Higher-order spatiotemporal wave packets with Gouy phase dynamics

Spatiotemporal (ST) wave packets refer to a broad class of optical pulses whose spatial and temporal dependence cannot be treated separately. Such space time non-separability can induce exotic physical effects such as non-diffraction, non-transverse waves, and sub or superluminal propagation. Here, a family of ST non-separable pulses is presented, where a modal order is proposed to extend their spatiotemporal structural complexity, analogous to the spatial higher-order Gaussian modes. The modal order is strongly coupled to the Gouy phase, which can unveil anomalous spatiotemporal dynamics, including ultrafast cycle-switching evolution, ST self-healing, and sub- or super-luminal propagation. We further introduce a stretch parameter that stretches the temporal envelope while keeping the Gouy-phase coefficient unchanged. This stretch invariance decouples pulse duration from modal order, allowing us to tune the few-cycle width without shifting temporal-revival positions or altering the phase or group-velocity laws. Moreover, an approach to analyzing the phase velocity and group velocity of the higher-order ST modes is proposed to quantitatively characterize the sub- or supe-luminal effects. The method is universal for a larger group of complex structured ultrafast pulses, laying the basis for both fundamental physics and advanced applications in ultrafast optics and structured light.