Tailoring spatiotemporal wavepackets via two-dimensional space-time duality

Spatiotemporal (ST) beams-ultrafast optical wavepackets with customized spatial and temporal characteristics-present a significant contrast to conventional spatial-structured light and hold the potential to revolutionize our understanding and manipulation of light. However, progress in ST beam research has been constrained by the absence of a universal framework for its analysis and generation. Here, we introduce the concept of 'two-dimensional space-time duality', establishing a foundational duality between spatial-structured light and ST beams. We show that breaking the exact balance between paraxial diffraction and narrow-band dispersion is crucial for guiding the dynamics of ST wavepackets. Leveraging this insight, we pioneer a versatile complex-amplitude modulation strategy, enabling the precise crafting of ST beams with an exceptional fidelity exceeding 97%. Furthermore, we uncover a new range of ST wavepackets by harnessing the exact one-to-one relationship between scalar spatial-structured light and ST beams. Our results expand the toolkit for ST beam research and hold promise for applications across a diverse spectrum of wave-based physical systems.