  High harmonic generation (HHG) with longitudinal optical orbital angular
momentum has attracted much attention over the past decade. Here, we present
the first study on the HHG with transverse orbital angular momentum driven by
the spatiotemporal optical vortex (STOV) pulses. We show that the produced
spatial resolved harmonic spectra reveal unique structures, such as the
spatially spectral tilt and the fine interference patterns. We show these
spatio-spectral structures originate from both the macroscopic and microscopic
effect of spatiotemporal optical singularity in HHG. Employing two-color
counter-spin and counter-vorticity STOV pulses, we further discuss a robust
method to control the spatiotemporal topological charge and spectral structure
of high-order harmonics. The conservation rule of photon transverse orbital
angular momentum in HHG process is also discussed when mixing with photon spin
angular momenta.
