Spatiotemporal coherence engineering of light

Structured light with sculpted spatial and temporal degrees of freedom (DoFs) provides unprecedented opportunities across diverse scientific disciplines and areas of technology. However, spatiotemporal shaping is currently limited to deterministic DoFs of coherent pulsed beams. In contrast, the spatiotemporal coherence manipulation of light sources has not made any comparable headway, leaving the potential of partially coherent space-time wave packets essentially unfulfilled to date. Herein, we demonstrate theoretically and experimentally that salient features of light sources, such as their coherence width and structure, can be precisely tailored in the space-time domain. We formulate a space-time analogue of the celebrated van Cittert–Zernike theorem and utilize it to realize partially coherent wave packets with nontrivially structured spatiotemporal coherence in the laboratory. The evolution of wave packets with structured spatiotemporal coherence in free space or dispersive media differs in fundamental ways from that of conventional quasimonochromatic light with reduced spatial coherence. Our work establishes a versatile framework for manipulating the coherence of light fields in space and time, thereby paving the way for experimental studies of dynamic and noninvasive imaging, robust information transmission, remote sensing, and nonlinear frequency conversion, all topical areas of growing importance in both fundamental optical physics and photonics applications.