| Summary: | <p> This dissertation encompasses experimental and theoretical studies on two cornerstones of modern nonlinear optics: laser filamentation and harmonic generation. Laser filaments are self-guided light structures balanced by Kerr self-focusing and diffraction/plasma defocusing, enabling applications in lightning guiding, long-range spectroscopy, and high-precision laser weapons. Harmonic generation is a nonlinear process that up-converts optical frequencies, and it is a promising source of table-top, ultrashort X-ray/UV radiation. </p><p> The goal of this work is two-fold: control and visualization of nonlinear optical phenomena. First, variable focusing geometries are used to eliminate high-power laser multifilamentation, which is a stochastic process that is notoriously difficult to control. Next, two-color pump-probe experimental schemes are used to enhance third-harmonic generation in air by several orders of magnitude. Our experimental results agree well with calculations based on state-of-the-art unidirectional pulse propagation equations, which give insight into the physical mechanisms underlying our experimental findings. An overarching theme of this work is ultrafast visualization: by combining femtosecond-time-resolved pump-probe methods with advanced quantitative phase microscopy, we can visualize and quantitatively characterize dynamically-evolving micro-structures during various nonlinear laser-matter interactions. Finally, this work will describe some novel properties of mid-infrared and long-wavelength infrared ultrashort pulse propagation, with a focus on the generation of light bullets, which represent a holy grail of nonlinear optics.</p><p>
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