Spatiotemporal optical vortices and their transverse orbital angular momentum: propagation and high-order harmonics
This doctorate work is centered on spatiotemporal optical vortices (STOVs), with the aim of observing and understanding the upconversion in high-order harmonic generation (HHG) of their phase structure and transverse orbital angular momentum (OAM). The latter has recently received several definitions: we develop a unified formalism allowing, in these different frameworks, to explain and compare the transverse OAM associated with these pulses. Unlike the longitudinal OAM carried by spatial vortex modes, we conclude that no form of transverse or intrinsic OAM is carried by STOV photons in well-defined quanta. The coherent nature of HHG ensures nonetheless the multiplication of their topological charge by the harmonic order during the process. Experimentally, we demonstrate shaping of ultrashort STOV pulses from laser sources of 30 and 300 femtoseconds durations. We characterize them via spatially-resolved Fourier-transform spectral interferometry, then describe various aspects of their propagation: hypergeometric mode structure, influences of free-propagation and dispersion on their focusing, and evolution of the various intrinsic OAM. Finally, we demonstrate their upconversion in HHG: the spatiospectral structure of harmonic modes and its evolution with the position of the nonlinear medium confirm the production of STOV pulses at extreme ultraviolet wavelengths.