Space–time singularity dynamics for second harmonic spatiotemporal optical vortices

Spatiotemporal optical vortices (STOVs) have attracted significant attention for their unique properties. Recently, the second harmonic generation (SHG) of STOV pulses has been experimentally demonstrated, but the phase singularity dynamics during this process remain elusive. Here, we theoretically investigate the separation and tilting of the phase singularities in STOVs during the SHG. Using the nonlinear Maxwell equation, we show that singularity separation is governed by group velocity mismatch, with accurate predictions provided by a Simpson-type integral under weak spatiotemporal walk-off conditions. In addition, paraxial wave equation analysis reveals that propagation induces singularity tilting, driven by spatial phase shifts. Our results not only offer deeper insights into the spatiotemporal coupling induced by complex nonlinear interactions but also reveal the underlying physical mechanisms in frequency up-conversion of space–time light pulses.