Independent and controllable space-time autofocused dual Airyprime Hermite complex-variable-function Gaussian fractional wave packets

This work investigates the controllable spatiotemporal autofocusing characteristics of dual Airyprime Hermite complex-variable-function Gaussian (dAHCG) wave packets under the quadratic phase modulation (QPM) based on the fractional Schrödinger equation (FSE) optical system. By elaborately engineering the decay factor, distribution coefficient, Lévy index in both time and space domain, QPM coefficient and quadratic chirp, we achieve flexible control over the wave packet's morphology while enabling precise manipulation of its focal length and focal intensity. This approach facilitates simultaneous or asynchronous spatiotemporal self-focusing with significantly enhanced peak intensity at the space-time focal point. Our findings provide a new perspective on precisely tuning spatiotemporal self-focusing properties of wave packets and highlight the potential of these novel QPM-based wave packets in applications such as optical manipulation and laser processing.