This thesis focuses on the development of high harmonic generation (HHG) by using polarisation controlled quasi-phase matching QPM as well as related topics. A new class of QPM techniques called polarisation-controlled QPM is introduced where linear or circlar birefringence enables the modulation of the driving field's polarisation state called polarisation-beating QPM (PBQPM) for linear birefringence and optical rotation QPM (ORQPM) for circular birefringence respectively. PBQPM uses a linear birefringence to modulate periodically the driving pulse between linear and circular/elliptical polarisation states. Because elliptical or circular polarisation of the driving pulse suppresses harmonic generation, by appropriately matching the beat length of the driving field's polarisation state to the coherence length of the harmonic generation, QPM can be achieved. In the second technique, ORQPM, propagation of the driving radiation in a system exhibiting circular birefringence causes its plane of polarisation to rotate; by appropriately matching the period of rotation to the coherence length, it is possible to avoid destructive interference of the generated radiation. Not only does ORQPM have similar enhancements as true-phase matching, it is also the first proposed QPM source for circularly polarised high harmonics. The importance of phase modulation in QPM, especially relating to modebeating in hollow-core waveguides where harmonics is being generated are also explored theoretically. Based on this, a novel technique for analyzing random phase matching using a continuous phase-diffusion treatment has been developed; theoretical analytical models are shown to produce excellent agreement with simulations. It is further shown that random phase matching may be responsible for additional broadening of the high harmonic spectrum, especially at higher harmonic orders. Because mode and polarisation control is central to polarisation-controlled QPM, four waveguide mode decomposition techniques from single shot CCD data have been developed. The extraction of phase and coupling coefficients are demonstrated experimentally. A novel analytical general solution for the phase introduced by a phase-only spatial light modulator to generate a given far-field phase and amplitude was developed. The solution was demonstrated experimentally and shown to enable excellent control of the far-field amplitude and phase. Finally, circular and linear birefringent waveguides were explored. Analytic solutions to rectangular birefringent hollow-core waveguides were developed and some initial demonstration experiments were performed.

High Harmonic Generation (HHG) enables the production of bursts of coherent soft x-rays with attosecond pulse duration. This process arrises from the nonlinear interaction between intense infrared laser pulses and an ionizing gas medium. Soft x-ray photons are used for spectroscopy of inner-shell electron correlation and exchange processes, and the availability of attosecond pulse durations will enable these processes to be resolved on their natural time scales. The maximum or cutoff photon energy in HHG increases with both the intensity as well as the wavelength of the driving laser. It is highly desirable to increase the harmonic cutoff as this will allow for the generation of shorter attosecond pulses, as well as HHG spectroscopy of increasingly energetic electronic transitions. While the harmonic cutoff increases with laser wavelength, there is a corresponding decrease in harmonic yield. The first part of this thesis describes the experimental measurement of the wavelength scaling of HHG efficiency, which we report as lambda^(-6.3) in xenon, and lambda^(-6.5) in krypton. To increase the HHG cutoff, we have developed a 1.8 um source, with stable carrier envelope phase and a pulse duration of <2 optical cycles. The 1.8 um wavelength allowed for a significant increase in the harmonic cutoff compared to equivalent 800 nm sources, while still maintaing reasonable harmonic yield. By focusing this source into neon we have produced 400 eV harmonics that extend into the x-ray water window. In addition to providing a source of photons for a secondary target, the HHG spectrum caries the signature of the electronic structure of the generating medium. In krypton we observed a Cooper minimum at 85 eV, showing that photoionization cross sections can be measured with HHG. Measurements in xenon lead to the first clear observation of electron correlation effects during HHG, which manifest as a broad peak in the HHG spectrum centred at 100 eV. This thesis also describes several improvements to the HHG experiment including the development of an ionization detector for measuring laser intensity, as well as an investigation into the role of laser mode quality on HHG phase matching and efficiency.

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.

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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.