for the Frontier of Attosecond Science and Technology (IFAST), this scalability was demonstrated using a 350 mJ, 15 fs (10 TW) Ti:sapphire laser, which was used to generate a 100 nJ XUV continuum. This represented an order-of-magnitude improvement over typical attosecond pulse energies achievable by millijoule-level few-cycle lasers. To obtain the microjoule-level attosecond pulse energy required for performing all-attosecond experiments, the attosecond flux generated by the IFAST 10 TW system was still deficient by an order of magnitude. To this end, the laser system was upgraded to provide joule-level output energies while maintaining pulse compression to 15 fs, with a targeted peak power of 200 TW. This was accomplished by adding an additional Ti:sapphire amplifier to the existing 10 TW system and implementing a new pulse compression system to accommodate the higher pulse energy. Because this system operated at a 10 Hz repetition rate, stabilization of the carrier-envelope phase (CEP) -- important for controlling attosecond pulse production -- could not be achieved using traditional methods. Therefore, a new scheme was developed, demonstrating the first-ever control of CEP in a chirped-pulse amplifier (CPA) at low repetition rates. Finally, a new variation of optical gating was proposed as a way to improve the efficiency of the attosecond pulse generation process. This method was also predicted to allow for the generation of isolated attosecond pulses with longer driving laser pulses, as well as the extension of the high-energy photon cut-off of the XUV continuum.

The semiconductor Bloch equations (SBEs) are an insightful and well-established formalism for studying light-matter interactions in solids. When Coulomb interactions between electrons are omitted, the SBEs are simplified to a single particle model. The SBEs in this single electron approximation have been used extensively to model strong-field interactions in condensed matter. The SBEs in the length gauge provide an intuitive and numerically efficient model of high harmonic generation (HHG) in solids. In this approach, the SBEs involve Berry connections and transition dipole moments, which are gauge dependent structural quantities. This thesis studies the role of gauge symmetry in the SBEs, and how it can be exploited to facilitate efficient numerical analysis of HHG in solids. In the length gauge, the macroscopic current describing HHG can be decomposed into physically intuitive contributions. In particular, this leads to a contribution known as the "mixture" current, which has been overlooked by the HHG community until recently. We study the influence of this contribution using the analytic tight-binding model for gapped graphene. We derive an analytic gauge transformation that removes singular behaviour from the gapped graphene model, thus enabling efficient numerical integration of the SBEs. We also present an alternative approach for simulating dynamics in tight-binding models. Instead of simulating the SBEs in the usual basis of Bloch functions, we transform to the basis in which the tight-binding Hamiltonian is represented. The dipole matrix elements necessarily vanish in this basis, and the SBEs can be integrated using only the Hamiltonian matrix elements. We first generalize the SBEs to accomodate a non-diagonal Hamiltonian matrix, and we demonstrate this formalism numerically using two different tight-binding models. Finally, we derive a novel formulation of the SBEs which involve only gauge invariant matrix elements. Specifically, the Berry connections and transition dipole phases are replaced by a gauge invariant quantity known as the shift vector. This yields a fully gauge invariant description of HHG in solids, and the shift vector provides intuitive insight for HHG in systems with broken inversion symmetry. Further, the ability to describe HHG solely in terms of gauge invariant quantities raises new possibilities for tomographic reconstruction of crystal band structure, and this idea is discussed as a possible direction of future work.

Master of Science / Physics / Vinod Kumarappan / This report includes the experimental details and results of two experiments. The first experiment addresses carrier envelope phase (CEP) effects in higher order harmonic generation (HHG), and the second experiment is a pump-probe experiment on CO₂ molecules using ultrashort laser pulses. Ultrashort laser pulses that are only a few optical cycles long are of interest for studying different atomic and molecular processes. The CEP of such a pulse is an important parameter that can affect the experimental results. Because the laser pulses we used in the HHG experiment have random CEP, we tagged a given harmonic spectrum with the CEP of the fundamental laser pulse that generated it by measuring both shot-by-shot. The first chapter of this report is about the experimental details and the results we got from our CEP-tagged HHG experiment that enabled us to observe the interference of different quantum pathways. In the second experiment, discussed in the second chapter of this report, we tried to study the structure of the CO₂⁺ ion created by strong field ionization in a pump-probe experiment. For this experiment, we used an ultrashort laser pulse to ionize CO₂ molecules, and after various time delays we probed the ionic wave packet by ionizing CO₂⁺ with another ultrashort laser pulse. By performing Fourier analysis on the delay-dependent CO₂⁺⁺ yield, we were able to identify the populated states of CO₂⁺.

