A virtual source (VS) is a hypothetical source instead of an actual physical entity, but provides a distinctive perspective to understand physical fields in a source-free area. In this work, we generalize the VS theory to structured partially coherent light fields (PCLFs) by establishing the partially coherent inhomogeneous Helmholtz equation, then demonstrate that PCLFs can be generated from the incoherent extended VS in imaginary space. Especially, we put forward an understanding of the Gaussian Schell-model beam, which consists of a group of partially coherent paraxial complex rays. The mutual coherence between these rays depends on the included angle between them. In previous studies, the analytical solution of the partially coherent Airy beam was obtained with difficulty by the Huygens–Fresnel integral; however, by applying the VS, we put forward, to our knowledge, an unprecedented analytical solution for a partially coherent Airy beam. We believe this example will qualify the VS as an important perspective to understand structured PCLFs.

The group velocity in the free space of space-time wave packets (STWPs) and light bullets can be flexibly regulated by many advanced strategies; however, these regulations are restricted to only the longitudinal group velocity. In this work, a computational model based on catastrophe theory is proposed, to devise STWPs with both arbitrary transverse and longitudinal accelerations. In particular, we investigate the attenuation-free Pearcey–Gauss STWP, which enriches the family of non-diffracting STWPs. This work may advance the development of space-time structured light fields.