Second-harmonic generation and the conservation of spatiotemporal orbital angular momentum of light

Light with spatiotemporal orbital angular momentum (ST-OAM) is a recently discovered type of structured electromagnetic field with characteristic space-time spiral phase structure and transverse OAM. In this work, we present the first generation and characterization of the second-harmonic of ST-OAM pulses. By uncovering 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, we establish a general nonlinear scaling rule— analogous to that describing the spatial topological charges associated with the conventional longitudinal 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 finding thus confirms that a spatiotemporal phase winding, surrounding one or many phase singularities in space and time, can be interpreted as a new class of topological charge. 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, electron pulses, and beyond.