Doctor of Philosophy / Department of Physics / Zenghu Chang / The observation and control of dynamics in atomic and molecular targets requires the use of laser pulses with duration less than the characteristic timescale of the process which is to be manipulated. For electron dynamics, this time scale is on the order of attoseconds where 1 attosecond = 10[superscript]-18 seconds. In order to generate pulses on this time scale, different gating methods have been proposed. The idea is to extract or “gate” a single pulse from an attosecond pulse train and switch off all the other pulses. While previous methods have had some success, they are very difficult to implement and so far very few labs have access to these unique light sources. The purpose of this work is to introduce a new method, called double optical gating (DOG), and to demonstrate its effectiveness at generating high contrast single isolated attosecond pulses from multi-cycle lasers. First, the method is described in detail and is investigated in the spectral domain. The resulting attosecond pulses produced are then temporally characterized through attosecond streaking. A second method of gating, called generalized double optical gating (GDOG), is also introduced. This method allows attosecond pulse generation directly from a carrier-envelope phase un-stabilized laser system for the first time. Next the methods of DOG and GDOG are implemented in attosecond applications like high flux pulses and extreme broadband spectrum generation. Finally, the attosecond pulses themselves are used in experiments. First, an attosecond/femtosecond cross correlation is used for characterization of spatial and temporal properties of femtosecond pulses. Then, an attosecond pump, femtosecond probe experiment is conducted to observe and control electron dynamics in helium for the first time.

This dissertation is on the development of a laser system for the generation of femtosecond frequency combs in the vacuum-ultraviolet (VUV) via intracavity high-harmonic generation (HHG). The HHG process yields coherent vacuum ultraviolet (VUV) light resulting from the ionization of noble gases driven by intense near-IR femtosecond frequency combs in an optical enhancement cavity. An injection locked amplification cavity (fsAC) was developed in order to generate a high power femtosecond frequency combs based on a Ti:Sapphire oscillator. Detailed amplifier performance was investigated in order to evaluate the coherence of the pulse amplification process. A passive power enhancement cavity for fs pulses (fsEC) was designed for intracavity high harmonic generation. For maximum power enhancement and conversion efficiency, the intracavity dispersion was compensated and various design layouts tested. A careful analysis of the phase matching conditions was performed, taking into account the effect of reabsorption of the generated high harmonic light, to compare different cavity geometries and determine which would produce the most efficient harmonic yield. Numerical simulations were also performed to determine the level of intra-cavity ionization that could be sustained before disrupting the pulse enhancement process. Based on the results of these simulations and calculations, it was determined that for a xenon gas target, a moderate peak intensity of the order of ~ 5×10¹³W/cm² produces harmonics most efficiently.

Doctor of Philosophy / Department of Physics / Itzhak Ben-Itzhak and Charles Lewis Cocke / A commercially available modern laser can emit over 10^15 photons within a time window of a few tens of femtoseconds (10^-15 second), which can be focused into a spot size of about 10 um, resulting in a peak intensity above 10^14 W/cm^2. This paves the way for table-top strong field physics studies such as above threshold ionization (ATI), non-sequential double ionization (NSDI), high order harmonic generation (HHG), etc.. Among these strong laser-matter interactions, high order harmonic generation, which combines many photons of the fundamental laser field into a single photon, offers a unique way to generate light sources in the vacuum ultraviolet (VUV) or extreme ultraviolet (EUV) region. High order harmonic photons are emitted within a short time window from a few tens of femtoseconds down to a few hundreds of attoseconds (10^-18 second). This highly coherent nature of HHG allows it to be synchronized with an infrared (IR) laser pulse, and the pump-probe technique can be adopted to study ultrafast dynamic processes in a quantum system. The major work of this thesis is to develop a table-top VUV(EUV) light source based on HHG, and use it to study dynamic processes in atoms and small molecules with the VUV(EUV)-pump IR-probe method. A Cold Target Recoil Ion Momentum Spectroscopy (COLTRIMS) apparatus is used for momentum imaging of the interaction products. Two types of high harmonic pump pulses are generated and applied for pump-probe studies. The first one consists of several harmonics forming a short attosecond pulse train (APT) in the EUV regime (around 40 eV). We demonstrate that, (1) the auto-ionization process triggered by the EUV in cation carbon-monoxide and oxygen molecules can be modified by scanning the EUV-IR delay, (2) the phase information of quantum trajectories in bifurcated high harmonics can be extracted by performing an EUV-IR cross-correlation experiment, thus disclosing the macroscopic quantum control in HHG. The second type of high harmonic source implemented in this work is a single harmonic in the VUV regime (around 15 eV) filtered out from a monochromator. Experiments on D_2 molecules have been conducted using the 9th or the 11th harmonic as the pump pulse. Novel dissociative ionization pathways via highly excited states of D_2 have been revealed, thus suggesting potential applications for time-resolved studies and control of photochemistry processes.

