  Space-time (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, the progress in ST beam
research has been constrained by the absence of a universal framework for their
analysis and generation. Here, we introduce the concept of "two-dimensional ST
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 findings suggest a paradigm
shift opportunity in ST beam research and may apply to a broader range of wave
physics systems.
