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Structured inverse problems in ultrafast optics
Rosen, Daniel J.
Rosen, Daniel J.
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2024
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2025-05-26
Abstract
This thesis examines the intersection of structured inverse problems and optimization with ultrafast optics, presenting a hierarchy of problems in this intersection as well as novel contributions toward laser pulse characterization.
Structured inverse problems have blurred the lines between measurement and optimization over the past two decades; the advent of compressive sensing allowed previously established sensing limits to be overcome by exploiting signal structure with optimization.
Ultrafast optics studies physics at time scales beyond the reach of all previously conceived sensing modalities including devices and techniques used for conventional signal processing. At this new time scale the horizon of a multitude of physics is broadened: microscopy can be studied with frame rates approaching the lifetime of atomic interactions, energy can be delivered to materials with enough power to spark processes like fusion, and field intensities are so immense that non-linear (even relativistic) interactions with materials become commonplace. Characterizing ultrafast laser pulses can be a major challenge however because the pulse duration can be more than one-thousand times shorter than even the fastest time sampling electronics resolution interval. Complicating matters further, sensors that interact with light in this spectrum do so through light intensity, losing field phase information. While direct field sampling may be infeasible, studying ultrafast pulses is made possible by the physics of the ultrafast, through processes like second harmonic generation, and through the unique processing catalogued and expanded on in this thesis.
Our primary contributions revolve around the adaptation of modern signal processing optimization techniques to classical and novel pulse characterizations in ultrafast optics and include: (i) the application of Wirtinger gradient techniques to generalized problems in traditional pulse characterization, (ii) the formulation of pulse characterization as a fourth-order tensor forward problem to exploit tensor structure via iterative hard thresholding, (iii) the development of a new condensed sensing approach to pulse characterization, and (iv) the demonstration of this technique in a laboratory setting.
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