L'interaction d'une impulsion laser intense (~10¹⁴ W /cm²) et de courte durée (femtoseconde) avec un gaz rare induit une polarisation hautement non-linéaire dans le domaine spectral XUV; les harmoniques d'ordre élevés. En raison des propriétés spécifiques du rayonnement harmonique et de ses applications, cette thématique est particulièrement riche et fertile. La production efficace d'harmoniques d'ordres élevés repose à la fois sur la réponse non-linéaire de l'atome unique et un comportement collectif.Le fil directeur des études présentées dans cette thèse est la compréhension et le contrôle de l'accord de phase ou du quasi accord de phase en présence d'une ionisation substantielle du gaz générateur. Dans ce contexte, nous montrons l'importance de la longueur de cohérence sur l'accord de phase en génération d'harmoniques. Nous étudions sa dépendance en fonction de la focalisation du laser, de la pression mais aussi sa dépendance temporelle liée à l'ionisation, effet que nous avons mis en évidence lorsqu'on a cherché à optimiser une double impulsion harmonique. Le travail de développement, sur la station LASERIX, de la source à double impulsion harmonique générée à partir d'un même milieu gazeux et avec un délai picoseconde variable est présenté. Cette source possède un véritable potentiel d'applications scientifiques, injectée dans un milieu amplificateur plasma qu'on appelle laser X, la double impulsion permettra de sonder la réponse temporelle de ce type de milieu. Par ailleurs, des expériences et des simulations menées sur la génération d'harmoniques en propagation guidée visent ainsi à étendre les spectres harmoniques vers les courtes longueurs d'ondes, zone spectrale pour laquelle le laser X à plasmas est émis. Ceci donnera l'accès à une source offrant des caractéristiques complémentaires des lasers X, sources développées en parallèle sur la station LASERIX. / The interaction of an intense laser pulse of short duration with a rare gas induces a highly non-linear polarization in the XUV spectral range: the high order harmonics. Due to the specific properties of the harmonic radiation and its applications, this issue is particularly rich and fertile. The efficient production of high order harmonics is based both on the non-linear response of the single atom and on collective behavior.The principle of the research presented in this thesis is the understanding and control of phase matching or quasi-phase matching in the presence of substantial ionization in the generating gas. In this context, we show the importance of the coherence length on the phase matching in High harmonic generation. We study its dependence on laser focusing, pressure but also its time dependence related to ionization. Moreover, experiments and simulations aim at extending harmonic spectra towards shorter wavelengths, a spectral range for which the X Ray Laser is emitted. This will give access to a source with complementary characteristics as regards to X-ray lasers. This source shall be developed in parallel on the LASERIX station or injected in soft X-ray laser amplifiers.

En vue de la capture de réearrangements électroniques au sein d’une molécule ou au cours de réactions chimiques il est indispensable de développer un dispositif dont la résolution temporelle est attoseconde (as 1 as = 10−18 s). La voie naturelle est de rechercher des impulsions lumineuses dans cette gamme de durée. Leur fréquence centrale doit alors être dans la gamme UVX et couvrir plusieurs dizaines d’eVs. De plus, ses composantes fréquencielles doivent être synchronisées. Le processus de génération d’harmoniques d’ordre élevé (GHE) dans les gaz remplit ces exigences. Pendant ce processus, une impulsion laser de haute intensité est focalisée dans un jet de gaz, où son champ électrique courbe la barrière de potentiel d’un atome et permet l’ionisation tunnel d’un paquet d’ondes électronique (POE). Entrainé par le champ électrique du laser, le POE accélére et acquiert une énergie cinétique élevée. Dans le cas où il repasse au voisinage du coeur ionique cette énergie cinétique peut être émise sous la forme d’un photon UVX. Ces POE explorent la structure et la dynamique de l’ion dans un schéma d’auto-sonde: le POE émis à un instant donné revient lui même ultérieurement sonder l’ion. Plus précisément ce processus d’autosonde donne accès à la valeur complexe du dipôle de recombinaison moléculaire (DRM), lui-même determiné par les structures nucléaire et électronique de l’ion. Le dipôle de recombinaison, en rayonnant des harmoniques, encode ces caractéristiques dans l’amplitude, la phase et l’état de polarisation de l’émission harmonique. Grâce à la nature cohérente de la GHE nous pouvons mesurer ces trois paramètres.L’objectif de ma thèse de doctorat était double. En mettant en oeuvre des techniques avancées de caractérisation de l’amplitude, de la phase et de la polarisation des harmoniques nous avons dans un premier temps étudié la structure électronique de N2 et l’ionisation tunnel multi-canaux induite par le laser. Nous avons montré les reconstructions des plusieurs orbitals moléculaires et révélé la vibration nucléaire ultra-rapide en fonction des canaux d’ionisations. Dans un deuxième temps nous avons étudié la réflectivité et la dispersion de miroirs UVX à compensation de dérive de fréquence, fabriqués sur mesure. Ces miroirs autorisent la mise en forme temporelle d’une impulsion attoseconde, compriment la durée de l’impulsions où introduisent un TOD. Nous avons aussi proposé un nouveau façonneur d’impulsions. / 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.

