  Light with spatiotemporal orbital angular momentum (ST-OAM) is a recently
discovered type of structured and localized electromagnetic field. This field
carries characteristic space-time spiral phase structure and transverse
intrinsic OAM. In this work, we present the generation and characterization of
the second-harmonic of ST-OAM pulses. We uncovered the conservation of
transverse OAM in a second-harmonic generation process, where the space-time
topological charge of the fundamental field is doubled along with the optical
frequency. Our experiment thus suggests a general ST-OAM nonlinear scaling rule
- analogous to that in conventional OAM of light. Furthermore, we observe that
the topology of a second-harmonic ST-OAM pulse can be modified by complex
spatiotemporal astigmatism, giving rise to multiple phase singularities
separated in space and time. Our study opens a new route for nonlinear
conversion and scaling of light carrying ST-OAM with the potential for driving
other secondary ST-OAM sources of electromagnetic fields and beyond.
