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The propagation of a high peak power femtosecond laser pulse through a dielectric medium results in filamentation, a strongly nonlinear regime characterized by a narrow, high intensity core surrounded by a lower intensity energy “reservoir” region. The structure can propagate over many core diameter-based Rayleigh ranges.

When a pulse of sufficiently high power propagates through a medium, the medium response creates an intensity dependent lens, and the pulse begins to focus in a runaway process known as optical collapse. Collapse is invariably mitigated by an arrest mechanism, which becomes relevant as the pulse becomes increasingly intense. In air, collapse is arrested through plasma refraction when the pulse becomes intense enough to ionize the medium. Following arrest, the pulse begins to “filament” or self-guide. In gaseous media, energy deposited in the wake of filamentation eventually thermalizes prompting a neutral gas hydrodynamic response. The gas responds to a sudden localized pressure spike by launching a single cycle acoustic wave, leaving behind a heated, low density channel which gradually dissipates through thermal diffusion.

This dissertation presents a fundamental advance in the theory of optical collapse arrest, which is how a pulse transitions from the optical collapse regime to the filamentation regime. We provide experimental evidence, supported by theory and numerical simulation that pulses undergoing collapse arrest in air generate spatiotemporal optical vortices (STOVs), a new and previously unobserved type of optical vortex with phase and energy circulation in a spatiotemporal plane. We argue that STOV generation is universal to filamentation, applicable to all collapsing beams, independent of the initial conditions of the pulse or the details of the collapse arrest mechanism. Once formed, STOVs are essential for mediating intrapulse energy flows.

We also study the hydrodynamic response following filamentation, with the intent of engineering the response to construct a variety of neutral gas waveguides. In a proof-of-concept experiment, we demonstrate that a transverse array of filamenting pulses can be used to inscribe two distinct types of waveguides into the air: acoustic and thermal waveguides. These waveguides can be used to guide very high average power laser beams or as remote atmospheric collection lenses.