Spectrally resolved Extreme Ultraviolet Lensless Imaging With High-Order Harmonic Generation Sources

High harmonic generation (HHG) serves as a transformative gateway to the quantum dynamics of electrons, offering a unique perspective on the ultrafast processes that govern chemical and physical transformations at the atomic scale. By focusing intense laser pulses into a noble gas, we can coerce the gas's electrons into a nonlinear dance—where they absorb multiple photons, tunnel through their atomic potentials, and re-emit this energy as they snap back to lower energy states, producing bursts of extreme ultraviolet (EUV) and soft X-ray radiation. Combining HHG with lensless imaging paves the way for revolutionary technological advancements in imaging and diagnostics, probing dynamics previously veiled by the limits of temporal resolution. The focus of the second chapter is the application of HHG in coherent diffractive imaging (CDI), where the coherence and extreme ultraviolet wavelengths of HHG sources allow for imaging with high spatial resolution and chemical sensitivity. CDI, a lensless imaging technique, circumvents the resolution limits imposed by lens-based systems, exploiting the phase retrieval from diffraction patterns to reconstruct images of nanostructures and biological specimens. The unique properties of HHG-enhanced CDI lie in its ability to spectrally reconstruct the image of the object, providing a powerful tool for understanding the 3D structure of the object and its chemical composition. This chapter paves the way towards spectrally resolved ptychography. In the third chapter, we propose the concept of spatial entropy minimization as a computational design principle for both mono- and polychromatic focusing optics. We show that spatial entropy minimization yields conventional ZPs for monochromatic radiation. For polychromatic radiation, we observe a previously unexplored class of diffractive optical elements (DOEs), allowing for balanced spectral efficiency. We apply the proposed approach to the design of a binary ZP, tailored to multispectral focusing of extreme ultraviolet (EUV) radiation from a high-harmonic table top source. The polychromatic focusing properties of these ZPs are experimentally confirmed using ptychography. This work provides a new route towards polychromatic wavefront engineering at EUV and soft-X-ray wavelengths. The fourth chapter focus on the technical challenges and solutions associated with measuring and manipulating the wavefronts of high-order harmonic beams. Here we present a wavefront sensing solution based on multiplexed ptychography, with which we show spectrally-resolved, high-resolution beam reconstructions.using these high fidelity quantitative wavefront measurements, we investigate aberration transfer mechanisms in the high harmonic generation process, where we present and explain harmonic-order dependent astigmatism inheritance from the fundamental wavefront. This ptychographic wavefront sensing concept thus enables detailed studies of the high-harmonic generation process, such as spatiotemporal effects in attosecond pulse formation. The final chapter consolidates the chromatic aberrations inherent in the HHG process, highlighting their impact on the focusability and quality of generated beams across different harmonic orders. By systematically varying the generation conditions and employing sophisticated wavefront characterization techniques, we uncover the wavelength-dependent focusing properties of HHG beams. The insights gained from these studies are crucial for optimizing the generation and application of high harmonics in various scientific and technological arenas.