The generation of high-order harmonics opened an era of attosecond science wherein coherent light bursts are used to probe dynamic processes in matter with a time resolution short enough to resolve the motions of electrons. It enabled the development of extreme ultraviolet (XUV) and X-ray table-top sources with both temporal and spatial coherence, which provides the ability to shape the temporal and spatial structure of the XUV pulses. Scientists developed techniques to control and measure the temporal structure high harmonic emissions. These techniques exploited control of the driving laser pulse in the time domain and facilitated development of more advanced high-harmonic based XUV sources that have greatly impacted ultrafast measurements. In this thesis, I apply techniques to control and measure the spatial structure of high harmonic emissions, and discuss the underlying physics and potential applications of the interaction between spatially structured laser beams and materials. This study exploits the spatial degree of freedom in strong field interaction, which has not been given as much attention as the temporal degree of freedom. I use liquid crystal devices to shape the wave front of a fundamental laser beam to a vortex structure, then imprint this structured wave front onto XUV beams through high harmonic generation. This method provides an alternative to special XUV optics, which can manipulate the wave front of XUV radiation by all optical means. This result also reveals the conservation of orbital angular momentum in this extreme nonlinear wave mixing process. In addition to shaping the wave front, shaping the polarization of the driving beam also allows generation of circularly polarized the XUV radiation using a high harmonic source. This thesis also highlights the interplay between shaping the wave front and polarization in the high harmonic generation process. The topology of the structured beam can be maintained through this extreme nonlinear interaction due to the spin selection rules and spin-orbit conservation. Moreover, this thesis demonstrates an approach to integrate a vector beam into a broadband ultrafast light source and overcome the bandwidth limitation of mode converters. We use this approach to generate a few-cycle structured beam. In the future, this beam will be used to generate a strong ultrafast magnetic impulse in gas and solid targets by driving currents in a loop, which is a valuable tool for the future of magnetic metrology. The novel properties of structured laser beams discussed in this thesis expanded the capabilities of high harmonic based XUV sources and have opened a new field to explore this additional degree of freedom in strong field interactions.

Molecules are traditionally treated quantum mechanically using the Born-Oppenheimer formalism. In this formalism, different electronic states of the molecule are treated independently. However, most photo-initiated phenomena occurring in nature are driven by the couplings between different electronic states in both isolated molecules and molecular aggregates, and therefore occur beyond the Born-Oppenheimer formalism. These couplings are relevant in reactions relating to the perception of vision in the human eye, the oxidative damage and repair of DNA, the harvesting of light in photosynthesis, and the transfer of charge across large chains of molecules. While these reaction dynamics have traditionally been studied with visible and ultraviolet spectroscopy, attosecond XUV pulses formed through the process of high harmonic generation form a perfect tool for probing coupled electronic dynamics in molecules. In this thesis, I will present our work in using ultrafast, XUV spectroscopy to study these dynamics in molecules of increasing complexity. We begin by probing the relaxation dynamics of superexcited states in diatomic O₂. These states can relax via two types of electronic couplings, either through autoionization or neutral dissociation. We find that our pump-probe scheme can disentangle the two relaxation mechanisms and independently measure their contributing lifetimes. Next, we present our work in observing a coherent electron hole wavepacket initiated by the ionization of polyatomic CO₂ near a conical intersection. The electron-nuclear couplings near the conical intersection drive the electron hole between different orbital configurations. We find that we can not only measure the lifetime of quantum coherence in the electron hole wavepacket, but also control its evolution with a strong, infrared probing field. Finally, we propose an experiment to observe the migration of an electron hole across iodobenzene on the few-femtosecond timescale. We present experimental modifications made to the high harmonic generation set-up in order to probe this ultrafast and elusive charge migration. These results demonstrate the potential of ultrafast, XUV spectroscopy in probing the inner-workings of electronic couplings occurring in nature.