Frequency conversion of highly charged femtosecond spatiotemporal optical vortices in cascaded nonlinear crystals

The degrees of freedom inherent in spatiotemporal optical vortices (STOVs) afford intriguing opportunties to manipulate complex light fields for broad applications such as optical communication, light-matter interactions, particle manipulation, quantum optics, and electron acceleration in the relativistic regime. Unlike previous studies examining the second harmonic generation (SHG) of STOVs having an input topological charge (TC) $l^{\left(\omega \right)}=1$ at the fundamental frequency ω, here we experimentally demonstrate sequential second and third harmonic generation of STOVs to achieve greater spectral coverage, wavelength tunability, and what is more, TC values as great as $l^{\left(\omega \right)}=40$ . The large TC values are attributed to second (third) harmonic generation of an incident beam satisfying $l^{\left(2\omega \right)}=2l^{\left(\omega \right)}$ ( $l^{\left(3\omega \right)}=3l^{\left(\omega \right)}$ ). We found that wavelength tunability could be achieved by controlling the position of the phase singularity in the frequency domain while also optimizing the nonlinear phase matching condition. In this work, our experimental measurements extend the principle of conservation of the spatiotemporal topological charge to general nonlinear optical parametric processes, suggesting a fundamental approach to produce tunable and highly charged STOV deep into the ultraviolet regime.