Generation and periodic evolution of third harmonics carrying transverse orbital angular momentum in air-plasma filaments.

Spatiotemporal optical vortex (STOV) pulses, possessing inherent transverse orbital angular momentum (OAM) and exhibiting phase singularity and intensity null in the spatiotemporal (ST) domain, have received increasing attention in recent years. Here, we investigate theoretically the third harmonic generation and evolution properties of STOV pulses via the interaction of 800-nm-STOV pulses with air-plasma filaments. We show that beautiful third harmonic STOV pulses are generated at a propagation distance of several millimeters. During further propagation, the ST intensity profiles of the third harmonics undergo variations in a periodic way, leading to the distortion and subsequent restoration to the initial ring pattern. The periodic evolution is a result of the interference effects between the third harmonics generated with different phases. Consequently, the evolution period is roughly twice the dephasing length of the third harmonics. Meanwhile, additional singularities emerge in the intensity patterns due to destructive interference occurring at specific dephasing lengths for the specific frequency components. The high-frequency components experience destructive interference earlier than the low-frequency components during each evolution period because the dephasing length decreases with frequency. This results in the sequentially appearance of the additional singularities from top to bottom in the ST intensity patterns. The proposed scheme demonstrates a way for higher-order STOV generation and manipulation in air-plasma filaments, which can be of interest for experiments related to vortex light science.