Programmable spatiotemporal shaping for partially coherent structured wave packets

Providing more coherent light with space-time coupling offers unprecedented opportunities across diverse scientific disciplines and areas of technology. However, in many applications, tailored laser beams with partial coherence in space and time are desired. Here, we demonstrate a programmable approach for simultaneously shaping the intensity and coherence distributions of spatiotemporally coupled partially coherent wave packets. By jointly engineering the fractal speckle of a dynamic scatterer and applying tailored modulation of the illumination function, we experimentally generate partially coherent laser beams with arbitrarily designed intensity and nontrivial coherence distributions. The proposed approach is compatible with ultrafast laser pulses, enabling the on-demand generation of partially coherent space-time wave packets. The resulting spatiotemporally partially coherent wave packets exhibit non-separable space-time intensity profiles together with engineered spatiotemporal correlation distributions. This work provides a versatile framework for tailoring partially coherent light in space and time, with varied applications in relativistic laser-matter interaction, passive imaging and optical manipulation.