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

TL;DR

This paper demonstrates the generation and characterization of second-harmonic light with spatiotemporal orbital angular momentum (ST-OAM), revealing conservation laws and nonlinear scaling rules that advance the understanding of complex structured light fields.

Contribution

It introduces the first experimental observation of second-harmonic generation of ST-OAM and uncovers a nonlinear scaling rule for its topological charge, expanding the potential for complex light manipulation.

Findings

Conservation of transverse OAM in second-harmonic generation.

Doubling of space-time topological charge at second harmonic.

Modification of second-harmonic topology via spatiotemporal astigmatism.

Abstract

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.