The light source that has revolutionized attosecond science over the last decades is based on the process of high-harmonic generation (HHG), which is a unique method to generate a broadband coherent spectrum extending into the extreme-ultraviolet (XUV) range. The temporal and spatial resolution of HHG enables investigation of strong-field light-matter interaction in the ultrafast and ultrasmall dimensions, and finds applications in attosecond science, lensless imaging, and industrial metrology. Unfortunately, the intrinsic low conversion efficiency of HHG and the limited methods to control the generated XUV wavefront, slow down present research and future development of applications that are based on HHG. Control over the HHG process is essential to improve the conversion efficiency and XUV wavefront characteristics, in order to facilitate next-generation attosecond science and metrology. This thesis presents experimental techniques and results that demonstrate control over both gas-based and solid-based HHG in the extreme-ultraviolet regime. Additionally, the underlying mechanism and working principles are explained through theoretical models and simulations. In Chapter 4, we demonstrate divergence and yield optimization in polarization controlled two-color gas-based HHG. Imaging, spectroscopy, and metrology applications using HHG sources require high XUV brightness, related to the conversion efficiency and the focusability of the generated XUV pulses. We systematically investigate, both experimentally and theoretically, the effect of the relative polarization between the fundamental and its second harmonic in two-color HHG, and compare the results to a one-color configuration. In a perpendicular two-color field, the relative phase between the two colors can be used to manipulate the long or the short trajectories, allowing control over the divergence of the harmonics. In a parallel two-color field, the relative phase can be used to modify the ionization rate to select trajectories and additionally allows to enhance the total yield. Next, we describe extreme-ultraviolet shaping and imaging by HHG from nanostructured silica in Chapter 5. Tailoring of any XUV wavefront after generation is challenged by the lack of efficient optical elements and limits HHG applications. We demonstrate how HHG from a structured generation medium enables control over the phase, amplitude, and polarization properties of extreme-ultraviolet pulses. Moreover, we use the emitted patterns to reconstruct height profiles, probe the near-field confinement in nanostructures below the diffraction limit of the fundamental, and image complex structures using the coherent diffractive emission from the structures. In another experiment, we establish efficient extreme-ultraviolet high-order wavemixing from laser-dressed silica, described in Chapter 6. Solid-based HHG allows to produce a coherent, broadband, extreme-ultraviolet light source with tailored emission profiles, but is put at disadvantage due to the low conversion efficiency from infrared to XUV photons. Here, we overcome the low conversion efficiency by driving the HHG simultaneously with the fundamental and its second harmonic, in a non-collinear geometry. The observed high-order wave mixing emission follows perturbative intensity scalings and enhances the XUV efficiency by at least one order of magnitude. The underlying generation mechanism is described by a quantum theory, that reveals that solid HHG is boosted through laser-dressed states. Finally, we demonstrate transient grating high-harmonic spectroscopy in MgO in Chapter 7, and investigate how an excited carrier population influences solid-state HHG. Two crossed 266-nm pulses induce a transient grating of excited carrier population due to two-photon absorption in the MgO. The modification of the relative amplitude and phase of the harmonics at the generation plane results in diffraction in the far field. Preliminary analysis demonstrates that both the macroscopic propagation effects onto the fundamental and the microscopic generation mechanism of the HHG process contribute to the amplitude and phase modulation.

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