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Closed-form, analytical expressions for higher-order, multi-charged spatiotemporal optical vortices (STOVs) propagating in free space or non-dispersive media are provided. We consider two relevant and complementary situations where the multi-charged STOV spreads freely, and where it is focused. Previously reported multi-charged STOV breakup upon spreading is merely an effect of diffraction, not an instability effect. The focused STOV reverses the sign of its topological charge upon passage through the focus. While the spreading STOV carries transverse orbital angular momentum, the ideally focused STOV from the far field does not.
Miguel A. Porras (2022) studied this question.