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

Abstract

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.

Spatiotemporal Optical Vortices: Toward Tailoring Orbital Angular Momentum of Light in Full Space-Time

“…It can be clearly seen that the ST vortex with = 1 is converted into the second-harmonic vortex with = 2 during the nonlinear frequency doubling. This process could be expressed as 28…”

“…A scaling rule similar to the longitudinal OAM was uncovered, in which the Nth harmonic has a topological charge of N . As shown in Figure 5a, by cascading a nonlinear barium borate crystal (BBO) at the output of the ST vortex generator, Guan Gui et al 28 studied the nonlinear second-harmonic generation process of the transverse OAM beams. Hancock et al 29 demonstrated similar experimental results almost simultaneously (Figure 5b).…”